TSTP Solution File: ITP213_1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP213_1 : TPTP v8.1.2. Released v8.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n015.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 03:20:06 EDT 2023
% Result : Theorem 27.92s 28.22s
% Output : Proof 27.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 10.32/10.41 % Problem : ITP213_1 : TPTP v8.1.2. Released v8.0.0.
% 10.32/10.42 % Command : do_cvc5 %s %d
% 10.45/10.63 % Computer : n015.cluster.edu
% 10.45/10.63 % Model : x86_64 x86_64
% 10.45/10.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 10.45/10.63 % Memory : 8042.1875MB
% 10.45/10.63 % OS : Linux 3.10.0-693.el7.x86_64
% 10.45/10.63 % CPULimit : 300
% 10.45/10.63 % WCLimit : 300
% 10.45/10.63 % DateTime : Sun Aug 27 14:34:34 EDT 2023
% 10.45/10.63 % CPUTime :
% 21.12/21.33 %----Proving TF0_NAR, FOF, or CNF
% 27.92/28.22 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.ZB1YIf8E9V/cvc5---1.0.5_24498.p...
% 27.92/28.22 ------- get file name : TPTP file name is ITP213_1
% 27.92/28.22 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_24498.smt2...
% 27.92/28.22 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 27.92/28.22 % SZS status Theorem for ITP213_1
% 27.92/28.22 % SZS output start Proof for ITP213_1
% 27.92/28.22 (
% 27.92/28.22 (let ((_let_1 (tptp.hoare_new_addrs tptp.h2 tptp.as tptp.h))) (let ((_let_2 (tptp.aa_a_assn tptp.q tptp.r2))) (let ((_let_3 (tptp.rep_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn _let_2) tptp.r)))) (let ((_let_4 (tptp.pp (tptp.aa_Pro2991721470636411351t_bool _let_3 (tptp.produc7507926704131184380et_nat tptp.h _let_1))))) (let ((_let_5 (not _let_4))) (let ((_let_6 (tptp.insert_Product_unit tptp.product_Unity tptp.bot_bo3957492148770167129t_unit))) (let ((_let_7 (tptp.insert9069300056098147895at_nat (tptp.produc2922128104949294807at_nat tptp.bot_bo2099793752762293965at_nat tptp.bot_bo2099793752762293965at_nat) tptp.bot_bo228742789529271731at_nat))) (let ((_let_8 (tptp.map_fu3095037182338179920l_bool tptp.code_nat_of_natural tptp.id_bool))) (let ((_let_9 (tptp.insert_bool tptp.fTrue tptp.bot_bot_set_bool))) (let ((_let_10 (tptp.finite3254316476582989077op_nat tptp.top_top_set_nat))) (let ((_let_11 (tptp.collec3392354462482085612at_nat (tptp.produc8955392012077580105t_bool tptp.ord_less_nat)))) (let ((_let_12 (tptp.aa_fun6875833325056119164at_nat tptp.produc4528391901023682385at_nat tptp.aTP_Lamm_amy))) (let ((_let_13 (tptp.bNF_re2241393799969408733at_nat tptp.intrel tptp.intrel))) (let ((_let_14 (tptp.aa_fun6875833325056119164at_nat tptp.produc4528391901023682385at_nat tptp.aTP_Lamm_ana))) (let ((_let_15 (tptp.aa_fun174371099813217148t_bool tptp.produc5023667602222594023t_bool tptp.aTP_Lamm_amw))) (let ((_let_16 (tptp.bNF_re3189209160384574813l_bool tptp.intrel tptp.fequal_bool))) (let ((_let_17 (tptp.aa_fun174371099813217148t_bool tptp.produc5023667602222594023t_bool tptp.aTP_Lamm_amu))) (let ((_let_18 (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))) (let ((_let_19 (tptp.produc6842872674320459806at_nat tptp.minus_minus_nat))) (let ((_let_20 (tptp.produc2626176000494625587at_nat tptp.aTP_Lamm_ams))) (let ((_let_21 (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))) (let ((_let_22 (tptp.aa_fun6875833325056119164at_nat tptp.produc4528391901023682385at_nat tptp.aTP_Lamm_amr))) (let ((_let_23 (tptp.bNF_re7400052026677387805at_int tptp.pcr_int tptp.pcr_int))) (let ((_let_24 (tptp.bNF_re1498568104593929552l_bool tptp.pcr_int tptp.fequal_bool))) (let ((_let_25 (tptp.bNF_re8279943556446156061nt_rat tptp.pcr_rat tptp.pcr_rat))) (let ((_let_26 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))) (let ((_let_27 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int))) (let ((_let_28 (tptp.bNF_re7145576690424134365nt_int tptp.ratrel tptp.ratrel))) (let ((_let_29 (tptp.bNF_re9007465950226028919l_bool tptp.fequal_int tptp.fequal_bool))) (let ((_let_30 (tptp.bNF_re6223507645442431167l_bool tptp.fequal_nat tptp.fequal_bool))) (let ((_let_31 (tptp.map_fu5673905371560938248nt_rat tptp.rep_Rat tptp.abs_Rat))) (let ((_let_32 (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_33 (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat))) (let ((_let_34 (tptp.map_fu6396621194128205665l_bool tptp.code_int_of_integer tptp.id_bool))) (let ((_let_35 (tptp.map_fu6608131713810608381l_bool tptp.rep_Integ tptp.id_bool))) (let ((_let_36 (tptp.map_fu3667384564859982768at_int tptp.rep_Integ tptp.abs_Integ))) (let ((_let_37 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_38 (not (tptp.pp (tptp.aa_Code_integer_bool _let_37 tptp.zero_z3403309356797280102nteger))))) (let ((_let_39 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_40 (tptp.pp (tptp.aa_Code_integer_bool _let_39 tptp.zero_z3403309356797280102nteger)))) (let ((_let_41 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (let ((_let_42 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_43 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_44 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_45 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_33))) (let ((_let_46 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger _let_43))) (let ((_let_47 (tptp.aa_int_fun_int_bool tptp.ord_less_int _let_32))) (let ((_let_48 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_49 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_50 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_32))) (let ((_let_51 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_33))) (let ((_let_52 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger _let_43))) (let ((_let_53 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat))) (let ((_let_54 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (let ((_let_55 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int))) (let ((_let_56 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int))) (let ((_let_57 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat))) (let ((_let_58 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer))) (let ((_let_59 (not (tptp.pp (tptp.aa_int_bool _let_44 tptp.zero_zero_int))))) (let ((_let_60 (tptp.pp (tptp.aa_int_bool _let_48 tptp.zero_zero_int)))) (let ((_let_61 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat))) (let ((_let_62 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat))) (let ((_let_63 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (let ((_let_64 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_65 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat))) (let ((_let_66 (tptp.pp (tptp.aa_int_bool _let_44 tptp.one_one_int)))) (let ((_let_67 (tptp.pp (tptp.aa_nat_bool _let_63 tptp.one_one_nat)))) (let ((_let_68 (tptp.pp (tptp.aa_rat_bool _let_42 tptp.one_one_rat)))) (let ((_let_69 (tptp.pp (tptp.aa_Code_integer_bool _let_37 tptp.one_one_Code_integer)))) (let ((_let_70 (tptp.ordering_top_nat tptp.aTP_Lamm_df tptp.aTP_Lamm_dg))) (let ((_let_71 (tptp.pp (tptp.aa_int_bool _let_48 tptp.one_one_int)))) (let ((_let_72 (tptp.pp (tptp.aa_nat_bool _let_64 tptp.one_one_nat)))) (let ((_let_73 (tptp.pp (tptp.aa_rat_bool _let_49 tptp.one_one_rat)))) (let ((_let_74 (tptp.pp (tptp.aa_Code_integer_bool _let_39 tptp.one_one_Code_integer)))) (let ((_let_75 (tptp.collect_nat tptp.aTP_Lamm_ag))) (let ((_let_76 (tptp.collect_nat tptp.aTP_Lamm_ah))) (let ((_let_77 (forall ((P tptp.assn) (H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat) (Q tptp.assn) (As3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn P) (tptp.produc7507926704131184380et_nat H As))) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn Q) (tptp.produc7507926704131184380et_nat H As3))) (=> (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat As) As3) tptp.bot_bot_set_nat) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn P) Q)) (tptp.produc7507926704131184380et_nat H (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat As) As3)))))))))) (let ((_let_78 (tptp.hoare_new_addrs tptp.h2 tptp.as1 tptp.h))) (let ((_let_79 (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn _let_2) (tptp.produc7507926704131184380et_nat tptp.h _let_78))))) (let ((_let_80 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat _let_78) tptp.as2))) (let ((_let_81 (= _let_1 _let_80))) (let ((_let_82 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat _let_78) tptp.as2))) (let ((_let_83 (= _let_82 tptp.bot_bot_set_nat))) (let ((_let_84 (tptp.rep_assn tptp.r))) (let ((_let_85 (tptp.pp (tptp.aa_Pro2991721470636411351t_bool _let_84 (tptp.produc7507926704131184380et_nat tptp.h tptp.as2))))) (let ((_let_86 (tptp.pp (tptp.aa_Pro2991721470636411351t_bool _let_3 (tptp.produc7507926704131184380et_nat tptp.h _let_80))))) (let ((_let_87 (ASSUME :args (_let_81)))) (let ((_let_88 (ASSUME :args (_let_5)))) (let ((_let_89 (= tptp.bot_bot_set_nat _let_82))) (let ((_let_90 (not _let_89))) (let ((_let_91 (not _let_85))) (let ((_let_92 (not _let_79))) (let ((_let_93 (or _let_92 _let_91 _let_90 _let_86))) (let ((_let_94 (forall ((P tptp.assn) (H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat) (Q tptp.assn) (As3 tptp.set_nat)) (or (not (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn P) (tptp.produc7507926704131184380et_nat H As)))) (not (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn Q) (tptp.produc7507926704131184380et_nat H As3)))) (not (= tptp.bot_bot_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat As) As3))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn P) Q)) (tptp.produc7507926704131184380et_nat H (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat As) As3)))))))) (let ((_let_95 (EQ_RESOLVE (ASSUME :args (_let_77)) (MACRO_SR_EQ_INTRO :args (_let_77 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_96 (not _let_86))) (let ((_let_97 (not _let_81))) (let ((_let_98 (ASSUME :args (_let_86)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_98 _let_87 _let_88) :args (_let_81 _let_5 _let_86)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_88)) (CONG (CONG (REFL :args (_let_3)) (CONG (REFL :args (tptp.h)) (SYMM (SYMM _let_87)) :args (APPLY_UF tptp.produc7507926704131184380et_nat)) :args (APPLY_UF tptp.aa_Pro2991721470636411351t_bool)) :args (APPLY_UF tptp.pp)) (TRUE_INTRO _let_98))) :args (_let_86 _let_81 _let_5)) :args ((not (and _let_81 _let_5 _let_86)) SB_LITERAL))) (CONG (REFL :args (_let_97)) (MACRO_SR_PRED_INTRO :args ((= (not _let_5) _let_4))) (REFL :args (_let_96)) :args (or))) :args ((or _let_4 _let_97 _let_96))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_93)) :args ((or _let_91 _let_90 _let_92 _let_86 (not _let_93)))) (ASSUME :args (_let_85)) (SYMM (ASSUME :args (_let_83))) (ASSUME :args (_let_79)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_95 :args (_let_2 tptp.h _let_78 tptp.r tptp.as2 QUANTIFIERS_INST_E_MATCHING ((tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn P) Q)) (tptp.produc7507926704131184380et_nat H (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat As) As3)))))) :args (_let_94))) _let_95 :args (_let_93 false _let_94)) :args (_let_86 false _let_85 false _let_89 false _let_79 false _let_93)) _let_88 _let_87 :args (false false _let_86 true _let_4 false _let_81)) :args ((= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat tptp.as1) tptp.as2) tptp.bot_bot_set_nat) _let_85 (tptp.pp (tptp.aa_Pro2991721470636411351t_bool _let_84 (tptp.produc7507926704131184380et_nat tptp.h2 tptp.as2))) _let_83 _let_81 (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (= (tptp.hoare_new_addrs H As H) As)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn tptp.p) (tptp.produc7507926704131184380et_nat tptp.h2 tptp.as1))) _let_79 (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn tptp.p) tptp.r)) (tptp.produc7507926704131184380et_nat tptp.h2 tptp.as))) (not (forall ((As1 tptp.set_nat) (As2 tptp.set_nat)) (=> (= tptp.as (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat As1) As2)) (=> (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat As1) As2) tptp.bot_bot_set_nat) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn tptp.p) (tptp.produc7507926704131184380et_nat tptp.h2 As1))) (not (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn tptp.r) (tptp.produc7507926704131184380et_nat tptp.h2 As2))))))))) (forall ((X tptp.assn) (Y tptp.assn)) (= (= (tptp.rep_assn X) (tptp.rep_assn Y)) (= X Y))) (forall ((P tptp.assn) (Q tptp.assn) (H tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (tptp.produc7507926704131184380et_nat H tptp.bot_bot_set_nat))) (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn P) Q)) _let_1)) (and (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn P) _let_1)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn Q) _let_1)))))) (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.relH tptp.as2 tptp.h2) tptp.h)) (forall ((X1 tptp.fun_Pr6001797050664311790t_bool) (X2 tptp.produc3658429121746597890et_nat) (Y1 tptp.fun_Pr6001797050664311790t_bool) (Y2 tptp.produc3658429121746597890et_nat)) (= (= (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat X1) X2) (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))) (forall ((X1 tptp.fun_Pr6001797050664311790t_bool) (X2 tptp.produc6108883039684432031et_nat) (Y1 tptp.fun_Pr6001797050664311790t_bool) (Y2 tptp.produc6108883039684432031et_nat)) (= (= (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat X1) X2) (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))) (forall ((X1 tptp.fun_Pr9164807099015279978e_term) (X2 tptp.product_prod_int_int) (Y1 tptp.fun_Pr9164807099015279978e_term) (Y2 tptp.product_prod_int_int)) (= (= (tptp.aa_Pro3513184699142849729nt_int (tptp.aa_fun1388719692539776744nt_int tptp.produc1560874099174258678nt_int X1) X2) (tptp.aa_Pro3513184699142849729nt_int (tptp.aa_fun1388719692539776744nt_int tptp.produc1560874099174258678nt_int Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))) (forall ((X1 tptp.fun_in6429348457993719614e_term) (X2 tptp.product_prod_int_int) (Y1 tptp.fun_in6429348457993719614e_term) (Y2 tptp.product_prod_int_int)) (= (= (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int X1) X2) (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))) (forall ((X1 tptp.a) (X2 tptp.produc6653097349344004940it_nat) (Y1 tptp.a) (Y2 tptp.produc6653097349344004940it_nat)) (= (= (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat X1) X2) (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))) (forall ((A tptp.fun_Pr6001797050664311790t_bool) (B tptp.produc3658429121746597890et_nat) (A2 tptp.fun_Pr6001797050664311790t_bool) (B2 tptp.produc3658429121746597890et_nat)) (= (= (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat A) B) (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat A2) B2)) (and (= A A2) (= B B2)))) (forall ((A tptp.fun_Pr6001797050664311790t_bool) (B tptp.produc6108883039684432031et_nat) (A2 tptp.fun_Pr6001797050664311790t_bool) (B2 tptp.produc6108883039684432031et_nat)) (= (= (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat A) B) (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat A2) B2)) (and (= A A2) (= B B2)))) (forall ((A tptp.fun_Pr9164807099015279978e_term) (B tptp.product_prod_int_int) (A2 tptp.fun_Pr9164807099015279978e_term) (B2 tptp.product_prod_int_int)) (= (= (tptp.aa_Pro3513184699142849729nt_int (tptp.aa_fun1388719692539776744nt_int tptp.produc1560874099174258678nt_int A) B) (tptp.aa_Pro3513184699142849729nt_int (tptp.aa_fun1388719692539776744nt_int tptp.produc1560874099174258678nt_int A2) B2)) (and (= A A2) (= B B2)))) (forall ((A tptp.fun_in6429348457993719614e_term) (B tptp.product_prod_int_int) (A2 tptp.fun_in6429348457993719614e_term) (B2 tptp.product_prod_int_int)) (= (= (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int A) B) (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int A2) B2)) (and (= A A2) (= B B2)))) (forall ((A tptp.a) (B tptp.produc6653097349344004940it_nat) (A2 tptp.a) (B2 tptp.produc6653097349344004940it_nat)) (= (= (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat A) B) (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat A2) B2)) (and (= A A2) (= B B2)))) (forall ((A3 tptp.assn) (B3 tptp.assn) (H tptp.produc3658429121746597890et_nat)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn A3) B3)) H)) (exists ((H1 tptp.produc3658429121746597890et_nat) (H2 tptp.produc3658429121746597890et_nat)) (and (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn A3) H1)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn B3) H2)))))) (forall ((A tptp.assn) (B tptp.assn) (H tptp.produc3658429121746597890et_nat)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn A) B)) H)) (not (=> (exists ((X_1 tptp.produc3658429121746597890et_nat)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn A) X_1))) (forall ((H_2 tptp.produc3658429121746597890et_nat)) (not (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn B) H_2)))))))) (tptp.hoare_hoare_triple_a tptp.p tptp.c tptp.q) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.lim_Product_unit tptp.h2)) (tptp.lim_Product_unit tptp.h))) (= tptp.as (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat tptp.as1) tptp.as2)) (forall ((P tptp.assn) (H tptp.heap_e7401611519738050253t_unit) (H3 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (tptp.rep_assn P))) (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool _let_1 (tptp.produc7507926704131184380et_nat H tptp.bot_bot_set_nat))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool _let_1 (tptp.produc7507926704131184380et_nat H3 tptp.bot_bot_set_nat)))))) (forall ((As tptp.set_nat) (As3 tptp.set_nat) (H tptp.heap_e7401611519738050253t_unit) (H3 tptp.heap_e7401611519738050253t_unit)) (= (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.relH (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat As) As3) H) H3)) (and (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.relH As H) H3)) (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.relH As3 H) H3))))) (forall ((X tptp.produc1542783094787327164et_nat)) (not (forall ((P2 tptp.fun_Pr6001797050664311790t_bool) (Q2 tptp.fun_Pr6001797050664311790t_bool) (H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (not (= X (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat P2) (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat Q2) (tptp.produc7507926704131184380et_nat H4 As4)))))))) (forall ((As tptp.set_nat) (H tptp.heap_e7401611519738050253t_unit) (H3 tptp.heap_e7401611519738050253t_unit)) (=> (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.relH As H) H3)) (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.relH As H3) H)))) (forall ((As tptp.set_nat) (H12 tptp.heap_e7401611519738050253t_unit) (H22 tptp.heap_e7401611519738050253t_unit) (H32 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (tptp.relH As H12))) (=> (tptp.pp (tptp.aa_hea1793595068369496646t_bool _let_1 H22)) (=> (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.relH As H22) H32)) (tptp.pp (tptp.aa_hea1793595068369496646t_bool _let_1 H32)))))) (forall ((As tptp.set_nat) (H tptp.heap_e7401611519738050253t_unit) (H3 tptp.heap_e7401611519738050253t_unit) (P tptp.assn)) (let ((_let_1 (tptp.rep_assn P))) (=> (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.relH As H) H3)) (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool _let_1 (tptp.produc7507926704131184380et_nat H As))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool _let_1 (tptp.produc7507926704131184380et_nat H3 As))))))) (forall ((P tptp.assn) (C tptp.heap_Time_Heap_a) (Q tptp.fun_a_assn)) (=> (forall ((H4 tptp.produc3658429121746597890et_nat)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn P) H4)) (tptp.hoare_hoare_triple_a P C Q))) (tptp.hoare_hoare_triple_a P C Q))) (forall ((A3 tptp.assn) (B3 tptp.assn) (H tptp.produc3658429121746597890et_nat)) (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn A3) B3)) H)) (exists ((Hr tptp.heap_e7401611519738050253t_unit) (As12 tptp.set_nat) (As22 tptp.set_nat)) (and (= H (tptp.produc7507926704131184380et_nat Hr (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat As12) As22))) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat As12) As22) tptp.bot_bot_set_nat) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn A3) (tptp.produc7507926704131184380et_nat Hr As12))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn B3) (tptp.produc7507926704131184380et_nat Hr As22))))))) _let_77 (forall ((P tptp.fun_Pr229822445725053876t_bool) (X tptp.produc1542783094787327164et_nat)) (=> (forall ((A4 tptp.fun_Pr6001797050664311790t_bool) (B4 tptp.fun_Pr6001797050664311790t_bool) (C2 tptp.heap_e7401611519738050253t_unit) (D tptp.set_nat)) (tptp.pp (tptp.aa_Pro6092667153363046813t_bool P (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat A4) (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat B4) (tptp.produc7507926704131184380et_nat C2 D)))))) (tptp.pp (tptp.aa_Pro6092667153363046813t_bool P X)))) (forall ((P tptp.fun_Pr3073222722562426257t_bool) (X tptp.produc6108883039684432031et_nat)) (=> (forall ((A4 tptp.fun_Pr6001797050664311790t_bool) (B4 tptp.heap_e7401611519738050253t_unit) (C2 tptp.set_nat)) (tptp.pp (tptp.aa_Pro7454463142485379962t_bool P (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat A4) (tptp.produc7507926704131184380et_nat B4 C2))))) (tptp.pp (tptp.aa_Pro7454463142485379962t_bool P X)))) (forall ((P tptp.fun_Pr229822445725053876t_bool) (X tptp.produc1542783094787327164et_nat)) (=> (forall ((A4 tptp.fun_Pr6001797050664311790t_bool) (B4 tptp.fun_Pr6001797050664311790t_bool) (C2 tptp.produc3658429121746597890et_nat)) (tptp.pp (tptp.aa_Pro6092667153363046813t_bool P (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat A4) (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat B4) C2))))) (tptp.pp (tptp.aa_Pro6092667153363046813t_bool P X)))) (forall ((P tptp.fun_Pr6019674992625747500t_bool) (X tptp.produc4441460161354545860nt_int)) (=> (forall ((A4 tptp.fun_Pr9164807099015279978e_term) (B4 tptp.int) (C2 tptp.int)) (tptp.pp (tptp.aa_Pro5031108791230793749t_bool P (tptp.aa_Pro3513184699142849729nt_int (tptp.aa_fun1388719692539776744nt_int tptp.produc1560874099174258678nt_int A4) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int B4) C2))))) (tptp.pp (tptp.aa_Pro5031108791230793749t_bool P X)))) (forall ((P tptp.fun_Pr5504123824928244736t_bool) (X tptp.produc6768802789813714928nt_int)) (=> (forall ((A4 tptp.fun_in6429348457993719614e_term) (B4 tptp.int) (C2 tptp.int)) (tptp.pp (tptp.aa_Pro7591400126937138665t_bool P (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int A4) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int B4) C2))))) (tptp.pp (tptp.aa_Pro7591400126937138665t_bool P X)))) (forall ((P tptp.fun_Pr2906233850362575543t_bool) (X tptp.produc3260487557148687353it_nat)) (=> (forall ((A4 tptp.a) (B4 tptp.heap_e7401611519738050253t_unit) (C2 tptp.nat)) (tptp.pp (tptp.aa_Pro8278066377857552544t_bool P (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat A4) (tptp.produc584006145561248582it_nat B4 C2))))) (tptp.pp (tptp.aa_Pro8278066377857552544t_bool P X)))) (forall ((Y tptp.produc1542783094787327164et_nat)) (not (forall ((A4 tptp.fun_Pr6001797050664311790t_bool) (B4 tptp.fun_Pr6001797050664311790t_bool) (C2 tptp.heap_e7401611519738050253t_unit) (D tptp.set_nat)) (not (= Y (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat A4) (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat B4) (tptp.produc7507926704131184380et_nat C2 D)))))))) (forall ((Y tptp.produc6108883039684432031et_nat)) (not (forall ((A4 tptp.fun_Pr6001797050664311790t_bool) (B4 tptp.heap_e7401611519738050253t_unit) (C2 tptp.set_nat)) (not (= Y (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat A4) (tptp.produc7507926704131184380et_nat B4 C2))))))) (forall ((Y tptp.produc1542783094787327164et_nat)) (not (forall ((A4 tptp.fun_Pr6001797050664311790t_bool) (B4 tptp.fun_Pr6001797050664311790t_bool) (C2 tptp.produc3658429121746597890et_nat)) (not (= Y (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat A4) (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat B4) C2))))))) (forall ((Y tptp.produc4441460161354545860nt_int)) (not (forall ((A4 tptp.fun_Pr9164807099015279978e_term) (B4 tptp.int) (C2 tptp.int)) (not (= Y (tptp.aa_Pro3513184699142849729nt_int (tptp.aa_fun1388719692539776744nt_int tptp.produc1560874099174258678nt_int A4) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int B4) C2))))))) (forall ((Y tptp.produc6768802789813714928nt_int)) (not (forall ((A4 tptp.fun_in6429348457993719614e_term) (B4 tptp.int) (C2 tptp.int)) (not (= Y (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int A4) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int B4) C2))))))) (forall ((Y tptp.produc3260487557148687353it_nat)) (not (forall ((A4 tptp.a) (B4 tptp.heap_e7401611519738050253t_unit) (C2 tptp.nat)) (not (= Y (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat A4) (tptp.produc584006145561248582it_nat B4 C2))))))) (forall ((A tptp.fun_Pr6001797050664311790t_bool) (B tptp.produc3658429121746597890et_nat) (A2 tptp.fun_Pr6001797050664311790t_bool) (B2 tptp.produc3658429121746597890et_nat)) (=> (= (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat A) B) (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat A2) B2)) (not (=> (= A A2) (not (= B B2)))))) (forall ((A tptp.fun_Pr6001797050664311790t_bool) (B tptp.produc6108883039684432031et_nat) (A2 tptp.fun_Pr6001797050664311790t_bool) (B2 tptp.produc6108883039684432031et_nat)) (=> (= (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat A) B) (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat A2) B2)) (not (=> (= A A2) (not (= B B2)))))) (forall ((A tptp.fun_Pr9164807099015279978e_term) (B tptp.product_prod_int_int) (A2 tptp.fun_Pr9164807099015279978e_term) (B2 tptp.product_prod_int_int)) (=> (= (tptp.aa_Pro3513184699142849729nt_int (tptp.aa_fun1388719692539776744nt_int tptp.produc1560874099174258678nt_int A) B) (tptp.aa_Pro3513184699142849729nt_int (tptp.aa_fun1388719692539776744nt_int tptp.produc1560874099174258678nt_int A2) B2)) (not (=> (= A A2) (not (= B B2)))))) (forall ((A tptp.fun_in6429348457993719614e_term) (B tptp.product_prod_int_int) (A2 tptp.fun_in6429348457993719614e_term) (B2 tptp.product_prod_int_int)) (=> (= (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int A) B) (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int A2) B2)) (not (=> (= A A2) (not (= B B2)))))) (forall ((A tptp.a) (B tptp.produc6653097349344004940it_nat) (A2 tptp.a) (B2 tptp.produc6653097349344004940it_nat)) (=> (= (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat A) B) (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat A2) B2)) (not (=> (= A A2) (not (= B B2)))))) (forall ((P tptp.fun_Pr3073222722562426257t_bool) (P3 tptp.produc6108883039684432031et_nat)) (=> (forall ((A4 tptp.fun_Pr6001797050664311790t_bool) (B4 tptp.produc3658429121746597890et_nat)) (tptp.pp (tptp.aa_Pro7454463142485379962t_bool P (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat A4) B4)))) (tptp.pp (tptp.aa_Pro7454463142485379962t_bool P P3)))) (forall ((P tptp.fun_Pr229822445725053876t_bool) (P3 tptp.produc1542783094787327164et_nat)) (=> (forall ((A4 tptp.fun_Pr6001797050664311790t_bool) (B4 tptp.produc6108883039684432031et_nat)) (tptp.pp (tptp.aa_Pro6092667153363046813t_bool P (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat A4) B4)))) (tptp.pp (tptp.aa_Pro6092667153363046813t_bool P P3)))) (forall ((P tptp.fun_Pr6019674992625747500t_bool) (P3 tptp.produc4441460161354545860nt_int)) (=> (forall ((A4 tptp.fun_Pr9164807099015279978e_term) (B4 tptp.product_prod_int_int)) (tptp.pp (tptp.aa_Pro5031108791230793749t_bool P (tptp.aa_Pro3513184699142849729nt_int (tptp.aa_fun1388719692539776744nt_int tptp.produc1560874099174258678nt_int A4) B4)))) (tptp.pp (tptp.aa_Pro5031108791230793749t_bool P P3)))) (forall ((P tptp.fun_Pr5504123824928244736t_bool) (P3 tptp.produc6768802789813714928nt_int)) (=> (forall ((A4 tptp.fun_in6429348457993719614e_term) (B4 tptp.product_prod_int_int)) (tptp.pp (tptp.aa_Pro7591400126937138665t_bool P (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int A4) B4)))) (tptp.pp (tptp.aa_Pro7591400126937138665t_bool P P3)))) (forall ((P tptp.fun_Pr2906233850362575543t_bool) (P3 tptp.produc3260487557148687353it_nat)) (=> (forall ((A4 tptp.a) (B4 tptp.produc6653097349344004940it_nat)) (tptp.pp (tptp.aa_Pro8278066377857552544t_bool P (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat A4) B4)))) (tptp.pp (tptp.aa_Pro8278066377857552544t_bool P P3)))) (forall ((P3 tptp.produc6108883039684432031et_nat)) (exists ((X3 tptp.fun_Pr6001797050664311790t_bool) (Y3 tptp.produc3658429121746597890et_nat)) (= P3 (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat X3) Y3)))) (forall ((P3 tptp.produc1542783094787327164et_nat)) (exists ((X3 tptp.fun_Pr6001797050664311790t_bool) (Y3 tptp.produc6108883039684432031et_nat)) (= P3 (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat X3) Y3)))) (forall ((P3 tptp.produc4441460161354545860nt_int)) (exists ((X3 tptp.fun_Pr9164807099015279978e_term) (Y3 tptp.product_prod_int_int)) (= P3 (tptp.aa_Pro3513184699142849729nt_int (tptp.aa_fun1388719692539776744nt_int tptp.produc1560874099174258678nt_int X3) Y3)))) (forall ((P3 tptp.produc6768802789813714928nt_int)) (exists ((X3 tptp.fun_in6429348457993719614e_term) (Y3 tptp.product_prod_int_int)) (= P3 (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int X3) Y3)))) (forall ((P3 tptp.produc3260487557148687353it_nat)) (exists ((X3 tptp.a) (Y3 tptp.produc6653097349344004940it_nat)) (= P3 (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat X3) Y3)))) (forall ((A tptp.product_prod_nat_nat) (P tptp.fun_Pr7757163693017731481t_bool)) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat A) (tptp.collec3392354462482085612at_nat P))) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool P A)))) (forall ((A tptp.bool) (P tptp.fun_bool_bool)) (= (tptp.pp (tptp.member_bool A (tptp.collect_bool P))) (tptp.pp (tptp.aa_bool_bool P A)))) (forall ((A tptp.product_prod_int_int) (P tptp.fun_Pr803113274115125473t_bool)) (= (tptp.member5262025264175285858nt_int A (tptp.collec213857154873943460nt_int P)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool P A)))) (forall ((A tptp.list_nat) (P tptp.fun_list_nat_bool)) (= (tptp.member_list_nat A (tptp.collect_list_nat P)) (tptp.pp (tptp.aa_list_nat_bool P A)))) (forall ((A tptp.set_nat) (P tptp.fun_set_nat_bool)) (= (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat A) (tptp.collect_set_nat P))) (tptp.pp (tptp.aa_set_nat_bool P A)))) (forall ((A tptp.nat) (P tptp.fun_nat_bool)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A) (tptp.collect_nat P))) (tptp.pp (tptp.aa_nat_bool P A)))) (forall ((A tptp.int) (P tptp.fun_int_bool)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A) (tptp.collect_int P))) (tptp.pp (tptp.aa_int_bool P A)))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.collec3392354462482085612at_nat (tptp.aTP_Lamm_a A3)) A3)) (forall ((A3 tptp.set_bool)) (= (tptp.collect_bool (tptp.aTP_Lamm_aa A3)) A3)) (forall ((A3 tptp.set_Pr958786334691620121nt_int)) (= (tptp.collec213857154873943460nt_int (tptp.aTP_Lamm_ab A3)) A3)) (forall ((A3 tptp.set_list_nat)) (= (tptp.collect_list_nat (tptp.aTP_Lamm_ac A3)) A3)) (forall ((A3 tptp.set_set_nat)) (= (tptp.collect_set_nat (tptp.aTP_Lamm_ad A3)) A3)) (forall ((A3 tptp.set_nat)) (= (tptp.collect_nat (tptp.aTP_Lamm_ae A3)) A3)) (forall ((A3 tptp.set_int)) (= (tptp.collect_int (tptp.aTP_Lamm_af A3)) A3)) (forall ((P tptp.fun_Pr803113274115125473t_bool) (Q tptp.fun_Pr803113274115125473t_bool)) (=> (forall ((X3 tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool P X3)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool Q X3)))) (= (tptp.collec213857154873943460nt_int P) (tptp.collec213857154873943460nt_int Q)))) (forall ((P tptp.fun_list_nat_bool) (Q tptp.fun_list_nat_bool)) (=> (forall ((X3 tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool P X3)) (tptp.pp (tptp.aa_list_nat_bool Q X3)))) (= (tptp.collect_list_nat P) (tptp.collect_list_nat Q)))) (forall ((P tptp.fun_set_nat_bool) (Q tptp.fun_set_nat_bool)) (=> (forall ((X3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool P X3)) (tptp.pp (tptp.aa_set_nat_bool Q X3)))) (= (tptp.collect_set_nat P) (tptp.collect_set_nat Q)))) (forall ((P tptp.fun_nat_bool) (Q tptp.fun_nat_bool)) (=> (forall ((X3 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool P X3)) (tptp.pp (tptp.aa_nat_bool Q X3)))) (= (tptp.collect_nat P) (tptp.collect_nat Q)))) (forall ((P tptp.fun_int_bool) (Q tptp.fun_int_bool)) (=> (forall ((X3 tptp.int)) (= (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool Q X3)))) (= (tptp.collect_int P) (tptp.collect_int Q)))) (forall ((Y tptp.produc6108883039684432031et_nat)) (not (forall ((A4 tptp.fun_Pr6001797050664311790t_bool) (B4 tptp.produc3658429121746597890et_nat)) (not (= Y (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat A4) B4)))))) (forall ((Y tptp.produc1542783094787327164et_nat)) (not (forall ((A4 tptp.fun_Pr6001797050664311790t_bool) (B4 tptp.produc6108883039684432031et_nat)) (not (= Y (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat A4) B4)))))) (forall ((Y tptp.produc4441460161354545860nt_int)) (not (forall ((A4 tptp.fun_Pr9164807099015279978e_term) (B4 tptp.product_prod_int_int)) (not (= Y (tptp.aa_Pro3513184699142849729nt_int (tptp.aa_fun1388719692539776744nt_int tptp.produc1560874099174258678nt_int A4) B4)))))) (forall ((Y tptp.produc6768802789813714928nt_int)) (not (forall ((A4 tptp.fun_in6429348457993719614e_term) (B4 tptp.product_prod_int_int)) (not (= Y (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int A4) B4)))))) (forall ((Y tptp.produc3260487557148687353it_nat)) (not (forall ((A4 tptp.a) (B4 tptp.produc6653097349344004940it_nat)) (not (= Y (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat A4) B4)))))) (forall ((X tptp.produc3658429121746597890et_nat)) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (not (= X (tptp.produc7507926704131184380et_nat H4 As4)))))) (forall ((P tptp.assn) (Q tptp.assn) (R tptp.assn)) (let ((_let_1 (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn P))) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.aa_assn_assn _let_1 Q)) R) (tptp.aa_assn_assn _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn Q) R))))) (forall ((P tptp.assn) (Q tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn P) Q) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn Q) P))) (forall ((T tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat T) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat S) T)) T)) (forall ((T tptp.set_Pr8693737435421807431at_nat) (S tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat T) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat S) T)) T)) (forall ((T tptp.set_Pr8551490117392284871at_nat) (S tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat T) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat S) T)) T)) (forall ((T tptp.set_Pr4329608150637261639at_nat) (S tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat T) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat S) T)) T)) (forall ((T tptp.set_nat) (S tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat T) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat S) T)) T)) (forall ((S tptp.set_Pr1261947904930325089at_nat) (T tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat S) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat S) T)) S)) (forall ((S tptp.set_Pr8693737435421807431at_nat) (T tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat S) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat S) T)) S)) (forall ((S tptp.set_Pr8551490117392284871at_nat) (T tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat S) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat S) T)) S)) (forall ((S tptp.set_Pr4329608150637261639at_nat) (T tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat S) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat S) T)) S)) (forall ((S tptp.set_nat) (T tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat S) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat S) T)) S)) (forall ((S tptp.set_Pr1261947904930325089at_nat) (T tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat S) T)) T) T)) (forall ((S tptp.set_Pr8693737435421807431at_nat) (T tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat S) T)) T) T)) (forall ((S tptp.set_Pr8551490117392284871at_nat) (T tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat S) T)) T) T)) (forall ((S tptp.set_Pr4329608150637261639at_nat) (T tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat S) T)) T) T)) (forall ((S tptp.set_nat) (T tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat S) T)) T) T)) (forall ((S tptp.set_Pr1261947904930325089at_nat) (T tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat S) T)) S) S)) (forall ((S tptp.set_Pr8693737435421807431at_nat) (T tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat S) T)) S) S)) (forall ((S tptp.set_Pr8551490117392284871at_nat) (T tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat S) T)) S) S)) (forall ((S tptp.set_Pr4329608150637261639at_nat) (T tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat S) T)) S) S)) (forall ((S tptp.set_nat) (T tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat S) T)) S) S)) (forall ((T tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat T) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat S) T)) T)) (forall ((T tptp.set_Pr8693737435421807431at_nat) (S tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat T) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat S) T)) T)) (forall ((T tptp.set_Pr8551490117392284871at_nat) (S tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat T) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat S) T)) T)) (forall ((T tptp.set_Pr4329608150637261639at_nat) (S tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat T) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat S) T)) T)) (forall ((T tptp.set_nat) (S tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat T) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat S) T)) T)) (forall ((S tptp.set_Pr1261947904930325089at_nat) (T tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat S) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat S) T)) S)) (forall ((S tptp.set_Pr8693737435421807431at_nat) (T tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat S) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat S) T)) S)) (forall ((S tptp.set_Pr8551490117392284871at_nat) (T tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat S) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat S) T)) S)) (forall ((S tptp.set_Pr4329608150637261639at_nat) (T tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat S) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat S) T)) S)) (forall ((S tptp.set_nat) (T tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat S) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat S) T)) S)) (forall ((S tptp.set_Pr1261947904930325089at_nat) (T tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat S) T)) T) T)) (forall ((S tptp.set_Pr8693737435421807431at_nat) (T tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat S) T)) T) T)) (forall ((S tptp.set_Pr8551490117392284871at_nat) (T tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat S) T)) T) T)) (forall ((S tptp.set_Pr4329608150637261639at_nat) (T tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat S) T)) T) T)) (forall ((S tptp.set_nat) (T tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat S) T)) T) T)) (forall ((S tptp.set_Pr1261947904930325089at_nat) (T tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat S) T)) S) S)) (forall ((S tptp.set_Pr8693737435421807431at_nat) (T tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat S) T)) S) S)) (forall ((S tptp.set_Pr8551490117392284871at_nat) (T tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat S) T)) S) S)) (forall ((S tptp.set_Pr4329608150637261639at_nat) (T tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat S) T)) S) S)) (forall ((S tptp.set_nat) (T tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat S) T)) S) S)) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (= (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3) B3) tptp.bot_bo5327735625951526323at_nat) (and (= A3 tptp.bot_bo5327735625951526323at_nat) (= B3 tptp.bot_bo5327735625951526323at_nat)))) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (= (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3) B3) tptp.bot_bo8422036546324065075at_nat) (and (= A3 tptp.bot_bo8422036546324065075at_nat) (= B3 tptp.bot_bo8422036546324065075at_nat)))) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (= (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3) B3) tptp.bot_bo228742789529271731at_nat) (and (= A3 tptp.bot_bo228742789529271731at_nat) (= B3 tptp.bot_bo228742789529271731at_nat)))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat A3) B3) tptp.bot_bo2099793752762293965at_nat) (and (= A3 tptp.bot_bo2099793752762293965at_nat) (= B3 tptp.bot_bo2099793752762293965at_nat)))) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool)) (= (= (tptp.aa_set_bool_set_bool (tptp.aa_set4734229006438377534t_bool tptp.sup_sup_set_bool A3) B3) tptp.bot_bot_set_bool) (and (= A3 tptp.bot_bot_set_bool) (= B3 tptp.bot_bot_set_bool)))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3) tptp.bot_bot_set_nat) (and (= A3 tptp.bot_bot_set_nat) (= B3 tptp.bot_bot_set_nat)))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3) tptp.bot_bot_set_int) (and (= A3 tptp.bot_bot_set_int) (= B3 tptp.bot_bot_set_int)))) (forall ((X tptp.assn) (Y tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn X) Y)) X)) (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.sup_sup_Product_unit X) Y)) X)) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat X) Y)) X)) (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat X) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat X) Y)) X)) (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat X) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat X) Y)) X)) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat X) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat X) Y)) X)) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat X) Y)) X)) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat X) Y)) X)) (forall ((X tptp.assn) (Y tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn X) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X) Y)) X)) (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.sup_sup_Product_unit X) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X) Y)) X)) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat X) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X) Y)) X)) (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat X) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat X) Y)) X)) (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat X) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat X) Y)) X)) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat X) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat X) Y)) X)) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat X) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X) Y)) X)) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat X) Y)) X)) (forall ((X tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat tptp.bot_bo5327735625951526323at_nat) X) X)) (forall ((X tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat tptp.bot_bo8422036546324065075at_nat) X) X)) (forall ((X tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat tptp.bot_bo228742789529271731at_nat) X) X)) (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat tptp.bot_bo2099793752762293965at_nat) X) X)) (forall ((X tptp.set_bool)) (= (tptp.aa_set_bool_set_bool (tptp.aa_set4734229006438377534t_bool tptp.sup_sup_set_bool tptp.bot_bot_set_bool) X) X)) (forall ((X tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat tptp.bot_bot_set_nat) X) X)) (forall ((X tptp.set_int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int tptp.bot_bot_set_int) X) X)) (forall ((P tptp.fun_Pr803113274115125473t_bool)) (= (= tptp.bot_bo1796632182523588997nt_int (tptp.collec213857154873943460nt_int P)) (forall ((X4 tptp.product_prod_int_int)) (not (tptp.pp (tptp.aa_Pro4501881432599481050t_bool P X4)))))) (forall ((P tptp.fun_list_nat_bool)) (= (= tptp.bot_bot_set_list_nat (tptp.collect_list_nat P)) (forall ((X4 tptp.list_nat)) (not (tptp.pp (tptp.aa_list_nat_bool P X4)))))) (forall ((P tptp.fun_set_nat_bool)) (= (= tptp.bot_bot_set_set_nat (tptp.collect_set_nat P)) (forall ((X4 tptp.set_nat)) (not (tptp.pp (tptp.aa_set_nat_bool P X4)))))) (forall ((P tptp.fun_Pr7757163693017731481t_bool)) (= (= tptp.bot_bo2099793752762293965at_nat (tptp.collec3392354462482085612at_nat P)) (forall ((X4 tptp.product_prod_nat_nat)) (not (tptp.pp (tptp.aa_Pro2232559814647311250t_bool P X4)))))) (forall ((P tptp.fun_bool_bool)) (= (= tptp.bot_bot_set_bool (tptp.collect_bool P)) (forall ((X4 tptp.bool)) (not (tptp.pp (tptp.aa_bool_bool P X4)))))) (forall ((P tptp.fun_nat_bool)) (= (= tptp.bot_bot_set_nat (tptp.collect_nat P)) (forall ((X4 tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool P X4)))))) (forall ((P tptp.fun_int_bool)) (= (= tptp.bot_bot_set_int (tptp.collect_int P)) (forall ((X4 tptp.int)) (not (tptp.pp (tptp.aa_int_bool P X4)))))) (forall ((P tptp.fun_Pr803113274115125473t_bool)) (= (= (tptp.collec213857154873943460nt_int P) tptp.bot_bo1796632182523588997nt_int) (forall ((X4 tptp.product_prod_int_int)) (not (tptp.pp (tptp.aa_Pro4501881432599481050t_bool P X4)))))) (forall ((P tptp.fun_list_nat_bool)) (= (= (tptp.collect_list_nat P) tptp.bot_bot_set_list_nat) (forall ((X4 tptp.list_nat)) (not (tptp.pp (tptp.aa_list_nat_bool P X4)))))) (forall ((P tptp.fun_set_nat_bool)) (= (= (tptp.collect_set_nat P) tptp.bot_bot_set_set_nat) (forall ((X4 tptp.set_nat)) (not (tptp.pp (tptp.aa_set_nat_bool P X4)))))) (forall ((P tptp.fun_Pr7757163693017731481t_bool)) (= (= (tptp.collec3392354462482085612at_nat P) tptp.bot_bo2099793752762293965at_nat) (forall ((X4 tptp.product_prod_nat_nat)) (not (tptp.pp (tptp.aa_Pro2232559814647311250t_bool P X4)))))) (forall ((P tptp.fun_bool_bool)) (= (= (tptp.collect_bool P) tptp.bot_bot_set_bool) (forall ((X4 tptp.bool)) (not (tptp.pp (tptp.aa_bool_bool P X4)))))) (forall ((P tptp.fun_nat_bool)) (= (= (tptp.collect_nat P) tptp.bot_bot_set_nat) (forall ((X4 tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool P X4)))))) (forall ((P tptp.fun_int_bool)) (= (= (tptp.collect_int P) tptp.bot_bot_set_int) (forall ((X4 tptp.int)) (not (tptp.pp (tptp.aa_int_bool P X4)))))) (forall ((A3 tptp.set_set_nat)) (= (forall ((X4 tptp.set_nat)) (not (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat X4) A3)))) (= A3 tptp.bot_bot_set_set_nat))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (forall ((X4 tptp.product_prod_nat_nat)) (not (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat X4) A3)))) (= A3 tptp.bot_bo2099793752762293965at_nat))) (forall ((A3 tptp.set_bool)) (= (forall ((X4 tptp.bool)) (not (tptp.pp (tptp.member_bool X4 A3)))) (= A3 tptp.bot_bot_set_bool))) (forall ((A3 tptp.set_nat)) (= (forall ((X4 tptp.nat)) (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A3)))) (= A3 tptp.bot_bot_set_nat))) (forall ((A3 tptp.set_int)) (= (forall ((X4 tptp.int)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A3)))) (= A3 tptp.bot_bot_set_int))) (forall ((C tptp.set_nat)) (not (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat C) tptp.bot_bot_set_set_nat)))) (forall ((C tptp.product_prod_nat_nat)) (not (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat C) tptp.bot_bo2099793752762293965at_nat)))) (forall ((C tptp.bool)) (not (tptp.pp (tptp.member_bool C tptp.bot_bot_set_bool)))) (forall ((C tptp.nat)) (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat C) tptp.bot_bot_set_nat)))) (forall ((C tptp.int)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.member_int C) tptp.bot_bot_set_int)))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (let ((_let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X) Y))) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat _let_1) Y) _let_1))) (forall ((X tptp.assn) (Y tptp.assn)) (let ((_let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X) Y))) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn _let_1) Y) _let_1))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat X) Y))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat _let_1) Y) _let_1))) (forall ((X tptp.product_unit) (Y tptp.product_unit)) (let ((_let_1 (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X) Y))) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit _let_1) Y) _let_1))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X) Y))) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat _let_1) Y) _let_1))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A) B))) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat _let_1) B) _let_1))) (forall ((A tptp.assn) (B tptp.assn)) (let ((_let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A) B))) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn _let_1) B) _let_1))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat A) B))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat _let_1) B) _let_1))) (forall ((A tptp.product_unit) (B tptp.product_unit)) (let ((_let_1 (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit A) B))) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit _let_1) B) _let_1))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A) B))) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat _let_1) B) _let_1))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X))) (let ((_let_2 (tptp.aa_set_nat_set_nat _let_1 Y))) (= (tptp.aa_set_nat_set_nat _let_1 _let_2) _let_2)))) (forall ((X tptp.assn) (Y tptp.assn)) (let ((_let_1 (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X))) (let ((_let_2 (tptp.aa_assn_assn _let_1 Y))) (= (tptp.aa_assn_assn _let_1 _let_2) _let_2)))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat X))) (let ((_let_2 (tptp.aa_nat_nat _let_1 Y))) (= (tptp.aa_nat_nat _let_1 _let_2) _let_2)))) (forall ((X tptp.product_unit) (Y tptp.product_unit)) (let ((_let_1 (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X))) (let ((_let_2 (tptp.aa_Pro8294289767544744956t_unit _let_1 Y))) (= (tptp.aa_Pro8294289767544744956t_unit _let_1 _let_2) _let_2)))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X))) (let ((_let_2 (tptp.aa_set8868280134176360700at_nat _let_1 Y))) (= (tptp.aa_set8868280134176360700at_nat _let_1 _let_2) _let_2)))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A))) (let ((_let_2 (tptp.aa_set_nat_set_nat _let_1 B))) (= (tptp.aa_set_nat_set_nat _let_1 _let_2) _let_2)))) (forall ((A tptp.assn) (B tptp.assn)) (let ((_let_1 (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A))) (let ((_let_2 (tptp.aa_assn_assn _let_1 B))) (= (tptp.aa_assn_assn _let_1 _let_2) _let_2)))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat A))) (let ((_let_2 (tptp.aa_nat_nat _let_1 B))) (= (tptp.aa_nat_nat _let_1 _let_2) _let_2)))) (forall ((A tptp.product_unit) (B tptp.product_unit)) (let ((_let_1 (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit A))) (let ((_let_2 (tptp.aa_Pro8294289767544744956t_unit _let_1 B))) (= (tptp.aa_Pro8294289767544744956t_unit _let_1 _let_2) _let_2)))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A))) (let ((_let_2 (tptp.aa_set8868280134176360700at_nat _let_1 B))) (= (tptp.aa_set8868280134176360700at_nat _let_1 _let_2) _let_2)))) (forall ((X tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X) X) X)) (forall ((X tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X) X) X)) (forall ((X tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat X) X) X)) (forall ((X tptp.product_unit)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X) X) X)) (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X) X) X)) (forall ((A tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A) A) A)) (forall ((A tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A) A) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat A) A) A)) (forall ((A tptp.product_unit)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit A) A) A)) (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A) A) A)) (forall ((A tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A) B))) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat _let_1) B) _let_1))) (forall ((A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A) B))) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat _let_1) B) _let_1))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A) B))) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat _let_1) B) _let_1))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A) B))) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat _let_1) B) _let_1))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat A) B))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat _let_1) B) _let_1))) (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat X))) (let ((_let_2 (tptp.aa_set5535132180132642428at_nat _let_1 Y))) (= (tptp.aa_set5535132180132642428at_nat _let_1 _let_2) _let_2)))) (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat X))) (let ((_let_2 (tptp.aa_set6734554978791863420at_nat _let_1 Y))) (= (tptp.aa_set6734554978791863420at_nat _let_1 _let_2) _let_2)))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat X))) (let ((_let_2 (tptp.aa_set4883462369968598652at_nat _let_1 Y))) (= (tptp.aa_set4883462369968598652at_nat _let_1 _let_2) _let_2)))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat X))) (let ((_let_2 (tptp.aa_set_nat_set_nat _let_1 Y))) (= (tptp.aa_set_nat_set_nat _let_1 _let_2) _let_2)))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat X))) (let ((_let_2 (tptp.aa_nat_nat _let_1 Y))) (= (tptp.aa_nat_nat _let_1 _let_2) _let_2)))) (forall ((A tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A))) (let ((_let_2 (tptp.aa_set5535132180132642428at_nat _let_1 B))) (= (tptp.aa_set5535132180132642428at_nat _let_1 _let_2) _let_2)))) (forall ((A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A))) (let ((_let_2 (tptp.aa_set6734554978791863420at_nat _let_1 B))) (= (tptp.aa_set6734554978791863420at_nat _let_1 _let_2) _let_2)))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A))) (let ((_let_2 (tptp.aa_set4883462369968598652at_nat _let_1 B))) (= (tptp.aa_set4883462369968598652at_nat _let_1 _let_2) _let_2)))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A))) (let ((_let_2 (tptp.aa_set_nat_set_nat _let_1 B))) (= (tptp.aa_set_nat_set_nat _let_1 _let_2) _let_2)))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat A))) (let ((_let_2 (tptp.aa_nat_nat _let_1 B))) (= (tptp.aa_nat_nat _let_1 _let_2) _let_2)))) (forall ((X tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat X) X) X)) (forall ((X tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat X) X) X)) (forall ((X tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat X) X) X)) (forall ((X tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat X) X) X)) (forall ((X tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat X) X) X)) (forall ((A tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A) A) A)) (forall ((A tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A) A) A)) (forall ((A tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A) A) A)) (forall ((A tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A) A) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat A) A) A)) (forall ((C tptp.bool) (A3 tptp.set_bool) (B3 tptp.set_bool)) (= (tptp.pp (tptp.member_bool C (tptp.inf_inf_set_bool A3 B3))) (and (tptp.pp (tptp.member_bool C A3)) (tptp.pp (tptp.member_bool C B3))))) (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (tptp.member_set_nat C))) (= (tptp.pp (tptp.aa_set_set_nat_bool _let_1 (tptp.inf_inf_set_set_nat A3 B3))) (and (tptp.pp (tptp.aa_set_set_nat_bool _let_1 A3)) (tptp.pp (tptp.aa_set_set_nat_bool _let_1 B3)))))) (forall ((C tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (tptp.member_int C))) (= (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))) (and (tptp.pp (tptp.aa_set_int_bool _let_1 A3)) (tptp.pp (tptp.aa_set_int_bool _let_1 B3)))))) (forall ((C tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.member_nat C))) (= (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3))) (and (tptp.pp (tptp.aa_set_nat_bool _let_1 A3)) (tptp.pp (tptp.aa_set_nat_bool _let_1 B3)))))) (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat C))) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3))) (and (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 A3)) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 B3)))))) (forall ((C tptp.bool) (A3 tptp.set_bool) (B3 tptp.set_bool)) (=> (tptp.pp (tptp.member_bool C A3)) (=> (tptp.pp (tptp.member_bool C B3)) (tptp.pp (tptp.member_bool C (tptp.inf_inf_set_bool A3 B3)))))) (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (tptp.member_set_nat C))) (=> (tptp.pp (tptp.aa_set_set_nat_bool _let_1 A3)) (=> (tptp.pp (tptp.aa_set_set_nat_bool _let_1 B3)) (tptp.pp (tptp.aa_set_set_nat_bool _let_1 (tptp.inf_inf_set_set_nat A3 B3))))))) (forall ((C tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (tptp.member_int C))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 A3)) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 B3)) (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))))))) (forall ((C tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.member_nat C))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A3)) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 B3)) (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3))))))) (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat C))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 A3)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 B3)) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3))))))) (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat C))) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat A3) B3))) (or (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 A3)) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 B3)))))) (forall ((C tptp.bool) (A3 tptp.set_bool) (B3 tptp.set_bool)) (= (tptp.pp (tptp.member_bool C (tptp.aa_set_bool_set_bool (tptp.aa_set4734229006438377534t_bool tptp.sup_sup_set_bool A3) B3))) (or (tptp.pp (tptp.member_bool C A3)) (tptp.pp (tptp.member_bool C B3))))) (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (tptp.member_set_nat C))) (= (tptp.pp (tptp.aa_set_set_nat_bool _let_1 (tptp.sup_sup_set_set_nat A3 B3))) (or (tptp.pp (tptp.aa_set_set_nat_bool _let_1 A3)) (tptp.pp (tptp.aa_set_set_nat_bool _let_1 B3)))))) (forall ((C tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (tptp.member_int C))) (= (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3))) (or (tptp.pp (tptp.aa_set_int_bool _let_1 A3)) (tptp.pp (tptp.aa_set_int_bool _let_1 B3)))))) (forall ((C tptp.produc859450856879609959at_nat) (A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (= (tptp.member8206827879206165904at_nat C (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3) B3)) (or (tptp.member8206827879206165904at_nat C A3) (tptp.member8206827879206165904at_nat C B3)))) (forall ((C tptp.produc4166570645942440679at_nat) (A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (= (tptp.member6689249552917799696at_nat C (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3) B3)) (or (tptp.member6689249552917799696at_nat C A3) (tptp.member6689249552917799696at_nat C B3)))) (forall ((C tptp.produc3843707927480180839at_nat) (A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (= (tptp.member8757157785044589968at_nat C (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3) B3)) (or (tptp.member8757157785044589968at_nat C A3) (tptp.member8757157785044589968at_nat C B3)))) (forall ((C tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.member_nat C))) (= (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3))) (or (tptp.pp (tptp.aa_set_nat_bool _let_1 A3)) (tptp.pp (tptp.aa_set_nat_bool _let_1 B3)))))) (forall ((C tptp.product_prod_nat_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat C))) (=> (=> (not (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 B3))) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 A3))) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat A3) B3)))))) (forall ((C tptp.bool) (B3 tptp.set_bool) (A3 tptp.set_bool)) (=> (=> (not (tptp.pp (tptp.member_bool C B3))) (tptp.pp (tptp.member_bool C A3))) (tptp.pp (tptp.member_bool C (tptp.aa_set_bool_set_bool (tptp.aa_set4734229006438377534t_bool tptp.sup_sup_set_bool A3) B3))))) (forall ((C tptp.set_nat) (B3 tptp.set_set_nat) (A3 tptp.set_set_nat)) (let ((_let_1 (tptp.member_set_nat C))) (=> (=> (not (tptp.pp (tptp.aa_set_set_nat_bool _let_1 B3))) (tptp.pp (tptp.aa_set_set_nat_bool _let_1 A3))) (tptp.pp (tptp.aa_set_set_nat_bool _let_1 (tptp.sup_sup_set_set_nat A3 B3)))))) (forall ((C tptp.int) (B3 tptp.set_int) (A3 tptp.set_int)) (let ((_let_1 (tptp.member_int C))) (=> (=> (not (tptp.pp (tptp.aa_set_int_bool _let_1 B3))) (tptp.pp (tptp.aa_set_int_bool _let_1 A3))) (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3)))))) (forall ((C tptp.produc859450856879609959at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (A3 tptp.set_Pr8693737435421807431at_nat)) (=> (=> (not (tptp.member8206827879206165904at_nat C B3)) (tptp.member8206827879206165904at_nat C A3)) (tptp.member8206827879206165904at_nat C (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3) B3)))) (forall ((C tptp.produc4166570645942440679at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (A3 tptp.set_Pr8551490117392284871at_nat)) (=> (=> (not (tptp.member6689249552917799696at_nat C B3)) (tptp.member6689249552917799696at_nat C A3)) (tptp.member6689249552917799696at_nat C (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3) B3)))) (forall ((C tptp.produc3843707927480180839at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (A3 tptp.set_Pr4329608150637261639at_nat)) (=> (=> (not (tptp.member8757157785044589968at_nat C B3)) (tptp.member8757157785044589968at_nat C A3)) (tptp.member8757157785044589968at_nat C (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3) B3)))) (forall ((C tptp.nat) (B3 tptp.set_nat) (A3 tptp.set_nat)) (let ((_let_1 (tptp.member_nat C))) (=> (=> (not (tptp.pp (tptp.aa_set_nat_bool _let_1 B3))) (tptp.pp (tptp.aa_set_nat_bool _let_1 A3))) (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)))))) (forall ((P tptp.assn) (Q tptp.assn) (H tptp.produc3658429121746597890et_nat)) (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn P) Q)) H)) (or (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn P) H)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn Q) H))))) (forall ((P tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn tptp.bot_bot_assn) P) tptp.bot_bot_assn)) (forall ((P tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn P) tptp.bot_bot_assn) tptp.bot_bot_assn)) (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A))) (= (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat B) C))) (and (tptp.pp (tptp.aa_set_nat_bool _let_1 B)) (tptp.pp (tptp.aa_set_nat_bool _let_1 C)))))) (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn A))) (= (tptp.pp (tptp.aa_assn_bool _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn B) C))) (and (tptp.pp (tptp.aa_assn_bool _let_1 B)) (tptp.pp (tptp.aa_assn_bool _let_1 C)))))) (forall ((A tptp.product_unit) (B tptp.product_unit) (C tptp.product_unit)) (let ((_let_1 (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit A))) (= (tptp.pp (tptp.aa_Product_unit_bool _let_1 (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit B) C))) (and (tptp.pp (tptp.aa_Product_unit_bool _let_1 B)) (tptp.pp (tptp.aa_Product_unit_bool _let_1 C)))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A))) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat B) C))) (and (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 B)) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 C)))))) (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (let ((_let_1 (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A))) (= (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int B) C))) (and (tptp.pp (tptp.aa_set_int_bool _let_1 B)) (tptp.pp (tptp.aa_set_int_bool _let_1 C)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat B) C))) (and (tptp.pp (tptp.aa_rat_bool _let_1 B)) (tptp.pp (tptp.aa_rat_bool _let_1 C)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat B) C))) (and (tptp.pp (tptp.aa_nat_bool _let_1 B)) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int B) C))) (and (tptp.pp (tptp.aa_int_bool _let_1 B)) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat X))) (= (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat Y) Z))) (and (tptp.pp (tptp.aa_set_nat_bool _let_1 Y)) (tptp.pp (tptp.aa_set_nat_bool _let_1 Z)))))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn X))) (= (tptp.pp (tptp.aa_assn_bool _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn Y) Z))) (and (tptp.pp (tptp.aa_assn_bool _let_1 Y)) (tptp.pp (tptp.aa_assn_bool _let_1 Z)))))) (forall ((X tptp.product_unit) (Y tptp.product_unit) (Z tptp.product_unit)) (let ((_let_1 (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit X))) (= (tptp.pp (tptp.aa_Product_unit_bool _let_1 (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit Y) Z))) (and (tptp.pp (tptp.aa_Product_unit_bool _let_1 Y)) (tptp.pp (tptp.aa_Product_unit_bool _let_1 Z)))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat X))) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat Y) Z))) (and (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 Y)) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 Z)))))) (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X))) (= (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int Y) Z))) (and (tptp.pp (tptp.aa_set_int_bool _let_1 Y)) (tptp.pp (tptp.aa_set_int_bool _let_1 Z)))))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat Y) Z))) (and (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (tptp.pp (tptp.aa_rat_bool _let_1 Z)))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat Y) Z))) (and (tptp.pp (tptp.aa_nat_bool _let_1 Y)) (tptp.pp (tptp.aa_nat_bool _let_1 Z)))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int Y) Z))) (and (tptp.pp (tptp.aa_int_bool _let_1 Y)) (tptp.pp (tptp.aa_int_bool _let_1 Z)))))) (forall ((B tptp.set_Pr8693737435421807431at_nat) (C tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat)) (= (tptp.ord_le3000389064537975527at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat B) C) A) (and (tptp.ord_le3000389064537975527at_nat B A) (tptp.ord_le3000389064537975527at_nat C A)))) (forall ((B tptp.set_Pr8551490117392284871at_nat) (C tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat)) (= (tptp.ord_le8081472938463900775at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat B) C) A) (and (tptp.ord_le8081472938463900775at_nat B A) (tptp.ord_le8081472938463900775at_nat C A)))) (forall ((B tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (= (tptp.ord_le1268244103169919719at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat B) C) A) (and (tptp.ord_le1268244103169919719at_nat B A) (tptp.ord_le1268244103169919719at_nat C A)))) (forall ((B tptp.set_nat) (C tptp.set_nat) (A tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat B) C)) A)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B) A)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat C) A))))) (forall ((B tptp.set_int) (C tptp.set_int) (A tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int B) C)) A)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) A)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int C) A))))) (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat B) C)) A)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) A))))) (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat B) C)) A)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) A))))) (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int B) C)) A)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) A))))) (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (= (tptp.ord_le3000389064537975527at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat X) Y) Z) (and (tptp.ord_le3000389064537975527at_nat X Z) (tptp.ord_le3000389064537975527at_nat Y Z)))) (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat)) (= (tptp.ord_le8081472938463900775at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat X) Y) Z) (and (tptp.ord_le8081472938463900775at_nat X Z) (tptp.ord_le8081472938463900775at_nat Y Z)))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (= (tptp.ord_le1268244103169919719at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat X) Y) Z) (and (tptp.ord_le1268244103169919719at_nat X Z) (tptp.ord_le1268244103169919719at_nat Y Z)))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat X) Y)) Z)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat X) Z)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat Y) Z))))) (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int X) Y)) Z)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X) Z)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int Y) Z))))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat X) Y)) Z)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Z)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) Z))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat X) Y)) Z)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Z)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) Z))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int X) Y)) Z)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) Z))))) (forall ((X tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X) tptp.bot_bot_assn) tptp.bot_bot_assn)) (forall ((X tptp.product_unit)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X) tptp.bot_bot_Product_unit) tptp.bot_bot_Product_unit)) (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X) tptp.bot_bo2099793752762293965at_nat) tptp.bot_bo2099793752762293965at_nat)) (forall ((X tptp.set_bool)) (= (tptp.inf_inf_set_bool X tptp.bot_bot_set_bool) tptp.bot_bot_set_bool)) (forall ((X tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X) tptp.bot_bot_set_nat) tptp.bot_bot_set_nat)) (forall ((X tptp.set_int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int X) tptp.bot_bot_set_int) tptp.bot_bot_set_int)) (forall ((X tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn tptp.bot_bot_assn) X) tptp.bot_bot_assn)) (forall ((X tptp.product_unit)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit tptp.bot_bot_Product_unit) X) tptp.bot_bot_Product_unit)) (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat tptp.bot_bo2099793752762293965at_nat) X) tptp.bot_bo2099793752762293965at_nat)) (forall ((X tptp.set_bool)) (= (tptp.inf_inf_set_bool tptp.bot_bot_set_bool X) tptp.bot_bot_set_bool)) (forall ((X tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat tptp.bot_bot_set_nat) X) tptp.bot_bot_set_nat)) (forall ((X tptp.set_int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int tptp.bot_bot_set_int) X) tptp.bot_bot_set_int)) (forall ((A tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A) tptp.bot_bo5327735625951526323at_nat) A)) (forall ((A tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A) tptp.bot_bo8422036546324065075at_nat) A)) (forall ((A tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A) tptp.bot_bo228742789529271731at_nat) A)) (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat A) tptp.bot_bo2099793752762293965at_nat) A)) (forall ((A tptp.set_bool)) (= (tptp.aa_set_bool_set_bool (tptp.aa_set4734229006438377534t_bool tptp.sup_sup_set_bool A) tptp.bot_bot_set_bool) A)) (forall ((A tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A) tptp.bot_bot_set_nat) A)) (forall ((A tptp.set_int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A) tptp.bot_bot_set_int) A)) (forall ((A tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat)) (= (= tptp.bot_bo5327735625951526323at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A) B)) (and (= A tptp.bot_bo5327735625951526323at_nat) (= B tptp.bot_bo5327735625951526323at_nat)))) (forall ((A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (= (= tptp.bot_bo8422036546324065075at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A) B)) (and (= A tptp.bot_bo8422036546324065075at_nat) (= B tptp.bot_bo8422036546324065075at_nat)))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (= (= tptp.bot_bo228742789529271731at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A) B)) (and (= A tptp.bot_bo228742789529271731at_nat) (= B tptp.bot_bo228742789529271731at_nat)))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (= tptp.bot_bo2099793752762293965at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat A) B)) (and (= A tptp.bot_bo2099793752762293965at_nat) (= B tptp.bot_bo2099793752762293965at_nat)))) (forall ((A tptp.set_bool) (B tptp.set_bool)) (= (= tptp.bot_bot_set_bool (tptp.aa_set_bool_set_bool (tptp.aa_set4734229006438377534t_bool tptp.sup_sup_set_bool A) B)) (and (= A tptp.bot_bot_set_bool) (= B tptp.bot_bot_set_bool)))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (= tptp.bot_bot_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A) B)) (and (= A tptp.bot_bot_set_nat) (= B tptp.bot_bot_set_nat)))) (forall ((A tptp.set_int) (B tptp.set_int)) (= (= tptp.bot_bot_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A) B)) (and (= A tptp.bot_bot_set_int) (= B tptp.bot_bot_set_int)))) (forall ((A tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat tptp.bot_bo5327735625951526323at_nat) A) A)) (forall ((A tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat tptp.bot_bo8422036546324065075at_nat) A) A)) (forall ((A tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat tptp.bot_bo228742789529271731at_nat) A) A)) (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat tptp.bot_bo2099793752762293965at_nat) A) A)) (forall ((A tptp.set_bool)) (= (tptp.aa_set_bool_set_bool (tptp.aa_set4734229006438377534t_bool tptp.sup_sup_set_bool tptp.bot_bot_set_bool) A) A)) (forall ((A tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat tptp.bot_bot_set_nat) A) A)) (forall ((A tptp.set_int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int tptp.bot_bot_set_int) A) A)) (forall ((A tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat)) (= (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A) B) tptp.bot_bo5327735625951526323at_nat) (and (= A tptp.bot_bo5327735625951526323at_nat) (= B tptp.bot_bo5327735625951526323at_nat)))) (forall ((A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (= (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A) B) tptp.bot_bo8422036546324065075at_nat) (and (= A tptp.bot_bo8422036546324065075at_nat) (= B tptp.bot_bo8422036546324065075at_nat)))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (= (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A) B) tptp.bot_bo228742789529271731at_nat) (and (= A tptp.bot_bo228742789529271731at_nat) (= B tptp.bot_bo228742789529271731at_nat)))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat A) B) tptp.bot_bo2099793752762293965at_nat) (and (= A tptp.bot_bo2099793752762293965at_nat) (= B tptp.bot_bo2099793752762293965at_nat)))) (forall ((A tptp.set_bool) (B tptp.set_bool)) (= (= (tptp.aa_set_bool_set_bool (tptp.aa_set4734229006438377534t_bool tptp.sup_sup_set_bool A) B) tptp.bot_bot_set_bool) (and (= A tptp.bot_bot_set_bool) (= B tptp.bot_bot_set_bool)))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A) B) tptp.bot_bot_set_nat) (and (= A tptp.bot_bot_set_nat) (= B tptp.bot_bot_set_nat)))) (forall ((A tptp.set_int) (B tptp.set_int)) (= (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A) B) tptp.bot_bot_set_int) (and (= A tptp.bot_bot_set_int) (= B tptp.bot_bot_set_int)))) (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat)) (= (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat X) Y) tptp.bot_bo5327735625951526323at_nat) (and (= X tptp.bot_bo5327735625951526323at_nat) (= Y tptp.bot_bo5327735625951526323at_nat)))) (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat)) (= (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat X) Y) tptp.bot_bo8422036546324065075at_nat) (and (= X tptp.bot_bo8422036546324065075at_nat) (= Y tptp.bot_bo8422036546324065075at_nat)))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (= (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat X) Y) tptp.bot_bo228742789529271731at_nat) (and (= X tptp.bot_bo228742789529271731at_nat) (= Y tptp.bot_bo228742789529271731at_nat)))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat X) Y) tptp.bot_bo2099793752762293965at_nat) (and (= X tptp.bot_bo2099793752762293965at_nat) (= Y tptp.bot_bo2099793752762293965at_nat)))) (forall ((X tptp.set_bool) (Y tptp.set_bool)) (= (= (tptp.aa_set_bool_set_bool (tptp.aa_set4734229006438377534t_bool tptp.sup_sup_set_bool X) Y) tptp.bot_bot_set_bool) (and (= X tptp.bot_bot_set_bool) (= Y tptp.bot_bot_set_bool)))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat X) Y) tptp.bot_bot_set_nat) (and (= X tptp.bot_bot_set_nat) (= Y tptp.bot_bot_set_nat)))) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int X) Y) tptp.bot_bot_set_int) (and (= X tptp.bot_bot_set_int) (= Y tptp.bot_bot_set_int)))) (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat)) (= (= tptp.bot_bo5327735625951526323at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat X) Y)) (and (= X tptp.bot_bo5327735625951526323at_nat) (= Y tptp.bot_bo5327735625951526323at_nat)))) (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat)) (= (= tptp.bot_bo8422036546324065075at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat X) Y)) (and (= X tptp.bot_bo8422036546324065075at_nat) (= Y tptp.bot_bo8422036546324065075at_nat)))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (= (= tptp.bot_bo228742789529271731at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat X) Y)) (and (= X tptp.bot_bo228742789529271731at_nat) (= Y tptp.bot_bo228742789529271731at_nat)))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (= tptp.bot_bo2099793752762293965at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat X) Y)) (and (= X tptp.bot_bo2099793752762293965at_nat) (= Y tptp.bot_bo2099793752762293965at_nat)))) (forall ((X tptp.set_bool) (Y tptp.set_bool)) (= (= tptp.bot_bot_set_bool (tptp.aa_set_bool_set_bool (tptp.aa_set4734229006438377534t_bool tptp.sup_sup_set_bool X) Y)) (and (= X tptp.bot_bot_set_bool) (= Y tptp.bot_bot_set_bool)))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (= tptp.bot_bot_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat X) Y)) (and (= X tptp.bot_bot_set_nat) (= Y tptp.bot_bot_set_nat)))) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (= tptp.bot_bot_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int X) Y)) (and (= X tptp.bot_bot_set_int) (= Y tptp.bot_bot_set_int)))) (forall ((X tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat X) tptp.bot_bo5327735625951526323at_nat) X)) (forall ((X tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat X) tptp.bot_bo8422036546324065075at_nat) X)) (forall ((X tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat X) tptp.bot_bo228742789529271731at_nat) X)) (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat X) tptp.bot_bo2099793752762293965at_nat) X)) (forall ((X tptp.set_bool)) (= (tptp.aa_set_bool_set_bool (tptp.aa_set4734229006438377534t_bool tptp.sup_sup_set_bool X) tptp.bot_bot_set_bool) X)) (forall ((X tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat X) tptp.bot_bot_set_nat) X)) (forall ((X tptp.set_int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int X) tptp.bot_bot_set_int) X)) (forall ((P tptp.assn) (Q tptp.assn) (H tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (tptp.produc7507926704131184380et_nat H tptp.bot_bot_set_nat))) (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn P) Q)) _let_1)) (and (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn P) _let_1)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn Q) _let_1)))))) (forall ((P tptp.assn) (Q tptp.assn) (H tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (tptp.produc7507926704131184380et_nat H tptp.bot_bot_set_nat))) (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn P) Q)) _let_1)) (or (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn P) _let_1)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn Q) _let_1)))))) (= tptp.bot_bo1796632182523588997nt_int (tptp.collec213857154873943460nt_int tptp.bot_bo6051839928536000373t_bool)) (= tptp.bot_bot_set_list_nat (tptp.collect_list_nat tptp.bot_bo6469247547558333820t_bool)) (= tptp.bot_bot_set_set_nat (tptp.collect_set_nat tptp.bot_bo8343409700046576086t_bool)) (= tptp.bot_bo2099793752762293965at_nat (tptp.collec3392354462482085612at_nat tptp.bot_bo3782518310583830573t_bool)) (= tptp.bot_bot_set_bool (tptp.collect_bool tptp.bot_bo4756488196683355415l_bool)) (= tptp.bot_bot_set_nat (tptp.collect_nat tptp.bot_bot_fun_nat_bool)) (= tptp.bot_bot_set_int (tptp.collect_int tptp.bot_bot_fun_int_bool)) (forall ((P tptp.assn) (Q tptp.assn) (H tptp.produc3658429121746597890et_nat)) (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn P) Q)) H)) (and (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn P) H)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn Q) H))))) (forall ((H tptp.produc3658429121746597890et_nat)) (not (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn tptp.bot_bot_assn) H)))) (forall ((A3 tptp.assn) (B3 tptp.assn) (C3 tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn A3) B3)) C3) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn A3) C3)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn B3) C3)))) (forall ((C3 tptp.assn) (A3 tptp.assn) (B3 tptp.assn)) (let ((_let_1 (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn C3))) (= (tptp.aa_assn_assn _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn A3) B3)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn (tptp.aa_assn_assn _let_1 A3)) (tptp.aa_assn_assn _let_1 B3))))) (forall ((A3 tptp.set_set_nat)) (= (exists ((X4 tptp.set_nat)) (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat X4) A3))) (not (= A3 tptp.bot_bot_set_set_nat)))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (exists ((X4 tptp.product_prod_nat_nat)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat X4) A3))) (not (= A3 tptp.bot_bo2099793752762293965at_nat)))) (forall ((A3 tptp.set_bool)) (= (exists ((X4 tptp.bool)) (tptp.pp (tptp.member_bool X4 A3))) (not (= A3 tptp.bot_bot_set_bool)))) (forall ((A3 tptp.set_nat)) (= (exists ((X4 tptp.nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A3))) (not (= A3 tptp.bot_bot_set_nat)))) (forall ((A3 tptp.set_int)) (= (exists ((X4 tptp.int)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A3))) (not (= A3 tptp.bot_bot_set_int)))) (forall ((A3 tptp.set_set_nat)) (=> (forall ((Y3 tptp.set_nat)) (not (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat Y3) A3)))) (= A3 tptp.bot_bot_set_set_nat))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((Y3 tptp.product_prod_nat_nat)) (not (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat Y3) A3)))) (= A3 tptp.bot_bo2099793752762293965at_nat))) (forall ((A3 tptp.set_bool)) (=> (forall ((Y3 tptp.bool)) (not (tptp.pp (tptp.member_bool Y3 A3)))) (= A3 tptp.bot_bot_set_bool))) (forall ((A3 tptp.set_nat)) (=> (forall ((Y3 tptp.nat)) (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Y3) A3)))) (= A3 tptp.bot_bot_set_nat))) (forall ((A3 tptp.set_int)) (=> (forall ((Y3 tptp.int)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Y3) A3)))) (= A3 tptp.bot_bot_set_int))) (forall ((A3 tptp.set_set_nat) (A tptp.set_nat)) (=> (= A3 tptp.bot_bot_set_set_nat) (not (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat A) A3))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (A tptp.product_prod_nat_nat)) (=> (= A3 tptp.bot_bo2099793752762293965at_nat) (not (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat A) A3))))) (forall ((A3 tptp.set_bool) (A tptp.bool)) (=> (= A3 tptp.bot_bot_set_bool) (not (tptp.pp (tptp.member_bool A A3))))) (forall ((A3 tptp.set_nat) (A tptp.nat)) (=> (= A3 tptp.bot_bot_set_nat) (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A) A3))))) (forall ((A3 tptp.set_int) (A tptp.int)) (=> (= A3 tptp.bot_bot_set_int) (not (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A) A3))))) (forall ((A tptp.set_nat)) (not (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat A) tptp.bot_bot_set_set_nat)))) (forall ((A tptp.product_prod_nat_nat)) (not (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat A) tptp.bot_bo2099793752762293965at_nat)))) (forall ((A tptp.bool)) (not (tptp.pp (tptp.member_bool A tptp.bot_bot_set_bool)))) (forall ((A tptp.nat)) (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A) tptp.bot_bot_set_nat)))) (forall ((A tptp.int)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A) tptp.bot_bot_set_int)))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X))) (let ((_let_2 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat Y))) (= (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat _let_2 Z)) (tptp.aa_set_nat_set_nat _let_2 (tptp.aa_set_nat_set_nat _let_1 Z)))))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X))) (let ((_let_2 (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn Y))) (= (tptp.aa_assn_assn _let_1 (tptp.aa_assn_assn _let_2 Z)) (tptp.aa_assn_assn _let_2 (tptp.aa_assn_assn _let_1 Z)))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat X))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat Y))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat _let_2 Z)) (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat _let_1 Z)))))) (forall ((X tptp.product_unit) (Y tptp.product_unit) (Z tptp.product_unit)) (let ((_let_1 (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X))) (let ((_let_2 (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit Y))) (= (tptp.aa_Pro8294289767544744956t_unit _let_1 (tptp.aa_Pro8294289767544744956t_unit _let_2 Z)) (tptp.aa_Pro8294289767544744956t_unit _let_2 (tptp.aa_Pro8294289767544744956t_unit _let_1 Z)))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X))) (let ((_let_2 (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat Y))) (= (tptp.aa_set8868280134176360700at_nat _let_1 (tptp.aa_set8868280134176360700at_nat _let_2 Z)) (tptp.aa_set8868280134176360700at_nat _let_2 (tptp.aa_set8868280134176360700at_nat _let_1 Z)))))) (forall ((B tptp.set_nat) (A tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat B))) (let ((_let_2 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A))) (= (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat _let_2 C)) (tptp.aa_set_nat_set_nat _let_2 (tptp.aa_set_nat_set_nat _let_1 C)))))) (forall ((B tptp.assn) (A tptp.assn) (C tptp.assn)) (let ((_let_1 (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn B))) (let ((_let_2 (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A))) (= (tptp.aa_assn_assn _let_1 (tptp.aa_assn_assn _let_2 C)) (tptp.aa_assn_assn _let_2 (tptp.aa_assn_assn _let_1 C)))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat B))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat A))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat _let_2 C)) (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat _let_1 C)))))) (forall ((B tptp.product_unit) (A tptp.product_unit) (C tptp.product_unit)) (let ((_let_1 (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit B))) (let ((_let_2 (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit A))) (= (tptp.aa_Pro8294289767544744956t_unit _let_1 (tptp.aa_Pro8294289767544744956t_unit _let_2 C)) (tptp.aa_Pro8294289767544744956t_unit _let_2 (tptp.aa_Pro8294289767544744956t_unit _let_1 C)))))) (forall ((B tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat B))) (let ((_let_2 (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A))) (= (tptp.aa_set8868280134176360700at_nat _let_1 (tptp.aa_set8868280134176360700at_nat _let_2 C)) (tptp.aa_set8868280134176360700at_nat _let_2 (tptp.aa_set8868280134176360700at_nat _let_1 C)))))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X) Y) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat Y) X))) (forall ((X tptp.assn) (Y tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X) Y) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn Y) X))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat X) Y) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat Y) X))) (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X) Y) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit Y) X))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X) Y) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat Y) X))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A) B) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat B) A))) (forall ((A tptp.assn) (B tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A) B) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn B) A))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat A) B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat B) A))) (forall ((A tptp.product_unit) (B tptp.product_unit)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit A) B) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit B) A))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A) B) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat B) A))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X))) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.aa_set_nat_set_nat _let_1 Y)) Z) (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat Y) Z))))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X))) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn (tptp.aa_assn_assn _let_1 Y)) Z) (tptp.aa_assn_assn _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn Y) Z))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat X))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat (tptp.aa_nat_nat _let_1 Y)) Z) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat Y) Z))))) (forall ((X tptp.product_unit) (Y tptp.product_unit) (Z tptp.product_unit)) (let ((_let_1 (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X))) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit (tptp.aa_Pro8294289767544744956t_unit _let_1 Y)) Z) (tptp.aa_Pro8294289767544744956t_unit _let_1 (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit Y) Z))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X))) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.aa_set8868280134176360700at_nat _let_1 Y)) Z) (tptp.aa_set8868280134176360700at_nat _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat Y) Z))))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A))) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.aa_set_nat_set_nat _let_1 B)) C) (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat B) C))))) (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A))) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn (tptp.aa_assn_assn _let_1 B)) C) (tptp.aa_assn_assn _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn B) C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat (tptp.aa_nat_nat _let_1 B)) C) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat B) C))))) (forall ((A tptp.product_unit) (B tptp.product_unit) (C tptp.product_unit)) (let ((_let_1 (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit A))) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit (tptp.aa_Pro8294289767544744956t_unit _let_1 B)) C) (tptp.aa_Pro8294289767544744956t_unit _let_1 (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit B) C))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A))) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.aa_set8868280134176360700at_nat _let_1 B)) C) (tptp.aa_set8868280134176360700at_nat _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat B) C))))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X) Y) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat Y) X))) (forall ((X tptp.assn) (Y tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X) Y) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn Y) X))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat X) Y) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat Y) X))) (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X) Y) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit Y) X))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X) Y) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat Y) X))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X))) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.aa_set_nat_set_nat _let_1 Y)) Z) (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat Y) Z))))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X))) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn (tptp.aa_assn_assn _let_1 Y)) Z) (tptp.aa_assn_assn _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn Y) Z))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat X))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat (tptp.aa_nat_nat _let_1 Y)) Z) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat Y) Z))))) (forall ((X tptp.product_unit) (Y tptp.product_unit) (Z tptp.product_unit)) (let ((_let_1 (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X))) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit (tptp.aa_Pro8294289767544744956t_unit _let_1 Y)) Z) (tptp.aa_Pro8294289767544744956t_unit _let_1 (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit Y) Z))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X))) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.aa_set8868280134176360700at_nat _let_1 Y)) Z) (tptp.aa_set8868280134176360700at_nat _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat Y) Z))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X))) (let ((_let_2 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat Y))) (= (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat _let_2 Z)) (tptp.aa_set_nat_set_nat _let_2 (tptp.aa_set_nat_set_nat _let_1 Z)))))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X))) (let ((_let_2 (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn Y))) (= (tptp.aa_assn_assn _let_1 (tptp.aa_assn_assn _let_2 Z)) (tptp.aa_assn_assn _let_2 (tptp.aa_assn_assn _let_1 Z)))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat X))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat Y))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat _let_2 Z)) (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat _let_1 Z)))))) (forall ((X tptp.product_unit) (Y tptp.product_unit) (Z tptp.product_unit)) (let ((_let_1 (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X))) (let ((_let_2 (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit Y))) (= (tptp.aa_Pro8294289767544744956t_unit _let_1 (tptp.aa_Pro8294289767544744956t_unit _let_2 Z)) (tptp.aa_Pro8294289767544744956t_unit _let_2 (tptp.aa_Pro8294289767544744956t_unit _let_1 Z)))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X))) (let ((_let_2 (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat Y))) (= (tptp.aa_set8868280134176360700at_nat _let_1 (tptp.aa_set8868280134176360700at_nat _let_2 Z)) (tptp.aa_set8868280134176360700at_nat _let_2 (tptp.aa_set8868280134176360700at_nat _let_1 Z)))))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X))) (let ((_let_2 (tptp.aa_set_nat_set_nat _let_1 Y))) (= (tptp.aa_set_nat_set_nat _let_1 _let_2) _let_2)))) (forall ((X tptp.assn) (Y tptp.assn)) (let ((_let_1 (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X))) (let ((_let_2 (tptp.aa_assn_assn _let_1 Y))) (= (tptp.aa_assn_assn _let_1 _let_2) _let_2)))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat X))) (let ((_let_2 (tptp.aa_nat_nat _let_1 Y))) (= (tptp.aa_nat_nat _let_1 _let_2) _let_2)))) (forall ((X tptp.product_unit) (Y tptp.product_unit)) (let ((_let_1 (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X))) (let ((_let_2 (tptp.aa_Pro8294289767544744956t_unit _let_1 Y))) (= (tptp.aa_Pro8294289767544744956t_unit _let_1 _let_2) _let_2)))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X))) (let ((_let_2 (tptp.aa_set8868280134176360700at_nat _let_1 Y))) (= (tptp.aa_set8868280134176360700at_nat _let_1 _let_2) _let_2)))) (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat X))) (let ((_let_2 (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat Y))) (= (tptp.aa_set5535132180132642428at_nat _let_1 (tptp.aa_set5535132180132642428at_nat _let_2 Z)) (tptp.aa_set5535132180132642428at_nat _let_2 (tptp.aa_set5535132180132642428at_nat _let_1 Z)))))) (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat X))) (let ((_let_2 (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat Y))) (= (tptp.aa_set6734554978791863420at_nat _let_1 (tptp.aa_set6734554978791863420at_nat _let_2 Z)) (tptp.aa_set6734554978791863420at_nat _let_2 (tptp.aa_set6734554978791863420at_nat _let_1 Z)))))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat X))) (let ((_let_2 (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat Y))) (= (tptp.aa_set4883462369968598652at_nat _let_1 (tptp.aa_set4883462369968598652at_nat _let_2 Z)) (tptp.aa_set4883462369968598652at_nat _let_2 (tptp.aa_set4883462369968598652at_nat _let_1 Z)))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat X))) (let ((_let_2 (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat Y))) (= (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat _let_2 Z)) (tptp.aa_set_nat_set_nat _let_2 (tptp.aa_set_nat_set_nat _let_1 Z)))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat X))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat Y))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat _let_2 Z)) (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat _let_1 Z)))))) (forall ((B tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat) (C tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat B))) (let ((_let_2 (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A))) (= (tptp.aa_set5535132180132642428at_nat _let_1 (tptp.aa_set5535132180132642428at_nat _let_2 C)) (tptp.aa_set5535132180132642428at_nat _let_2 (tptp.aa_set5535132180132642428at_nat _let_1 C)))))) (forall ((B tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat) (C tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat B))) (let ((_let_2 (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A))) (= (tptp.aa_set6734554978791863420at_nat _let_1 (tptp.aa_set6734554978791863420at_nat _let_2 C)) (tptp.aa_set6734554978791863420at_nat _let_2 (tptp.aa_set6734554978791863420at_nat _let_1 C)))))) (forall ((B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat B))) (let ((_let_2 (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A))) (= (tptp.aa_set4883462369968598652at_nat _let_1 (tptp.aa_set4883462369968598652at_nat _let_2 C)) (tptp.aa_set4883462369968598652at_nat _let_2 (tptp.aa_set4883462369968598652at_nat _let_1 C)))))) (forall ((B tptp.set_nat) (A tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat B))) (let ((_let_2 (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A))) (= (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat _let_2 C)) (tptp.aa_set_nat_set_nat _let_2 (tptp.aa_set_nat_set_nat _let_1 C)))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat B))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat A))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat _let_2 C)) (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat _let_1 C)))))) (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat X) Y) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat Y) X))) (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat X) Y) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat Y) X))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat X) Y) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat Y) X))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat X) Y) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat Y) X))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat X) Y) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat Y) X))) (forall ((A tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A) B) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat B) A))) (forall ((A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A) B) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat B) A))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A) B) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat B) A))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A) B) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat B) A))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat A) B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat B) A))) (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat X))) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat (tptp.aa_set5535132180132642428at_nat _let_1 Y)) Z) (tptp.aa_set5535132180132642428at_nat _let_1 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat Y) Z))))) (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat X))) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat (tptp.aa_set6734554978791863420at_nat _let_1 Y)) Z) (tptp.aa_set6734554978791863420at_nat _let_1 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat Y) Z))))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat X))) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat (tptp.aa_set4883462369968598652at_nat _let_1 Y)) Z) (tptp.aa_set4883462369968598652at_nat _let_1 (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat Y) Z))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat X))) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.aa_set_nat_set_nat _let_1 Y)) Z) (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat Y) Z))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat X))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat (tptp.aa_nat_nat _let_1 Y)) Z) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat Y) Z))))) (forall ((A tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat) (C tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A))) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat (tptp.aa_set5535132180132642428at_nat _let_1 B)) C) (tptp.aa_set5535132180132642428at_nat _let_1 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat B) C))))) (forall ((A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat) (C tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A))) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat (tptp.aa_set6734554978791863420at_nat _let_1 B)) C) (tptp.aa_set6734554978791863420at_nat _let_1 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat B) C))))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A))) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat (tptp.aa_set4883462369968598652at_nat _let_1 B)) C) (tptp.aa_set4883462369968598652at_nat _let_1 (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat B) C))))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A))) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.aa_set_nat_set_nat _let_1 B)) C) (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat B) C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat (tptp.aa_nat_nat _let_1 B)) C) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat B) C))))) (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat X) Y) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat Y) X))) (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat X) Y) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat Y) X))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat X) Y) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat Y) X))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat X) Y) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat Y) X))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat X) Y) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat Y) X))) (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat X))) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat (tptp.aa_set5535132180132642428at_nat _let_1 Y)) Z) (tptp.aa_set5535132180132642428at_nat _let_1 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat Y) Z))))) (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat X))) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat (tptp.aa_set6734554978791863420at_nat _let_1 Y)) Z) (tptp.aa_set6734554978791863420at_nat _let_1 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat Y) Z))))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat X))) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat (tptp.aa_set4883462369968598652at_nat _let_1 Y)) Z) (tptp.aa_set4883462369968598652at_nat _let_1 (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat Y) Z))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat X))) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.aa_set_nat_set_nat _let_1 Y)) Z) (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat Y) Z))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat X))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat (tptp.aa_nat_nat _let_1 Y)) Z) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat Y) Z))))) (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat X))) (let ((_let_2 (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat Y))) (= (tptp.aa_set5535132180132642428at_nat _let_1 (tptp.aa_set5535132180132642428at_nat _let_2 Z)) (tptp.aa_set5535132180132642428at_nat _let_2 (tptp.aa_set5535132180132642428at_nat _let_1 Z)))))) (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat X))) (let ((_let_2 (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat Y))) (= (tptp.aa_set6734554978791863420at_nat _let_1 (tptp.aa_set6734554978791863420at_nat _let_2 Z)) (tptp.aa_set6734554978791863420at_nat _let_2 (tptp.aa_set6734554978791863420at_nat _let_1 Z)))))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat X))) (let ((_let_2 (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat Y))) (= (tptp.aa_set4883462369968598652at_nat _let_1 (tptp.aa_set4883462369968598652at_nat _let_2 Z)) (tptp.aa_set4883462369968598652at_nat _let_2 (tptp.aa_set4883462369968598652at_nat _let_1 Z)))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat X))) (let ((_let_2 (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat Y))) (= (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat _let_2 Z)) (tptp.aa_set_nat_set_nat _let_2 (tptp.aa_set_nat_set_nat _let_1 Z)))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat X))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat Y))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat _let_2 Z)) (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat _let_1 Z)))))) (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat X))) (let ((_let_2 (tptp.aa_set5535132180132642428at_nat _let_1 Y))) (= (tptp.aa_set5535132180132642428at_nat _let_1 _let_2) _let_2)))) (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat X))) (let ((_let_2 (tptp.aa_set6734554978791863420at_nat _let_1 Y))) (= (tptp.aa_set6734554978791863420at_nat _let_1 _let_2) _let_2)))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat X))) (let ((_let_2 (tptp.aa_set4883462369968598652at_nat _let_1 Y))) (= (tptp.aa_set4883462369968598652at_nat _let_1 _let_2) _let_2)))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat X))) (let ((_let_2 (tptp.aa_set_nat_set_nat _let_1 Y))) (= (tptp.aa_set_nat_set_nat _let_1 _let_2) _let_2)))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat X))) (let ((_let_2 (tptp.aa_nat_nat _let_1 Y))) (= (tptp.aa_nat_nat _let_1 _let_2) _let_2)))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C3 tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3))) (let ((_let_2 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat B3))) (= (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat _let_2 C3)) (tptp.aa_set_nat_set_nat _let_2 (tptp.aa_set_nat_set_nat _let_1 C3)))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3))) (let ((_let_2 (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat B3))) (= (tptp.aa_set8868280134176360700at_nat _let_1 (tptp.aa_set8868280134176360700at_nat _let_2 C3)) (tptp.aa_set8868280134176360700at_nat _let_2 (tptp.aa_set8868280134176360700at_nat _let_1 C3)))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3))) (let ((_let_2 (tptp.aa_set_nat_set_nat _let_1 B3))) (= (tptp.aa_set_nat_set_nat _let_1 _let_2) _let_2)))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3))) (let ((_let_2 (tptp.aa_set8868280134176360700at_nat _let_1 B3))) (= (tptp.aa_set8868280134176360700at_nat _let_1 _let_2) _let_2)))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat B3) A3))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat B3) A3))) (forall ((A3 tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) A3) A3)) (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) A3) A3)) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C3 tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3))) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.aa_set_nat_set_nat _let_1 B3)) C3) (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat B3) C3))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3))) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.aa_set8868280134176360700at_nat _let_1 B3)) C3) (tptp.aa_set8868280134176360700at_nat _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat B3) C3))))) (forall ((C tptp.bool) (A3 tptp.set_bool) (B3 tptp.set_bool)) (=> (tptp.pp (tptp.member_bool C (tptp.inf_inf_set_bool A3 B3))) (tptp.pp (tptp.member_bool C B3)))) (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (tptp.member_set_nat C))) (=> (tptp.pp (tptp.aa_set_set_nat_bool _let_1 (tptp.inf_inf_set_set_nat A3 B3))) (tptp.pp (tptp.aa_set_set_nat_bool _let_1 B3))))) (forall ((C tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (tptp.member_int C))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))) (tptp.pp (tptp.aa_set_int_bool _let_1 B3))))) (forall ((C tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.member_nat C))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3))) (tptp.pp (tptp.aa_set_nat_bool _let_1 B3))))) (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat C))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3))) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 B3))))) (forall ((C tptp.bool) (A3 tptp.set_bool) (B3 tptp.set_bool)) (=> (tptp.pp (tptp.member_bool C (tptp.inf_inf_set_bool A3 B3))) (tptp.pp (tptp.member_bool C A3)))) (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (tptp.member_set_nat C))) (=> (tptp.pp (tptp.aa_set_set_nat_bool _let_1 (tptp.inf_inf_set_set_nat A3 B3))) (tptp.pp (tptp.aa_set_set_nat_bool _let_1 A3))))) (forall ((C tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (tptp.member_int C))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))) (tptp.pp (tptp.aa_set_int_bool _let_1 A3))))) (forall ((C tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.member_nat C))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3))) (tptp.pp (tptp.aa_set_nat_bool _let_1 A3))))) (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat C))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3))) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 A3))))) (forall ((C tptp.bool) (A3 tptp.set_bool) (B3 tptp.set_bool)) (=> (tptp.pp (tptp.member_bool C (tptp.inf_inf_set_bool A3 B3))) (not (=> (tptp.pp (tptp.member_bool C A3)) (not (tptp.pp (tptp.member_bool C B3))))))) (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (tptp.member_set_nat C))) (=> (tptp.pp (tptp.aa_set_set_nat_bool _let_1 (tptp.inf_inf_set_set_nat A3 B3))) (not (=> (tptp.pp (tptp.aa_set_set_nat_bool _let_1 A3)) (not (tptp.pp (tptp.aa_set_set_nat_bool _let_1 B3)))))))) (forall ((C tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (tptp.member_int C))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))) (not (=> (tptp.pp (tptp.aa_set_int_bool _let_1 A3)) (not (tptp.pp (tptp.aa_set_int_bool _let_1 B3)))))))) (forall ((C tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.member_nat C))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3))) (not (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A3)) (not (tptp.pp (tptp.aa_set_nat_bool _let_1 B3)))))))) (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat C))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3))) (not (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 A3)) (not (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 B3)))))))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (C3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3))) (let ((_let_2 (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat B3))) (= (tptp.aa_set5535132180132642428at_nat _let_1 (tptp.aa_set5535132180132642428at_nat _let_2 C3)) (tptp.aa_set5535132180132642428at_nat _let_2 (tptp.aa_set5535132180132642428at_nat _let_1 C3)))))) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (C3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3))) (let ((_let_2 (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat B3))) (= (tptp.aa_set6734554978791863420at_nat _let_1 (tptp.aa_set6734554978791863420at_nat _let_2 C3)) (tptp.aa_set6734554978791863420at_nat _let_2 (tptp.aa_set6734554978791863420at_nat _let_1 C3)))))) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (C3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3))) (let ((_let_2 (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat B3))) (= (tptp.aa_set4883462369968598652at_nat _let_1 (tptp.aa_set4883462369968598652at_nat _let_2 C3)) (tptp.aa_set4883462369968598652at_nat _let_2 (tptp.aa_set4883462369968598652at_nat _let_1 C3)))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C3 tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3))) (let ((_let_2 (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat B3))) (= (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat _let_2 C3)) (tptp.aa_set_nat_set_nat _let_2 (tptp.aa_set_nat_set_nat _let_1 C3)))))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3))) (let ((_let_2 (tptp.aa_set5535132180132642428at_nat _let_1 B3))) (= (tptp.aa_set5535132180132642428at_nat _let_1 _let_2) _let_2)))) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3))) (let ((_let_2 (tptp.aa_set6734554978791863420at_nat _let_1 B3))) (= (tptp.aa_set6734554978791863420at_nat _let_1 _let_2) _let_2)))) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3))) (let ((_let_2 (tptp.aa_set4883462369968598652at_nat _let_1 B3))) (= (tptp.aa_set4883462369968598652at_nat _let_1 _let_2) _let_2)))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3))) (let ((_let_2 (tptp.aa_set_nat_set_nat _let_1 B3))) (= (tptp.aa_set_nat_set_nat _let_1 _let_2) _let_2)))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3) B3) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat B3) A3))) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3) B3) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat B3) A3))) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3) B3) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat B3) A3))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat B3) A3))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3) A3) A3)) (forall ((A3 tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3) A3) A3)) (forall ((A3 tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3) A3) A3)) (forall ((A3 tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) A3) A3)) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (C3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3))) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat (tptp.aa_set5535132180132642428at_nat _let_1 B3)) C3) (tptp.aa_set5535132180132642428at_nat _let_1 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat B3) C3))))) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (C3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3))) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat (tptp.aa_set6734554978791863420at_nat _let_1 B3)) C3) (tptp.aa_set6734554978791863420at_nat _let_1 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat B3) C3))))) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (C3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3))) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat (tptp.aa_set4883462369968598652at_nat _let_1 B3)) C3) (tptp.aa_set4883462369968598652at_nat _let_1 (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat B3) C3))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C3 tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3))) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.aa_set_nat_set_nat _let_1 B3)) C3) (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat B3) C3))))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (P tptp.fun_Pr446604468264085555t_bool)) (= (forall ((X4 tptp.produc859450856879609959at_nat)) (=> (tptp.member8206827879206165904at_nat X4 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3) B3)) (tptp.pp (tptp.aa_Pro6098352494050694700t_bool P X4)))) (and (forall ((X4 tptp.produc859450856879609959at_nat)) (=> (tptp.member8206827879206165904at_nat X4 A3) (tptp.pp (tptp.aa_Pro6098352494050694700t_bool P X4)))) (forall ((X4 tptp.produc859450856879609959at_nat)) (=> (tptp.member8206827879206165904at_nat X4 B3) (tptp.pp (tptp.aa_Pro6098352494050694700t_bool P X4))))))) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (P tptp.fun_Pr3976602594631769267t_bool)) (= (forall ((X4 tptp.produc4166570645942440679at_nat)) (=> (tptp.member6689249552917799696at_nat X4 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3) B3)) (tptp.pp (tptp.aa_Pro5063669228512387756t_bool P X4)))) (and (forall ((X4 tptp.produc4166570645942440679at_nat)) (=> (tptp.member6689249552917799696at_nat X4 A3) (tptp.pp (tptp.aa_Pro5063669228512387756t_bool P X4)))) (forall ((X4 tptp.produc4166570645942440679at_nat)) (=> (tptp.member6689249552917799696at_nat X4 B3) (tptp.pp (tptp.aa_Pro5063669228512387756t_bool P X4))))))) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (P tptp.fun_Pr1607443439640623155t_bool)) (= (forall ((X4 tptp.produc3843707927480180839at_nat)) (=> (tptp.member8757157785044589968at_nat X4 (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3) B3)) (tptp.pp (tptp.aa_Pro1809015098595223084t_bool P X4)))) (and (forall ((X4 tptp.produc3843707927480180839at_nat)) (=> (tptp.member8757157785044589968at_nat X4 A3) (tptp.pp (tptp.aa_Pro1809015098595223084t_bool P X4)))) (forall ((X4 tptp.produc3843707927480180839at_nat)) (=> (tptp.member8757157785044589968at_nat X4 B3) (tptp.pp (tptp.aa_Pro1809015098595223084t_bool P X4))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (P tptp.fun_nat_bool)) (= (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3))) (tptp.pp (tptp.aa_nat_bool P X4)))) (and (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A3)) (tptp.pp (tptp.aa_nat_bool P X4)))) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) B3)) (tptp.pp (tptp.aa_nat_bool P X4))))))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (P tptp.fun_Pr446604468264085555t_bool)) (= (exists ((X4 tptp.produc859450856879609959at_nat)) (and (tptp.member8206827879206165904at_nat X4 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3) B3)) (tptp.pp (tptp.aa_Pro6098352494050694700t_bool P X4)))) (or (exists ((X4 tptp.produc859450856879609959at_nat)) (and (tptp.member8206827879206165904at_nat X4 A3) (tptp.pp (tptp.aa_Pro6098352494050694700t_bool P X4)))) (exists ((X4 tptp.produc859450856879609959at_nat)) (and (tptp.member8206827879206165904at_nat X4 B3) (tptp.pp (tptp.aa_Pro6098352494050694700t_bool P X4))))))) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (P tptp.fun_Pr3976602594631769267t_bool)) (= (exists ((X4 tptp.produc4166570645942440679at_nat)) (and (tptp.member6689249552917799696at_nat X4 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3) B3)) (tptp.pp (tptp.aa_Pro5063669228512387756t_bool P X4)))) (or (exists ((X4 tptp.produc4166570645942440679at_nat)) (and (tptp.member6689249552917799696at_nat X4 A3) (tptp.pp (tptp.aa_Pro5063669228512387756t_bool P X4)))) (exists ((X4 tptp.produc4166570645942440679at_nat)) (and (tptp.member6689249552917799696at_nat X4 B3) (tptp.pp (tptp.aa_Pro5063669228512387756t_bool P X4))))))) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (P tptp.fun_Pr1607443439640623155t_bool)) (= (exists ((X4 tptp.produc3843707927480180839at_nat)) (and (tptp.member8757157785044589968at_nat X4 (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3) B3)) (tptp.pp (tptp.aa_Pro1809015098595223084t_bool P X4)))) (or (exists ((X4 tptp.produc3843707927480180839at_nat)) (and (tptp.member8757157785044589968at_nat X4 A3) (tptp.pp (tptp.aa_Pro1809015098595223084t_bool P X4)))) (exists ((X4 tptp.produc3843707927480180839at_nat)) (and (tptp.member8757157785044589968at_nat X4 B3) (tptp.pp (tptp.aa_Pro1809015098595223084t_bool P X4))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (P tptp.fun_nat_bool)) (= (exists ((X4 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3))) (tptp.pp (tptp.aa_nat_bool P X4)))) (or (exists ((X4 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A3)) (tptp.pp (tptp.aa_nat_bool P X4)))) (exists ((X4 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) B3)) (tptp.pp (tptp.aa_nat_bool P X4))))))) (forall ((C tptp.product_prod_nat_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat C))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 B3)) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat A3) B3)))))) (forall ((C tptp.bool) (B3 tptp.set_bool) (A3 tptp.set_bool)) (=> (tptp.pp (tptp.member_bool C B3)) (tptp.pp (tptp.member_bool C (tptp.aa_set_bool_set_bool (tptp.aa_set4734229006438377534t_bool tptp.sup_sup_set_bool A3) B3))))) (forall ((C tptp.set_nat) (B3 tptp.set_set_nat) (A3 tptp.set_set_nat)) (let ((_let_1 (tptp.member_set_nat C))) (=> (tptp.pp (tptp.aa_set_set_nat_bool _let_1 B3)) (tptp.pp (tptp.aa_set_set_nat_bool _let_1 (tptp.sup_sup_set_set_nat A3 B3)))))) (forall ((C tptp.int) (B3 tptp.set_int) (A3 tptp.set_int)) (let ((_let_1 (tptp.member_int C))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 B3)) (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3)))))) (forall ((C tptp.produc859450856879609959at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (A3 tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.member8206827879206165904at_nat C B3) (tptp.member8206827879206165904at_nat C (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3) B3)))) (forall ((C tptp.produc4166570645942440679at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (A3 tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.member6689249552917799696at_nat C B3) (tptp.member6689249552917799696at_nat C (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3) B3)))) (forall ((C tptp.produc3843707927480180839at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (A3 tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.member8757157785044589968at_nat C B3) (tptp.member8757157785044589968at_nat C (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3) B3)))) (forall ((C tptp.nat) (B3 tptp.set_nat) (A3 tptp.set_nat)) (let ((_let_1 (tptp.member_nat C))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 B3)) (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)))))) (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat C))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 A3)) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat A3) B3)))))) (forall ((C tptp.bool) (A3 tptp.set_bool) (B3 tptp.set_bool)) (=> (tptp.pp (tptp.member_bool C A3)) (tptp.pp (tptp.member_bool C (tptp.aa_set_bool_set_bool (tptp.aa_set4734229006438377534t_bool tptp.sup_sup_set_bool A3) B3))))) (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (tptp.member_set_nat C))) (=> (tptp.pp (tptp.aa_set_set_nat_bool _let_1 A3)) (tptp.pp (tptp.aa_set_set_nat_bool _let_1 (tptp.sup_sup_set_set_nat A3 B3)))))) (forall ((C tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (tptp.member_int C))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 A3)) (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3)))))) (forall ((C tptp.produc859450856879609959at_nat) (A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.member8206827879206165904at_nat C A3) (tptp.member8206827879206165904at_nat C (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3) B3)))) (forall ((C tptp.produc4166570645942440679at_nat) (A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.member6689249552917799696at_nat C A3) (tptp.member6689249552917799696at_nat C (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3) B3)))) (forall ((C tptp.produc3843707927480180839at_nat) (A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.member8757157785044589968at_nat C A3) (tptp.member8757157785044589968at_nat C (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3) B3)))) (forall ((C tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.member_nat C))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A3)) (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)))))) (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat C))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat A3) B3))) (=> (not (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 A3))) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 B3)))))) (forall ((C tptp.bool) (A3 tptp.set_bool) (B3 tptp.set_bool)) (=> (tptp.pp (tptp.member_bool C (tptp.aa_set_bool_set_bool (tptp.aa_set4734229006438377534t_bool tptp.sup_sup_set_bool A3) B3))) (=> (not (tptp.pp (tptp.member_bool C A3))) (tptp.pp (tptp.member_bool C B3))))) (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (tptp.member_set_nat C))) (=> (tptp.pp (tptp.aa_set_set_nat_bool _let_1 (tptp.sup_sup_set_set_nat A3 B3))) (=> (not (tptp.pp (tptp.aa_set_set_nat_bool _let_1 A3))) (tptp.pp (tptp.aa_set_set_nat_bool _let_1 B3)))))) (forall ((C tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (tptp.member_int C))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3))) (=> (not (tptp.pp (tptp.aa_set_int_bool _let_1 A3))) (tptp.pp (tptp.aa_set_int_bool _let_1 B3)))))) (forall ((C tptp.produc859450856879609959at_nat) (A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.member8206827879206165904at_nat C (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3) B3)) (=> (not (tptp.member8206827879206165904at_nat C A3)) (tptp.member8206827879206165904at_nat C B3)))) (forall ((C tptp.produc4166570645942440679at_nat) (A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.member6689249552917799696at_nat C (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3) B3)) (=> (not (tptp.member6689249552917799696at_nat C A3)) (tptp.member6689249552917799696at_nat C B3)))) (forall ((C tptp.produc3843707927480180839at_nat) (A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.member8757157785044589968at_nat C (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3) B3)) (=> (not (tptp.member8757157785044589968at_nat C A3)) (tptp.member8757157785044589968at_nat C B3)))) (forall ((C tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.member_nat C))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3))) (=> (not (tptp.pp (tptp.aa_set_nat_bool _let_1 A3))) (tptp.pp (tptp.aa_set_nat_bool _let_1 B3)))))) (forall ((B tptp.set_nat) (C tptp.set_nat) (A tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B) C)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A) B)) C)))) (forall ((B tptp.assn) (C tptp.assn) (A tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn B) C)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A) B)) C)))) (forall ((B tptp.product_unit) (C tptp.product_unit) (A tptp.product_unit)) (=> (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit B) C)) (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit A) B)) C)))) (forall ((B tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat B) C)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A) B)) C)))) (forall ((B tptp.set_int) (C tptp.set_int) (A tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) C)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A) B)) C)))) (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat A) B)) C)))) (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat A) B)) C)))) (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int A) B)) C)))) (forall ((A tptp.set_nat) (C tptp.set_nat) (B tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A) C)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A) B)) C)))) (forall ((A tptp.assn) (C tptp.assn) (B tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn A) C)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A) B)) C)))) (forall ((A tptp.product_unit) (C tptp.product_unit) (B tptp.product_unit)) (=> (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit A) C)) (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit A) B)) C)))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A) C)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A) B)) C)))) (forall ((A tptp.set_int) (C tptp.set_int) (B tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) C)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A) B)) C)))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat A) B)) C)))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat A) B)) C)))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int A) B)) C)))) (forall ((B tptp.set_nat) (A tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B) A)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A) B) B))) (forall ((B tptp.assn) (A tptp.assn)) (= (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn B) A)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A) B) B))) (forall ((B tptp.product_unit) (A tptp.product_unit)) (= (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit B) A)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit A) B) B))) (forall ((B tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat B) A)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A) B) B))) (forall ((B tptp.set_int) (A tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) A)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A) B) B))) (forall ((B tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat A) B) B))) (forall ((B tptp.nat) (A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat A) B) B))) (forall ((B tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int A) B) B))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A) B)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A) B) A))) (forall ((A tptp.assn) (B tptp.assn)) (= (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn A) B)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A) B) A))) (forall ((A tptp.product_unit) (B tptp.product_unit)) (= (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit A) B)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit A) B) A))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A) B)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A) B) A))) (forall ((A tptp.set_int) (B tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) B)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A) B) A))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat A) B) A))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat A) B) A))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int A) B) A))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A) B)) B))) (forall ((A tptp.assn) (B tptp.assn)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A) B)) B))) (forall ((A tptp.product_unit) (B tptp.product_unit)) (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit A) B)) B))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A) B)) B))) (forall ((A tptp.set_int) (B tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A) B)) B))) (forall ((A tptp.rat) (B tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat A) B)) B))) (forall ((A tptp.nat) (B tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat A) B)) B))) (forall ((A tptp.int) (B tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int A) B)) B))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A) B)) A))) (forall ((A tptp.assn) (B tptp.assn)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A) B)) A))) (forall ((A tptp.product_unit) (B tptp.product_unit)) (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit A) B)) A))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A) B)) A))) (forall ((A tptp.set_int) (B tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A) B)) A))) (forall ((A tptp.rat) (B tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat A) B)) A))) (forall ((A tptp.nat) (B tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat A) B)) A))) (forall ((A tptp.int) (B tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int A) B)) A))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A) B)) (= A (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A) B)))) (forall ((A tptp.assn) (B tptp.assn)) (= (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn A) B)) (= A (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A) B)))) (forall ((A tptp.product_unit) (B tptp.product_unit)) (= (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit A) B)) (= A (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit A) B)))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A) B)) (= A (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A) B)))) (forall ((A tptp.set_int) (B tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) B)) (= A (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A) B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (= A (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat A) B)))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat A) B)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int A) B)))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat X))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 Z)) (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat Y) Z))))))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn X))) (=> (tptp.pp (tptp.aa_assn_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_assn_bool _let_1 Z)) (tptp.pp (tptp.aa_assn_bool _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn Y) Z))))))) (forall ((X tptp.product_unit) (Y tptp.product_unit) (Z tptp.product_unit)) (let ((_let_1 (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit X))) (=> (tptp.pp (tptp.aa_Product_unit_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_Product_unit_bool _let_1 Z)) (tptp.pp (tptp.aa_Product_unit_bool _let_1 (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit Y) Z))))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat X))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 Z)) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat Y) Z))))))) (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 Z)) (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int Y) Z))))))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Z)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat Y) Z))))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 Z)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat Y) Z))))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X))) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Z)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int Y) Z))))))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 B)) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 C)) (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat B) C))))))) (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn A))) (=> (tptp.pp (tptp.aa_assn_bool _let_1 B)) (=> (tptp.pp (tptp.aa_assn_bool _let_1 C)) (tptp.pp (tptp.aa_assn_bool _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn B) C))))))) (forall ((A tptp.product_unit) (B tptp.product_unit) (C tptp.product_unit)) (let ((_let_1 (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit A))) (=> (tptp.pp (tptp.aa_Product_unit_bool _let_1 B)) (=> (tptp.pp (tptp.aa_Product_unit_bool _let_1 C)) (tptp.pp (tptp.aa_Product_unit_bool _let_1 (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit B) C))))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 B)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 C)) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat B) C))))))) (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (let ((_let_1 (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 B)) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 C)) (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int B) C))))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 C)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat B) C))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 C)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat B) C))))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (=> (tptp.pp (tptp.aa_int_bool _let_1 C)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int B) C))))))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat B) C))) (not (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 B)) (not (tptp.pp (tptp.aa_set_nat_bool _let_1 C)))))))) (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn A))) (=> (tptp.pp (tptp.aa_assn_bool _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn B) C))) (not (=> (tptp.pp (tptp.aa_assn_bool _let_1 B)) (not (tptp.pp (tptp.aa_assn_bool _let_1 C)))))))) (forall ((A tptp.product_unit) (B tptp.product_unit) (C tptp.product_unit)) (let ((_let_1 (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit A))) (=> (tptp.pp (tptp.aa_Product_unit_bool _let_1 (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit B) C))) (not (=> (tptp.pp (tptp.aa_Product_unit_bool _let_1 B)) (not (tptp.pp (tptp.aa_Product_unit_bool _let_1 C)))))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat B) C))) (not (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 B)) (not (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 C)))))))) (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (let ((_let_1 (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int B) C))) (not (=> (tptp.pp (tptp.aa_set_int_bool _let_1 B)) (not (tptp.pp (tptp.aa_set_int_bool _let_1 C)))))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat B) C))) (not (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (not (tptp.pp (tptp.aa_rat_bool _let_1 C)))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat B) C))) (not (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (not (tptp.pp (tptp.aa_nat_bool _let_1 C)))))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int B) C))) (not (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (not (tptp.pp (tptp.aa_int_bool _let_1 C)))))))) (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat Y) X)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X) Y) Y))) (forall ((Y tptp.assn) (X tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn Y) X)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X) Y) Y))) (forall ((Y tptp.product_unit) (X tptp.product_unit)) (=> (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit Y) X)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X) Y) Y))) (forall ((Y tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat Y) X)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X) Y) Y))) (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int Y) X)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int X) Y) Y))) (forall ((Y tptp.rat) (X tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat X) Y) Y))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat X) Y) Y))) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int X) Y) Y))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat X) Y)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X) Y) X))) (forall ((X tptp.assn) (Y tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn X) Y)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X) Y) X))) (forall ((X tptp.product_unit) (Y tptp.product_unit)) (=> (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit X) Y)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X) Y) X))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat X) Y)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X) Y) X))) (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X) Y)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int X) Y) X))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat X) Y) X))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat X) Y) X))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int X) Y) X))) (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B) A)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A) B) B))) (forall ((B tptp.assn) (A tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn B) A)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A) B) B))) (forall ((B tptp.product_unit) (A tptp.product_unit)) (=> (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit B) A)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit A) B) B))) (forall ((B tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat B) A)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A) B) B))) (forall ((B tptp.set_int) (A tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) A)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A) B) B))) (forall ((B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat A) B) B))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat A) B) B))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int A) B) B))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A) B)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A) B) A))) (forall ((A tptp.assn) (B tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn A) B)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A) B) A))) (forall ((A tptp.product_unit) (B tptp.product_unit)) (=> (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit A) B)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit A) B) A))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A) B)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A) B) A))) (forall ((A tptp.set_int) (B tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) B)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A) B) A))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat A) B) A))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat A) B) A))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int A) B) A))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat X) Y)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X) Y) X))) (forall ((X tptp.assn) (Y tptp.assn)) (= (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn X) Y)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X) Y) X))) (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit X) Y)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X) Y) X))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat X) Y)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X) Y) X))) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X) Y)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int X) Y) X))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat X) Y) X))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat X) Y) X))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int X) Y) X))) (forall ((F tptp.fun_se1909708154429037836et_nat) (X tptp.set_nat) (Y tptp.set_nat)) (=> (forall ((X3 tptp.set_nat) (Y3 tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat F X3) Y3)) X3))) (=> (forall ((X3 tptp.set_nat) (Y3 tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat F X3) Y3)) Y3))) (=> (forall ((X3 tptp.set_nat) (Y3 tptp.set_nat) (Z2 tptp.set_nat)) (let ((_let_1 (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat X3))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 Y3)) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 Z2)) (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat F Y3) Z2))))))) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X) Y) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat F X) Y)))))) (forall ((F tptp.fun_as3983628580203722482n_assn) (X tptp.assn) (Y tptp.assn)) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn F X3) Y3)) X3))) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn F X3) Y3)) Y3))) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn) (Z2 tptp.assn)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn X3))) (=> (tptp.pp (tptp.aa_assn_bool _let_1 Y3)) (=> (tptp.pp (tptp.aa_assn_bool _let_1 Z2)) (tptp.pp (tptp.aa_assn_bool _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn F Y3) Z2))))))) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X) Y) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn F X) Y)))))) (forall ((F tptp.fun_Pr3553901264588531491t_unit) (X tptp.product_unit) (Y tptp.product_unit)) (=> (forall ((X3 tptp.product_unit) (Y3 tptp.product_unit)) (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit F X3) Y3)) X3))) (=> (forall ((X3 tptp.product_unit) (Y3 tptp.product_unit)) (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit F X3) Y3)) Y3))) (=> (forall ((X3 tptp.product_unit) (Y3 tptp.product_unit) (Z2 tptp.product_unit)) (let ((_let_1 (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit X3))) (=> (tptp.pp (tptp.aa_Product_unit_bool _let_1 Y3)) (=> (tptp.pp (tptp.aa_Product_unit_bool _let_1 Z2)) (tptp.pp (tptp.aa_Product_unit_bool _let_1 (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit F Y3) Z2))))))) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X) Y) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit F X) Y)))))) (forall ((F tptp.fun_se3560235952666129655at_nat) (X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat F X3) Y3)) X3))) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat F X3) Y3)) Y3))) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat) (Z2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat X3))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 Y3)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 Z2)) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat F Y3) Z2))))))) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X) Y) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat F X) Y)))))) (forall ((F tptp.fun_se6573205548028396576et_int) (X tptp.set_int) (Y tptp.set_int)) (=> (forall ((X3 tptp.set_int) (Y3 tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int F X3) Y3)) X3))) (=> (forall ((X3 tptp.set_int) (Y3 tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int F X3) Y3)) Y3))) (=> (forall ((X3 tptp.set_int) (Y3 tptp.set_int) (Z2 tptp.set_int)) (let ((_let_1 (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X3))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 Y3)) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 Z2)) (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int F Y3) Z2))))))) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int X) Y) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int F X) Y)))))) (forall ((F tptp.fun_rat_fun_rat_rat) (X tptp.rat) (Y tptp.rat)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat F X3) Y3)) X3))) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat F X3) Y3)) Y3))) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat) (Z2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y3)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Z2)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat F Y3) Z2))))))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat X) Y) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat F X) Y)))))) (forall ((F tptp.fun_nat_fun_nat_nat) (X tptp.nat) (Y tptp.nat)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat F X3) Y3)) X3))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat F X3) Y3)) Y3))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 Y3)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 Z2)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat F Y3) Z2))))))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat X) Y) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat F X) Y)))))) (forall ((F tptp.fun_int_fun_int_int) (X tptp.int) (Y tptp.int)) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int F X3) Y3)) X3))) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int F X3) Y3)) Y3))) (=> (forall ((X3 tptp.int) (Y3 tptp.int) (Z2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X3))) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y3)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Z2)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int F Y3) Z2))))))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int X) Y) (tptp.aa_int_int (tptp.aa_int_fun_int_int F X) Y)))))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (= A (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A) B)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A) B)))) (forall ((A tptp.assn) (B tptp.assn)) (=> (= A (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A) B)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn A) B)))) (forall ((A tptp.product_unit) (B tptp.product_unit)) (=> (= A (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit A) B)) (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit A) B)))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (= A (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A) B)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A) B)))) (forall ((A tptp.set_int) (B tptp.set_int)) (=> (= A (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A) B)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) B)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (= A (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat A) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)))) (forall ((A tptp.int) (B tptp.int)) (=> (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A) B)) (= A (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A) B)))) (forall ((A tptp.assn) (B tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn A) B)) (= A (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A) B)))) (forall ((A tptp.product_unit) (B tptp.product_unit)) (=> (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit A) B)) (= A (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit A) B)))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A) B)) (= A (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A) B)))) (forall ((A tptp.set_int) (B tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) B)) (= A (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A) B)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (= A (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat A) B)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat A) B)))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int A) B)))) (forall ((B tptp.set_nat) (X tptp.set_nat) (A tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B) X)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A) B)) X)))) (forall ((B tptp.assn) (X tptp.assn) (A tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn B) X)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A) B)) X)))) (forall ((B tptp.product_unit) (X tptp.product_unit) (A tptp.product_unit)) (=> (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit B) X)) (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit A) B)) X)))) (forall ((B tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat B) X)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A) B)) X)))) (forall ((B tptp.set_int) (X tptp.set_int) (A tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) X)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A) B)) X)))) (forall ((B tptp.rat) (X tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat A) B)) X)))) (forall ((B tptp.nat) (X tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) X)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat A) B)) X)))) (forall ((B tptp.int) (X tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) X)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int A) B)) X)))) (forall ((A tptp.set_nat) (X tptp.set_nat) (B tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A) X)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A) B)) X)))) (forall ((A tptp.assn) (X tptp.assn) (B tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn A) X)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A) B)) X)))) (forall ((A tptp.product_unit) (X tptp.product_unit) (B tptp.product_unit)) (=> (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit A) X)) (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit A) B)) X)))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A) X)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A) B)) X)))) (forall ((A tptp.set_int) (X tptp.set_int) (B tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) X)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A) B)) X)))) (forall ((A tptp.rat) (X tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat A) B)) X)))) (forall ((A tptp.nat) (X tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) X)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat A) B)) X)))) (forall ((A tptp.int) (X tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) X)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int A) B)) X)))) (forall ((A tptp.set_nat) (C tptp.set_nat) (B tptp.set_nat) (D2 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A) C)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B) D2)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A) B)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat C) D2)))))) (forall ((A tptp.assn) (C tptp.assn) (B tptp.assn) (D2 tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn A) C)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn B) D2)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A) B)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn C) D2)))))) (forall ((A tptp.product_unit) (C tptp.product_unit) (B tptp.product_unit) (D2 tptp.product_unit)) (=> (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit A) C)) (=> (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit B) D2)) (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit A) B)) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit C) D2)))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (D2 tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A) C)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat B) D2)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A) B)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat C) D2)))))) (forall ((A tptp.set_int) (C tptp.set_int) (B tptp.set_int) (D2 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) C)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) D2)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A) B)) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int C) D2)))))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) C)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) D2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat A) B)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat C) D2)))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) C)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) D2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat A) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat C) D2)))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) C)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) D2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int C) D2)))))) (forall ((X tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat X))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 B)) (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A) B))))))) (forall ((X tptp.assn) (A tptp.assn) (B tptp.assn)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn X))) (=> (tptp.pp (tptp.aa_assn_bool _let_1 A)) (=> (tptp.pp (tptp.aa_assn_bool _let_1 B)) (tptp.pp (tptp.aa_assn_bool _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A) B))))))) (forall ((X tptp.product_unit) (A tptp.product_unit) (B tptp.product_unit)) (let ((_let_1 (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit X))) (=> (tptp.pp (tptp.aa_Product_unit_bool _let_1 A)) (=> (tptp.pp (tptp.aa_Product_unit_bool _let_1 B)) (tptp.pp (tptp.aa_Product_unit_bool _let_1 (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit A) B))))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat X))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 A)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 B)) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A) B))))))) (forall ((X tptp.set_int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 B)) (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A) B))))))) (forall ((X tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat A) B))))))) (forall ((X tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat A) B))))))) (forall ((X tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int A) B))))))) (forall ((X tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat X))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A) B))) (not (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A)) (not (tptp.pp (tptp.aa_set_nat_bool _let_1 B)))))))) (forall ((X tptp.assn) (A tptp.assn) (B tptp.assn)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn X))) (=> (tptp.pp (tptp.aa_assn_bool _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A) B))) (not (=> (tptp.pp (tptp.aa_assn_bool _let_1 A)) (not (tptp.pp (tptp.aa_assn_bool _let_1 B)))))))) (forall ((X tptp.product_unit) (A tptp.product_unit) (B tptp.product_unit)) (let ((_let_1 (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit X))) (=> (tptp.pp (tptp.aa_Product_unit_bool _let_1 (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit A) B))) (not (=> (tptp.pp (tptp.aa_Product_unit_bool _let_1 A)) (not (tptp.pp (tptp.aa_Product_unit_bool _let_1 B)))))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat X))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A) B))) (not (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 A)) (not (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 B)))))))) (forall ((X tptp.set_int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A) B))) (not (=> (tptp.pp (tptp.aa_set_int_bool _let_1 A)) (not (tptp.pp (tptp.aa_set_int_bool _let_1 B)))))))) (forall ((X tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat A) B))) (not (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (not (tptp.pp (tptp.aa_rat_bool _let_1 B)))))))) (forall ((X tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat A) B))) (not (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (not (tptp.pp (tptp.aa_nat_bool _let_1 B)))))))) (forall ((X tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X))) (=> (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int A) B))) (not (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (not (tptp.pp (tptp.aa_int_bool _let_1 B)))))))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X) Y)) Y))) (forall ((X tptp.assn) (Y tptp.assn)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X) Y)) Y))) (forall ((X tptp.product_unit) (Y tptp.product_unit)) (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X) Y)) Y))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X) Y)) Y))) (forall ((X tptp.set_int) (Y tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int X) Y)) Y))) (forall ((X tptp.rat) (Y tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat X) Y)) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat X) Y)) Y))) (forall ((X tptp.int) (Y tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int X) Y)) Y))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X) Y)) X))) (forall ((X tptp.assn) (Y tptp.assn)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X) Y)) X))) (forall ((X tptp.product_unit) (Y tptp.product_unit)) (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X) Y)) X))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X) Y)) X))) (forall ((X tptp.set_int) (Y tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int X) Y)) X))) (forall ((X tptp.rat) (Y tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat X) Y)) X))) (forall ((X tptp.nat) (Y tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat X) Y)) X))) (forall ((X tptp.int) (Y tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int X) Y)) X))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X) Y)) X))) (forall ((X tptp.assn) (Y tptp.assn)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X) Y)) X))) (forall ((X tptp.product_unit) (Y tptp.product_unit)) (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X) Y)) X))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X) Y)) X))) (forall ((X tptp.set_int) (Y tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int X) Y)) X))) (forall ((X tptp.rat) (Y tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat X) Y)) X))) (forall ((X tptp.nat) (Y tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat X) Y)) X))) (forall ((X tptp.int) (Y tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int X) Y)) X))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X) Y)) Y))) (forall ((X tptp.assn) (Y tptp.assn)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X) Y)) Y))) (forall ((X tptp.product_unit) (Y tptp.product_unit)) (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X) Y)) Y))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X) Y)) Y))) (forall ((X tptp.set_int) (Y tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int X) Y)) Y))) (forall ((X tptp.rat) (Y tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat X) Y)) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat X) Y)) Y))) (forall ((X tptp.int) (Y tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int X) Y)) Y))) (forall ((C tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.ord_le3000389064537975527at_nat C B) (tptp.ord_le3000389064537975527at_nat C (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A) B)))) (forall ((C tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.ord_le8081472938463900775at_nat C B) (tptp.ord_le8081472938463900775at_nat C (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A) B)))) (forall ((C tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.ord_le1268244103169919719at_nat C B) (tptp.ord_le1268244103169919719at_nat C (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A) B)))) (forall ((C tptp.set_nat) (B tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat C))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 B)) (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A) B)))))) (forall ((C tptp.set_int) (B tptp.set_int) (A tptp.set_int)) (let ((_let_1 (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int C))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 B)) (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A) B)))))) (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat A) B)))))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat A) B)))))) (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int A) B)))))) (forall ((C tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.ord_le3000389064537975527at_nat C A) (tptp.ord_le3000389064537975527at_nat C (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A) B)))) (forall ((C tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.ord_le8081472938463900775at_nat C A) (tptp.ord_le8081472938463900775at_nat C (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A) B)))) (forall ((C tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.ord_le1268244103169919719at_nat C A) (tptp.ord_le1268244103169919719at_nat C (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A) B)))) (forall ((C tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat C))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A)) (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A) B)))))) (forall ((C tptp.set_int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int C))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 A)) (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A) B)))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat A) B)))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat A) B)))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int A) B)))))) (forall ((A tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat)) (= (tptp.ord_le3000389064537975527at_nat A B) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A) B) B))) (forall ((A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (= (tptp.ord_le8081472938463900775at_nat A B) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A) B) B))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (= (tptp.ord_le1268244103169919719at_nat A B) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A) B) B))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A) B)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A) B) B))) (forall ((A tptp.set_int) (B tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) B)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A) B) B))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat A) B) B))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat A) B) B))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int A) B) B))) (forall ((B tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat)) (= (tptp.ord_le3000389064537975527at_nat B A) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A) B) A))) (forall ((B tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat)) (= (tptp.ord_le8081472938463900775at_nat B A) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A) B) A))) (forall ((B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (= (tptp.ord_le1268244103169919719at_nat B A) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A) B) A))) (forall ((B tptp.set_nat) (A tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B) A)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A) B) A))) (forall ((B tptp.set_int) (A tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) A)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A) B) A))) (forall ((B tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat A) B) A))) (forall ((B tptp.nat) (A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat A) B) A))) (forall ((B tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int A) B) A))) (forall ((B tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat)) (tptp.ord_le3000389064537975527at_nat B (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A) B))) (forall ((B tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat)) (tptp.ord_le8081472938463900775at_nat B (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A) B))) (forall ((B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (tptp.ord_le1268244103169919719at_nat B (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A) B))) (forall ((B tptp.set_nat) (A tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A) B)))) (forall ((B tptp.set_int) (A tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A) B)))) (forall ((B tptp.rat) (A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat A) B)))) (forall ((B tptp.nat) (A tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat A) B)))) (forall ((B tptp.int) (A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int A) B)))) (forall ((A tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat)) (tptp.ord_le3000389064537975527at_nat A (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A) B))) (forall ((A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (tptp.ord_le8081472938463900775at_nat A (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A) B))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (tptp.ord_le1268244103169919719at_nat A (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A) B))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A) B)))) (forall ((A tptp.set_int) (B tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A) B)))) (forall ((A tptp.rat) (B tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat A) B)))) (forall ((A tptp.nat) (B tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat A) B)))) (forall ((A tptp.int) (B tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int A) B)))) (forall ((B tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat)) (= (tptp.ord_le3000389064537975527at_nat B A) (= A (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A) B)))) (forall ((B tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat)) (= (tptp.ord_le8081472938463900775at_nat B A) (= A (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A) B)))) (forall ((B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (= (tptp.ord_le1268244103169919719at_nat B A) (= A (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A) B)))) (forall ((B tptp.set_nat) (A tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B) A)) (= A (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A) B)))) (forall ((B tptp.set_int) (A tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) A)) (= A (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A) B)))) (forall ((B tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (= A (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat A) B)))) (forall ((B tptp.nat) (A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat A) B)))) (forall ((B tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int A) B)))) (forall ((B tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat) (C tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.ord_le3000389064537975527at_nat B A) (=> (tptp.ord_le3000389064537975527at_nat C A) (tptp.ord_le3000389064537975527at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat B) C) A)))) (forall ((B tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat) (C tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.ord_le8081472938463900775at_nat B A) (=> (tptp.ord_le8081472938463900775at_nat C A) (tptp.ord_le8081472938463900775at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat B) C) A)))) (forall ((B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.ord_le1268244103169919719at_nat B A) (=> (tptp.ord_le1268244103169919719at_nat C A) (tptp.ord_le1268244103169919719at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat B) C) A)))) (forall ((B tptp.set_nat) (A tptp.set_nat) (C tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B) A)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat C) A)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat B) C)) A))))) (forall ((B tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) A)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int C) A)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int B) C)) A))))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat B) C)) A))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat B) C)) A))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int B) C)) A))))) (forall ((B tptp.set_Pr8693737435421807431at_nat) (C tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.ord_le3000389064537975527at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat B) C) A) (not (=> (tptp.ord_le3000389064537975527at_nat B A) (not (tptp.ord_le3000389064537975527at_nat C A)))))) (forall ((B tptp.set_Pr8551490117392284871at_nat) (C tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.ord_le8081472938463900775at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat B) C) A) (not (=> (tptp.ord_le8081472938463900775at_nat B A) (not (tptp.ord_le8081472938463900775at_nat C A)))))) (forall ((B tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.ord_le1268244103169919719at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat B) C) A) (not (=> (tptp.ord_le1268244103169919719at_nat B A) (not (tptp.ord_le1268244103169919719at_nat C A)))))) (forall ((B tptp.set_nat) (C tptp.set_nat) (A tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat B) C)) A)) (not (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B) A)) (not (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat C) A))))))) (forall ((B tptp.set_int) (C tptp.set_int) (A tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int B) C)) A)) (not (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) A)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int C) A))))))) (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat B) C)) A)) (not (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) A))))))) (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat B) C)) A)) (not (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) A))))))) (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int B) C)) A)) (not (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) A))))))) (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.ord_le3000389064537975527at_nat X Y) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat X) Y) Y))) (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.ord_le8081472938463900775at_nat X Y) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat X) Y) Y))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.ord_le1268244103169919719at_nat X Y) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat X) Y) Y))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat X) Y)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat X) Y) Y))) (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X) Y)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int X) Y) Y))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat X) Y) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat X) Y) Y))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int X) Y) Y))) (forall ((Y tptp.set_Pr8693737435421807431at_nat) (X tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.ord_le3000389064537975527at_nat Y X) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat X) Y) X))) (forall ((Y tptp.set_Pr8551490117392284871at_nat) (X tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.ord_le8081472938463900775at_nat Y X) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat X) Y) X))) (forall ((Y tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.ord_le1268244103169919719at_nat Y X) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat X) Y) X))) (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat Y) X)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat X) Y) X))) (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int Y) X)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int X) Y) X))) (forall ((Y tptp.rat) (X tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat X) Y) X))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat X) Y) X))) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int X) Y) X))) (forall ((A tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.ord_le3000389064537975527at_nat A B) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A) B) B))) (forall ((A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.ord_le8081472938463900775at_nat A B) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A) B) B))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.ord_le1268244103169919719at_nat A B) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A) B) B))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A) B)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A) B) B))) (forall ((A tptp.set_int) (B tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) B)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A) B) B))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat A) B) B))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat A) B) B))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int A) B) B))) (forall ((B tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.ord_le3000389064537975527at_nat B A) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A) B) A))) (forall ((B tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.ord_le8081472938463900775at_nat B A) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A) B) A))) (forall ((B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.ord_le1268244103169919719at_nat B A) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A) B) A))) (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B) A)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A) B) A))) (forall ((B tptp.set_int) (A tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) A)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A) B) A))) (forall ((B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat A) B) A))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat A) B) A))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int A) B) A))) (forall ((F tptp.fun_se8464659365716347869at_nat) (X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat)) (=> (forall ((X3 tptp.set_Pr8693737435421807431at_nat) (Y3 tptp.set_Pr8693737435421807431at_nat)) (tptp.ord_le3000389064537975527at_nat X3 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat F X3) Y3))) (=> (forall ((X3 tptp.set_Pr8693737435421807431at_nat) (Y3 tptp.set_Pr8693737435421807431at_nat)) (tptp.ord_le3000389064537975527at_nat Y3 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat F X3) Y3))) (=> (forall ((X3 tptp.set_Pr8693737435421807431at_nat) (Y3 tptp.set_Pr8693737435421807431at_nat) (Z2 tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.ord_le3000389064537975527at_nat Y3 X3) (=> (tptp.ord_le3000389064537975527at_nat Z2 X3) (tptp.ord_le3000389064537975527at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat F Y3) Z2) X3)))) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat X) Y) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat F X) Y)))))) (forall ((F tptp.fun_se6682931024248017501at_nat) (X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat)) (=> (forall ((X3 tptp.set_Pr8551490117392284871at_nat) (Y3 tptp.set_Pr8551490117392284871at_nat)) (tptp.ord_le8081472938463900775at_nat X3 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat F X3) Y3))) (=> (forall ((X3 tptp.set_Pr8551490117392284871at_nat) (Y3 tptp.set_Pr8551490117392284871at_nat)) (tptp.ord_le8081472938463900775at_nat Y3 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat F X3) Y3))) (=> (forall ((X3 tptp.set_Pr8551490117392284871at_nat) (Y3 tptp.set_Pr8551490117392284871at_nat) (Z2 tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.ord_le8081472938463900775at_nat Y3 X3) (=> (tptp.ord_le8081472938463900775at_nat Z2 X3) (tptp.ord_le8081472938463900775at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat F Y3) Z2) X3)))) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat X) Y) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat F X) Y)))))) (forall ((F tptp.fun_se177437144654672861at_nat) (X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (=> (forall ((X3 tptp.set_Pr4329608150637261639at_nat) (Y3 tptp.set_Pr4329608150637261639at_nat)) (tptp.ord_le1268244103169919719at_nat X3 (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat F X3) Y3))) (=> (forall ((X3 tptp.set_Pr4329608150637261639at_nat) (Y3 tptp.set_Pr4329608150637261639at_nat)) (tptp.ord_le1268244103169919719at_nat Y3 (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat F X3) Y3))) (=> (forall ((X3 tptp.set_Pr4329608150637261639at_nat) (Y3 tptp.set_Pr4329608150637261639at_nat) (Z2 tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.ord_le1268244103169919719at_nat Y3 X3) (=> (tptp.ord_le1268244103169919719at_nat Z2 X3) (tptp.ord_le1268244103169919719at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat F Y3) Z2) X3)))) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat X) Y) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat F X) Y)))))) (forall ((F tptp.fun_se1909708154429037836et_nat) (X tptp.set_nat) (Y tptp.set_nat)) (=> (forall ((X3 tptp.set_nat) (Y3 tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat X3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat F X3) Y3)))) (=> (forall ((X3 tptp.set_nat) (Y3 tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat Y3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat F X3) Y3)))) (=> (forall ((X3 tptp.set_nat) (Y3 tptp.set_nat) (Z2 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat Y3) X3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat Z2) X3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat F Y3) Z2)) X3))))) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat X) Y) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat F X) Y)))))) (forall ((F tptp.fun_se6573205548028396576et_int) (X tptp.set_int) (Y tptp.set_int)) (=> (forall ((X3 tptp.set_int) (Y3 tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int F X3) Y3)))) (=> (forall ((X3 tptp.set_int) (Y3 tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int Y3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int F X3) Y3)))) (=> (forall ((X3 tptp.set_int) (Y3 tptp.set_int) (Z2 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int Y3) X3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int Z2) X3)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int F Y3) Z2)) X3))))) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int X) Y) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int F X) Y)))))) (forall ((F tptp.fun_rat_fun_rat_rat) (X tptp.rat) (Y tptp.rat)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat F X3) Y3)))) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat F X3) Y3)))) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat) (Z2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y3) X3)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Z2) X3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat F Y3) Z2)) X3))))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat X) Y) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat F X) Y)))))) (forall ((F tptp.fun_nat_fun_nat_nat) (X tptp.nat) (Y tptp.nat)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat F X3) Y3)))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat F X3) Y3)))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y3) X3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Z2) X3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat F Y3) Z2)) X3))))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat X) Y) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat F X) Y)))))) (forall ((F tptp.fun_int_fun_int_int) (X tptp.int) (Y tptp.int)) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X3) (tptp.aa_int_int (tptp.aa_int_fun_int_int F X3) Y3)))) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y3) (tptp.aa_int_int (tptp.aa_int_fun_int_int F X3) Y3)))) (=> (forall ((X3 tptp.int) (Y3 tptp.int) (Z2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y3) X3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z2) X3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int F Y3) Z2)) X3))))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int X) Y) (tptp.aa_int_int (tptp.aa_int_fun_int_int F X) Y)))))) (forall ((A tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat)) (=> (= A (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A) B)) (tptp.ord_le3000389064537975527at_nat B A))) (forall ((A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (=> (= A (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A) B)) (tptp.ord_le8081472938463900775at_nat B A))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (=> (= A (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A) B)) (tptp.ord_le1268244103169919719at_nat B A))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (= A (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A) B)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B) A)))) (forall ((A tptp.set_int) (B tptp.set_int)) (=> (= A (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A) B)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) A)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (= A (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat A) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)))) (forall ((A tptp.int) (B tptp.int)) (=> (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)))) (forall ((B tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.ord_le3000389064537975527at_nat B A) (= A (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A) B)))) (forall ((B tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.ord_le8081472938463900775at_nat B A) (= A (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A) B)))) (forall ((B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.ord_le1268244103169919719at_nat B A) (= A (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A) B)))) (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B) A)) (= A (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A) B)))) (forall ((B tptp.set_int) (A tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) A)) (= A (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A) B)))) (forall ((B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (= A (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat A) B)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat A) B)))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int A) B)))) (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat)) (= (tptp.ord_le3000389064537975527at_nat X Y) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat X) Y) Y))) (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat)) (= (tptp.ord_le8081472938463900775at_nat X Y) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat X) Y) Y))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (= (tptp.ord_le1268244103169919719at_nat X Y) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat X) Y) Y))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat X) Y)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat X) Y) Y))) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X) Y)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int X) Y) Y))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat X) Y) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat X) Y) Y))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int X) Y) Y))) (forall ((Y tptp.set_Pr8693737435421807431at_nat) (X tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.ord_le3000389064537975527at_nat Y X) (=> (tptp.ord_le3000389064537975527at_nat Z X) (tptp.ord_le3000389064537975527at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat Y) Z) X)))) (forall ((Y tptp.set_Pr8551490117392284871at_nat) (X tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.ord_le8081472938463900775at_nat Y X) (=> (tptp.ord_le8081472938463900775at_nat Z X) (tptp.ord_le8081472938463900775at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat Y) Z) X)))) (forall ((Y tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.ord_le1268244103169919719at_nat Y X) (=> (tptp.ord_le1268244103169919719at_nat Z X) (tptp.ord_le1268244103169919719at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat Y) Z) X)))) (forall ((Y tptp.set_nat) (X tptp.set_nat) (Z tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat Y) X)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat Z) X)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat Y) Z)) X))))) (forall ((Y tptp.set_int) (X tptp.set_int) (Z tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int Y) X)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int Z) X)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int Y) Z)) X))))) (forall ((Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Z) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat Y) Z)) X))))) (forall ((Y tptp.nat) (X tptp.nat) (Z tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Z) X)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat Y) Z)) X))))) (forall ((Y tptp.int) (X tptp.int) (Z tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z) X)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int Y) Z)) X))))) (forall ((A tptp.set_Pr8693737435421807431at_nat) (C tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat) (D2 tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.ord_le3000389064537975527at_nat A C) (=> (tptp.ord_le3000389064537975527at_nat B D2) (tptp.ord_le3000389064537975527at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A) B) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat C) D2))))) (forall ((A tptp.set_Pr8551490117392284871at_nat) (C tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat) (D2 tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.ord_le8081472938463900775at_nat A C) (=> (tptp.ord_le8081472938463900775at_nat B D2) (tptp.ord_le8081472938463900775at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A) B) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat C) D2))))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (D2 tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.ord_le1268244103169919719at_nat A C) (=> (tptp.ord_le1268244103169919719at_nat B D2) (tptp.ord_le1268244103169919719at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A) B) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat C) D2))))) (forall ((A tptp.set_nat) (C tptp.set_nat) (B tptp.set_nat) (D2 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A) C)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B) D2)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A) B)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat C) D2)))))) (forall ((A tptp.set_int) (C tptp.set_int) (B tptp.set_int) (D2 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) C)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) D2)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A) B)) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int C) D2)))))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) C)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) D2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat A) B)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat C) D2)))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) C)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) D2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat A) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat C) D2)))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) C)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) D2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int C) D2)))))) (forall ((C tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat) (D2 tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.ord_le3000389064537975527at_nat C A) (=> (tptp.ord_le3000389064537975527at_nat D2 B) (tptp.ord_le3000389064537975527at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat C) D2) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A) B))))) (forall ((C tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat) (D2 tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.ord_le8081472938463900775at_nat C A) (=> (tptp.ord_le8081472938463900775at_nat D2 B) (tptp.ord_le8081472938463900775at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat C) D2) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A) B))))) (forall ((C tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat) (D2 tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.ord_le1268244103169919719at_nat C A) (=> (tptp.ord_le1268244103169919719at_nat D2 B) (tptp.ord_le1268244103169919719at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat C) D2) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A) B))))) (forall ((C tptp.set_nat) (A tptp.set_nat) (D2 tptp.set_nat) (B tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat C) A)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat D2) B)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat C) D2)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A) B)))))) (forall ((C tptp.set_int) (A tptp.set_int) (D2 tptp.set_int) (B tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int C) A)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int D2) B)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int C) D2)) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A) B)))))) (forall ((C tptp.rat) (A tptp.rat) (D2 tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat D2) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat C) D2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat A) B)))))) (forall ((C tptp.nat) (A tptp.nat) (D2 tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat D2) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat C) D2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat A) B)))))) (forall ((C tptp.int) (A tptp.int) (D2 tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int D2) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int C) D2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int A) B)))))) (forall ((X tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.ord_le3000389064537975527at_nat X B) (tptp.ord_le3000389064537975527at_nat X (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A) B)))) (forall ((X tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.ord_le8081472938463900775at_nat X B) (tptp.ord_le8081472938463900775at_nat X (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A) B)))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.ord_le1268244103169919719at_nat X B) (tptp.ord_le1268244103169919719at_nat X (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A) B)))) (forall ((X tptp.set_nat) (B tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat X))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 B)) (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A) B)))))) (forall ((X tptp.set_int) (B tptp.set_int) (A tptp.set_int)) (let ((_let_1 (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 B)) (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A) B)))))) (forall ((X tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat A) B)))))) (forall ((X tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat A) B)))))) (forall ((X tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int A) B)))))) (forall ((X tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.ord_le3000389064537975527at_nat X A) (tptp.ord_le3000389064537975527at_nat X (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A) B)))) (forall ((X tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.ord_le8081472938463900775at_nat X A) (tptp.ord_le8081472938463900775at_nat X (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A) B)))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.ord_le1268244103169919719at_nat X A) (tptp.ord_le1268244103169919719at_nat X (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A) B)))) (forall ((X tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat X))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A)) (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A) B)))))) (forall ((X tptp.set_int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 A)) (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A) B)))))) (forall ((X tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat A) B)))))) (forall ((X tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat A) B)))))) (forall ((X tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int A) B)))))) (forall ((Y tptp.set_Pr8693737435421807431at_nat) (X tptp.set_Pr8693737435421807431at_nat)) (tptp.ord_le3000389064537975527at_nat Y (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat X) Y))) (forall ((Y tptp.set_Pr8551490117392284871at_nat) (X tptp.set_Pr8551490117392284871at_nat)) (tptp.ord_le8081472938463900775at_nat Y (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat X) Y))) (forall ((Y tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat)) (tptp.ord_le1268244103169919719at_nat Y (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat X) Y))) (forall ((Y tptp.set_nat) (X tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat Y) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat X) Y)))) (forall ((Y tptp.set_int) (X tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int Y) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int X) Y)))) (forall ((Y tptp.rat) (X tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat X) Y)))) (forall ((Y tptp.nat) (X tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat X) Y)))) (forall ((Y tptp.int) (X tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int X) Y)))) (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat)) (tptp.ord_le3000389064537975527at_nat X (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat X) Y))) (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat)) (tptp.ord_le8081472938463900775at_nat X (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat X) Y))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (tptp.ord_le1268244103169919719at_nat X (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat X) Y))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat X) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat X) Y)))) (forall ((X tptp.set_int) (Y tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat X) Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat X) Y)))) (forall ((X tptp.int) (Y tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int X) Y)))) (forall ((A tptp.set_Pr8693737435421807431at_nat) (X tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.ord_le3000389064537975527at_nat A X) (=> (tptp.ord_le3000389064537975527at_nat B X) (tptp.ord_le3000389064537975527at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A) B) X)))) (forall ((A tptp.set_Pr8551490117392284871at_nat) (X tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.ord_le8081472938463900775at_nat A X) (=> (tptp.ord_le8081472938463900775at_nat B X) (tptp.ord_le8081472938463900775at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A) B) X)))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.ord_le1268244103169919719at_nat A X) (=> (tptp.ord_le1268244103169919719at_nat B X) (tptp.ord_le1268244103169919719at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A) B) X)))) (forall ((A tptp.set_nat) (X tptp.set_nat) (B tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A) X)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B) X)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A) B)) X))))) (forall ((A tptp.set_int) (X tptp.set_int) (B tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) X)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) X)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A) B)) X))))) (forall ((A tptp.rat) (X tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) X)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat A) B)) X))))) (forall ((A tptp.nat) (X tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) X)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) X)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat A) B)) X))))) (forall ((A tptp.int) (X tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) X)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) X)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int A) B)) X))))) (forall ((A tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat) (X tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.ord_le3000389064537975527at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A) B) X) (not (=> (tptp.ord_le3000389064537975527at_nat A X) (not (tptp.ord_le3000389064537975527at_nat B X)))))) (forall ((A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat) (X tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.ord_le8081472938463900775at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A) B) X) (not (=> (tptp.ord_le8081472938463900775at_nat A X) (not (tptp.ord_le8081472938463900775at_nat B X)))))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.ord_le1268244103169919719at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A) B) X) (not (=> (tptp.ord_le1268244103169919719at_nat A X) (not (tptp.ord_le1268244103169919719at_nat B X)))))) (forall ((A tptp.set_nat) (B tptp.set_nat) (X tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A) B)) X)) (not (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A) X)) (not (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B) X))))))) (forall ((A tptp.set_int) (B tptp.set_int) (X tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A) B)) X)) (not (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) X)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) X))))))) (forall ((A tptp.rat) (B tptp.rat) (X tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat A) B)) X)) (not (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) X)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) X))))))) (forall ((A tptp.nat) (B tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat A) B)) X)) (not (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) X)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) X))))))) (forall ((A tptp.int) (B tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int A) B)) X)) (not (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) X)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) X))))))) (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat)) (tptp.ord_le3000389064537975527at_nat X (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat X) Y))) (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat)) (tptp.ord_le8081472938463900775at_nat X (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat X) Y))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (tptp.ord_le1268244103169919719at_nat X (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat X) Y))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat X) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat X) Y)))) (forall ((X tptp.set_int) (Y tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat X) Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat X) Y)))) (forall ((X tptp.int) (Y tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int X) Y)))) (forall ((Y tptp.set_Pr8693737435421807431at_nat) (X tptp.set_Pr8693737435421807431at_nat)) (tptp.ord_le3000389064537975527at_nat Y (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat X) Y))) (forall ((Y tptp.set_Pr8551490117392284871at_nat) (X tptp.set_Pr8551490117392284871at_nat)) (tptp.ord_le8081472938463900775at_nat Y (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat X) Y))) (forall ((Y tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat)) (tptp.ord_le1268244103169919719at_nat Y (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat X) Y))) (forall ((Y tptp.set_nat) (X tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat Y) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat X) Y)))) (forall ((Y tptp.set_int) (X tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int Y) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int X) Y)))) (forall ((Y tptp.rat) (X tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat X) Y)))) (forall ((Y tptp.nat) (X tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat X) Y)))) (forall ((Y tptp.int) (X tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int X) Y)))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3) tptp.bot_bo2099793752762293965at_nat) (forall ((X4 tptp.product_prod_nat_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat X4) A3)) (forall ((Xa tptp.product_prod_nat_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat Xa) B3)) (not (= X4 Xa)))))))) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool)) (= (= (tptp.inf_inf_set_bool A3 B3) tptp.bot_bot_set_bool) (forall ((X4 tptp.bool)) (=> (tptp.pp (tptp.member_bool X4 A3)) (forall ((Xa tptp.bool)) (=> (tptp.pp (tptp.member_bool Xa B3)) (= (tptp.pp X4) (not (tptp.pp Xa))))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3) tptp.bot_bot_set_nat) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A3)) (forall ((Xa tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa) B3)) (not (= X4 Xa)))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3) tptp.bot_bot_set_int) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A3)) (forall ((Xa tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa) B3)) (not (= X4 Xa)))))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) tptp.bot_bo2099793752762293965at_nat) tptp.bot_bo2099793752762293965at_nat)) (forall ((A3 tptp.set_bool)) (= (tptp.inf_inf_set_bool A3 tptp.bot_bot_set_bool) tptp.bot_bot_set_bool)) (forall ((A3 tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) tptp.bot_bot_set_nat) tptp.bot_bot_set_nat)) (forall ((A3 tptp.set_int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) tptp.bot_bot_set_int) tptp.bot_bot_set_int)) (forall ((B3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat tptp.bot_bo2099793752762293965at_nat) B3) tptp.bot_bo2099793752762293965at_nat)) (forall ((B3 tptp.set_bool)) (= (tptp.inf_inf_set_bool tptp.bot_bot_set_bool B3) tptp.bot_bot_set_bool)) (forall ((B3 tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat tptp.bot_bot_set_nat) B3) tptp.bot_bot_set_nat)) (forall ((B3 tptp.set_int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int tptp.bot_bot_set_int) B3) tptp.bot_bot_set_int)) (forall ((A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (= (= (tptp.inf_inf_set_set_nat A3 B3) tptp.bot_bot_set_set_nat) (forall ((X4 tptp.set_nat)) (let ((_let_1 (tptp.member_set_nat X4))) (=> (tptp.pp (tptp.aa_set_set_nat_bool _let_1 A3)) (not (tptp.pp (tptp.aa_set_set_nat_bool _let_1 B3)))))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3) tptp.bot_bo2099793752762293965at_nat) (forall ((X4 tptp.product_prod_nat_nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat X4))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 A3)) (not (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 B3)))))))) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool)) (= (= (tptp.inf_inf_set_bool A3 B3) tptp.bot_bot_set_bool) (forall ((X4 tptp.bool)) (=> (tptp.pp (tptp.member_bool X4 A3)) (not (tptp.pp (tptp.member_bool X4 B3))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3) tptp.bot_bot_set_nat) (forall ((X4 tptp.nat)) (let ((_let_1 (tptp.member_nat X4))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A3)) (not (tptp.pp (tptp.aa_set_nat_bool _let_1 B3)))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3) tptp.bot_bot_set_int) (forall ((X4 tptp.int)) (let ((_let_1 (tptp.member_int X4))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 A3)) (not (tptp.pp (tptp.aa_set_int_bool _let_1 B3)))))))) (forall ((A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (=> (forall ((X3 tptp.set_nat)) (let ((_let_1 (tptp.member_set_nat X3))) (=> (tptp.pp (tptp.aa_set_set_nat_bool _let_1 A3)) (not (tptp.pp (tptp.aa_set_set_nat_bool _let_1 B3)))))) (= (tptp.inf_inf_set_set_nat A3 B3) tptp.bot_bot_set_set_nat))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.product_prod_nat_nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat X3))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 A3)) (not (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 B3)))))) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3) tptp.bot_bo2099793752762293965at_nat))) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool)) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 A3)) (not (tptp.pp (tptp.member_bool X3 B3))))) (= (tptp.inf_inf_set_bool A3 B3) tptp.bot_bot_set_bool))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (tptp.member_nat X3))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A3)) (not (tptp.pp (tptp.aa_set_nat_bool _let_1 B3)))))) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3) tptp.bot_bot_set_nat))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (forall ((X3 tptp.int)) (let ((_let_1 (tptp.member_int X3))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 A3)) (not (tptp.pp (tptp.aa_set_int_bool _let_1 B3)))))) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3) tptp.bot_bot_set_int))) (forall ((Y tptp.assn) (Z tptp.assn) (X tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn Y) Z)) X) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn Y) X)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn Z) X)))) (forall ((Y tptp.product_unit) (Z tptp.product_unit) (X tptp.product_unit)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.sup_sup_Product_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit Y) Z)) X) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.sup_sup_Product_unit Y) X)) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.sup_sup_Product_unit Z) X)))) (forall ((Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat Y) Z)) X) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat Y) X)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat Z) X)))) (forall ((Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat) (X tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat Y) Z)) X) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat Y) X)) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat Z) X)))) (forall ((Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat) (X tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat Y) Z)) X) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat Y) X)) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat Z) X)))) (forall ((Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat Y) Z)) X) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat Y) X)) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat Z) X)))) (forall ((Y tptp.set_nat) (Z tptp.set_nat) (X tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat Y) Z)) X) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat Y) X)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat Z) X)))) (forall ((Y tptp.nat) (Z tptp.nat) (X tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat Y) Z)) X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat Y) X)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat Z) X)))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn X))) (= (tptp.aa_assn_assn _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn Y) Z)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn (tptp.aa_assn_assn _let_1 Y)) (tptp.aa_assn_assn _let_1 Z))))) (forall ((X tptp.product_unit) (Y tptp.product_unit) (Z tptp.product_unit)) (let ((_let_1 (tptp.aa_Pro1375803928533059540t_unit tptp.sup_sup_Product_unit X))) (= (tptp.aa_Pro8294289767544744956t_unit _let_1 (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit Y) Z)) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit (tptp.aa_Pro8294289767544744956t_unit _let_1 Y)) (tptp.aa_Pro8294289767544744956t_unit _let_1 Z))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat X))) (= (tptp.aa_set8868280134176360700at_nat _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat Y) Z)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.aa_set8868280134176360700at_nat _let_1 Y)) (tptp.aa_set8868280134176360700at_nat _let_1 Z))))) (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat X))) (= (tptp.aa_set5535132180132642428at_nat _let_1 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat Y) Z)) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat (tptp.aa_set5535132180132642428at_nat _let_1 Y)) (tptp.aa_set5535132180132642428at_nat _let_1 Z))))) (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat X))) (= (tptp.aa_set6734554978791863420at_nat _let_1 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat Y) Z)) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat (tptp.aa_set6734554978791863420at_nat _let_1 Y)) (tptp.aa_set6734554978791863420at_nat _let_1 Z))))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat X))) (= (tptp.aa_set4883462369968598652at_nat _let_1 (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat Y) Z)) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat (tptp.aa_set4883462369968598652at_nat _let_1 Y)) (tptp.aa_set4883462369968598652at_nat _let_1 Z))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat X))) (= (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat Y) Z)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.aa_set_nat_set_nat _let_1 Y)) (tptp.aa_set_nat_set_nat _let_1 Z))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat X))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat Y) Z)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat (tptp.aa_nat_nat _let_1 Y)) (tptp.aa_nat_nat _let_1 Z))))) (forall ((Y tptp.assn) (Z tptp.assn) (X tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn Y) Z)) X) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn Y) X)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn Z) X)))) (forall ((Y tptp.product_unit) (Z tptp.product_unit) (X tptp.product_unit)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.sup_sup_Product_unit Y) Z)) X) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.sup_sup_Product_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit Y) X)) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit Z) X)))) (forall ((Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat Y) Z)) X) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat Y) X)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat Z) X)))) (forall ((Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat) (X tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat Y) Z)) X) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat Y) X)) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat Z) X)))) (forall ((Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat) (X tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat Y) Z)) X) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat Y) X)) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat Z) X)))) (forall ((Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat Y) Z)) X) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat Y) X)) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat Z) X)))) (forall ((Y tptp.set_nat) (Z tptp.set_nat) (X tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat Y) Z)) X) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat Y) X)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat Z) X)))) (forall ((Y tptp.nat) (Z tptp.nat) (X tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat Y) Z)) X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat Y) X)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat Z) X)))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X))) (= (tptp.aa_assn_assn _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn Y) Z)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn (tptp.aa_assn_assn _let_1 Y)) (tptp.aa_assn_assn _let_1 Z))))) (forall ((X tptp.product_unit) (Y tptp.product_unit) (Z tptp.product_unit)) (let ((_let_1 (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X))) (= (tptp.aa_Pro8294289767544744956t_unit _let_1 (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.sup_sup_Product_unit Y) Z)) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.sup_sup_Product_unit (tptp.aa_Pro8294289767544744956t_unit _let_1 Y)) (tptp.aa_Pro8294289767544744956t_unit _let_1 Z))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X))) (= (tptp.aa_set8868280134176360700at_nat _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat Y) Z)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat (tptp.aa_set8868280134176360700at_nat _let_1 Y)) (tptp.aa_set8868280134176360700at_nat _let_1 Z))))) (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat X))) (= (tptp.aa_set5535132180132642428at_nat _let_1 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat Y) Z)) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat (tptp.aa_set5535132180132642428at_nat _let_1 Y)) (tptp.aa_set5535132180132642428at_nat _let_1 Z))))) (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat X))) (= (tptp.aa_set6734554978791863420at_nat _let_1 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat Y) Z)) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat (tptp.aa_set6734554978791863420at_nat _let_1 Y)) (tptp.aa_set6734554978791863420at_nat _let_1 Z))))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat X))) (= (tptp.aa_set4883462369968598652at_nat _let_1 (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat Y) Z)) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat (tptp.aa_set4883462369968598652at_nat _let_1 Y)) (tptp.aa_set4883462369968598652at_nat _let_1 Z))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X))) (= (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat Y) Z)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.aa_set_nat_set_nat _let_1 Y)) (tptp.aa_set_nat_set_nat _let_1 Z))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat X))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat Y) Z)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat (tptp.aa_nat_nat _let_1 Y)) (tptp.aa_nat_nat _let_1 Z))))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X))) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn) (Z2 tptp.assn)) (let ((_let_1 (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn X3))) (= (tptp.aa_assn_assn _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn Y3) Z2)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn (tptp.aa_assn_assn _let_1 Y3)) (tptp.aa_assn_assn _let_1 Z2))))) (= (tptp.aa_assn_assn _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn Y) Z)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn (tptp.aa_assn_assn _let_1 Y)) (tptp.aa_assn_assn _let_1 Z)))))) (forall ((X tptp.product_unit) (Y tptp.product_unit) (Z tptp.product_unit)) (let ((_let_1 (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X))) (=> (forall ((X3 tptp.product_unit) (Y3 tptp.product_unit) (Z2 tptp.product_unit)) (let ((_let_1 (tptp.aa_Pro1375803928533059540t_unit tptp.sup_sup_Product_unit X3))) (= (tptp.aa_Pro8294289767544744956t_unit _let_1 (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit Y3) Z2)) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit (tptp.aa_Pro8294289767544744956t_unit _let_1 Y3)) (tptp.aa_Pro8294289767544744956t_unit _let_1 Z2))))) (= (tptp.aa_Pro8294289767544744956t_unit _let_1 (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.sup_sup_Product_unit Y) Z)) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.sup_sup_Product_unit (tptp.aa_Pro8294289767544744956t_unit _let_1 Y)) (tptp.aa_Pro8294289767544744956t_unit _let_1 Z)))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X))) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat) (Z2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat X3))) (= (tptp.aa_set8868280134176360700at_nat _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat Y3) Z2)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.aa_set8868280134176360700at_nat _let_1 Y3)) (tptp.aa_set8868280134176360700at_nat _let_1 Z2))))) (= (tptp.aa_set8868280134176360700at_nat _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat Y) Z)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat (tptp.aa_set8868280134176360700at_nat _let_1 Y)) (tptp.aa_set8868280134176360700at_nat _let_1 Z)))))) (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat X))) (=> (forall ((X3 tptp.set_Pr8693737435421807431at_nat) (Y3 tptp.set_Pr8693737435421807431at_nat) (Z2 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat X3))) (= (tptp.aa_set5535132180132642428at_nat _let_1 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat Y3) Z2)) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat (tptp.aa_set5535132180132642428at_nat _let_1 Y3)) (tptp.aa_set5535132180132642428at_nat _let_1 Z2))))) (= (tptp.aa_set5535132180132642428at_nat _let_1 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat Y) Z)) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat (tptp.aa_set5535132180132642428at_nat _let_1 Y)) (tptp.aa_set5535132180132642428at_nat _let_1 Z)))))) (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat X))) (=> (forall ((X3 tptp.set_Pr8551490117392284871at_nat) (Y3 tptp.set_Pr8551490117392284871at_nat) (Z2 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat X3))) (= (tptp.aa_set6734554978791863420at_nat _let_1 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat Y3) Z2)) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat (tptp.aa_set6734554978791863420at_nat _let_1 Y3)) (tptp.aa_set6734554978791863420at_nat _let_1 Z2))))) (= (tptp.aa_set6734554978791863420at_nat _let_1 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat Y) Z)) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat (tptp.aa_set6734554978791863420at_nat _let_1 Y)) (tptp.aa_set6734554978791863420at_nat _let_1 Z)))))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat X))) (=> (forall ((X3 tptp.set_Pr4329608150637261639at_nat) (Y3 tptp.set_Pr4329608150637261639at_nat) (Z2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat X3))) (= (tptp.aa_set4883462369968598652at_nat _let_1 (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat Y3) Z2)) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat (tptp.aa_set4883462369968598652at_nat _let_1 Y3)) (tptp.aa_set4883462369968598652at_nat _let_1 Z2))))) (= (tptp.aa_set4883462369968598652at_nat _let_1 (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat Y) Z)) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat (tptp.aa_set4883462369968598652at_nat _let_1 Y)) (tptp.aa_set4883462369968598652at_nat _let_1 Z)))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X))) (=> (forall ((X3 tptp.set_nat) (Y3 tptp.set_nat) (Z2 tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat X3))) (= (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat Y3) Z2)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.aa_set_nat_set_nat _let_1 Y3)) (tptp.aa_set_nat_set_nat _let_1 Z2))))) (= (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat Y) Z)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.aa_set_nat_set_nat _let_1 Y)) (tptp.aa_set_nat_set_nat _let_1 Z)))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat X))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat X3))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat Y3) Z2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat (tptp.aa_nat_nat _let_1 Y3)) (tptp.aa_nat_nat _let_1 Z2))))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat Y) Z)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat (tptp.aa_nat_nat _let_1 Y)) (tptp.aa_nat_nat _let_1 Z)))))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn X))) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn) (Z2 tptp.assn)) (let ((_let_1 (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X3))) (= (tptp.aa_assn_assn _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn Y3) Z2)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn (tptp.aa_assn_assn _let_1 Y3)) (tptp.aa_assn_assn _let_1 Z2))))) (= (tptp.aa_assn_assn _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn Y) Z)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn (tptp.aa_assn_assn _let_1 Y)) (tptp.aa_assn_assn _let_1 Z)))))) (forall ((X tptp.product_unit) (Y tptp.product_unit) (Z tptp.product_unit)) (let ((_let_1 (tptp.aa_Pro1375803928533059540t_unit tptp.sup_sup_Product_unit X))) (=> (forall ((X3 tptp.product_unit) (Y3 tptp.product_unit) (Z2 tptp.product_unit)) (let ((_let_1 (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X3))) (= (tptp.aa_Pro8294289767544744956t_unit _let_1 (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.sup_sup_Product_unit Y3) Z2)) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.sup_sup_Product_unit (tptp.aa_Pro8294289767544744956t_unit _let_1 Y3)) (tptp.aa_Pro8294289767544744956t_unit _let_1 Z2))))) (= (tptp.aa_Pro8294289767544744956t_unit _let_1 (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit Y) Z)) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit (tptp.aa_Pro8294289767544744956t_unit _let_1 Y)) (tptp.aa_Pro8294289767544744956t_unit _let_1 Z)))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat X))) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat) (Z2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X3))) (= (tptp.aa_set8868280134176360700at_nat _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat Y3) Z2)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat (tptp.aa_set8868280134176360700at_nat _let_1 Y3)) (tptp.aa_set8868280134176360700at_nat _let_1 Z2))))) (= (tptp.aa_set8868280134176360700at_nat _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat Y) Z)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.aa_set8868280134176360700at_nat _let_1 Y)) (tptp.aa_set8868280134176360700at_nat _let_1 Z)))))) (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat X))) (=> (forall ((X3 tptp.set_Pr8693737435421807431at_nat) (Y3 tptp.set_Pr8693737435421807431at_nat) (Z2 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat X3))) (= (tptp.aa_set5535132180132642428at_nat _let_1 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat Y3) Z2)) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat (tptp.aa_set5535132180132642428at_nat _let_1 Y3)) (tptp.aa_set5535132180132642428at_nat _let_1 Z2))))) (= (tptp.aa_set5535132180132642428at_nat _let_1 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat Y) Z)) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat (tptp.aa_set5535132180132642428at_nat _let_1 Y)) (tptp.aa_set5535132180132642428at_nat _let_1 Z)))))) (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat X))) (=> (forall ((X3 tptp.set_Pr8551490117392284871at_nat) (Y3 tptp.set_Pr8551490117392284871at_nat) (Z2 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat X3))) (= (tptp.aa_set6734554978791863420at_nat _let_1 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat Y3) Z2)) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat (tptp.aa_set6734554978791863420at_nat _let_1 Y3)) (tptp.aa_set6734554978791863420at_nat _let_1 Z2))))) (= (tptp.aa_set6734554978791863420at_nat _let_1 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat Y) Z)) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat (tptp.aa_set6734554978791863420at_nat _let_1 Y)) (tptp.aa_set6734554978791863420at_nat _let_1 Z)))))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat X))) (=> (forall ((X3 tptp.set_Pr4329608150637261639at_nat) (Y3 tptp.set_Pr4329608150637261639at_nat) (Z2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat X3))) (= (tptp.aa_set4883462369968598652at_nat _let_1 (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat Y3) Z2)) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat (tptp.aa_set4883462369968598652at_nat _let_1 Y3)) (tptp.aa_set4883462369968598652at_nat _let_1 Z2))))) (= (tptp.aa_set4883462369968598652at_nat _let_1 (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat Y) Z)) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat (tptp.aa_set4883462369968598652at_nat _let_1 Y)) (tptp.aa_set4883462369968598652at_nat _let_1 Z)))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat X))) (=> (forall ((X3 tptp.set_nat) (Y3 tptp.set_nat) (Z2 tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X3))) (= (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat Y3) Z2)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.aa_set_nat_set_nat _let_1 Y3)) (tptp.aa_set_nat_set_nat _let_1 Z2))))) (= (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat Y) Z)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.aa_set_nat_set_nat _let_1 Y)) (tptp.aa_set_nat_set_nat _let_1 Z)))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat X))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat X3))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat Y3) Z2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat (tptp.aa_nat_nat _let_1 Y3)) (tptp.aa_nat_nat _let_1 Z2))))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat Y) Z)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat (tptp.aa_nat_nat _let_1 Y)) (tptp.aa_nat_nat _let_1 Z)))))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3) tptp.bot_bo5327735625951526323at_nat) A3)) (forall ((A3 tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3) tptp.bot_bo8422036546324065075at_nat) A3)) (forall ((A3 tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3) tptp.bot_bo228742789529271731at_nat) A3)) (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat A3) tptp.bot_bo2099793752762293965at_nat) A3)) (forall ((A3 tptp.set_bool)) (= (tptp.aa_set_bool_set_bool (tptp.aa_set4734229006438377534t_bool tptp.sup_sup_set_bool A3) tptp.bot_bot_set_bool) A3)) (forall ((A3 tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) tptp.bot_bot_set_nat) A3)) (forall ((A3 tptp.set_int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) tptp.bot_bot_set_int) A3)) (forall ((B3 tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat tptp.bot_bo5327735625951526323at_nat) B3) B3)) (forall ((B3 tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat tptp.bot_bo8422036546324065075at_nat) B3) B3)) (forall ((B3 tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat tptp.bot_bo228742789529271731at_nat) B3) B3)) (forall ((B3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat tptp.bot_bo2099793752762293965at_nat) B3) B3)) (forall ((B3 tptp.set_bool)) (= (tptp.aa_set_bool_set_bool (tptp.aa_set4734229006438377534t_bool tptp.sup_sup_set_bool tptp.bot_bot_set_bool) B3) B3)) (forall ((B3 tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat tptp.bot_bot_set_nat) B3) B3)) (forall ((B3 tptp.set_int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int tptp.bot_bot_set_int) B3) B3)) (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (C3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat B3) C3)) A3) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat B3) A3)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat C3) A3)))) (forall ((B3 tptp.set_Pr8693737435421807431at_nat) (C3 tptp.set_Pr8693737435421807431at_nat) (A3 tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat B3) C3)) A3) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat B3) A3)) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat C3) A3)))) (forall ((B3 tptp.set_Pr8551490117392284871at_nat) (C3 tptp.set_Pr8551490117392284871at_nat) (A3 tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat B3) C3)) A3) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat B3) A3)) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat C3) A3)))) (forall ((B3 tptp.set_Pr4329608150637261639at_nat) (C3 tptp.set_Pr4329608150637261639at_nat) (A3 tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat B3) C3)) A3) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat B3) A3)) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat C3) A3)))) (forall ((B3 tptp.set_nat) (C3 tptp.set_nat) (A3 tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat B3) C3)) A3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat B3) A3)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat C3) A3)))) (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (C3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat B3) C3)) A3) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat B3) A3)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat C3) A3)))) (forall ((B3 tptp.set_Pr8693737435421807431at_nat) (C3 tptp.set_Pr8693737435421807431at_nat) (A3 tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat B3) C3)) A3) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat B3) A3)) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat C3) A3)))) (forall ((B3 tptp.set_Pr8551490117392284871at_nat) (C3 tptp.set_Pr8551490117392284871at_nat) (A3 tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat B3) C3)) A3) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat B3) A3)) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat C3) A3)))) (forall ((B3 tptp.set_Pr4329608150637261639at_nat) (C3 tptp.set_Pr4329608150637261639at_nat) (A3 tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat B3) C3)) A3) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat B3) A3)) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat C3) A3)))) (forall ((B3 tptp.set_nat) (C3 tptp.set_nat) (A3 tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat B3) C3)) A3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat B3) A3)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat C3) A3)))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat A3))) (= (tptp.aa_set8868280134176360700at_nat _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat B3) C3)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.aa_set8868280134176360700at_nat _let_1 B3)) (tptp.aa_set8868280134176360700at_nat _let_1 C3))))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (C3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3))) (= (tptp.aa_set5535132180132642428at_nat _let_1 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat B3) C3)) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat (tptp.aa_set5535132180132642428at_nat _let_1 B3)) (tptp.aa_set5535132180132642428at_nat _let_1 C3))))) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (C3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3))) (= (tptp.aa_set6734554978791863420at_nat _let_1 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat B3) C3)) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat (tptp.aa_set6734554978791863420at_nat _let_1 B3)) (tptp.aa_set6734554978791863420at_nat _let_1 C3))))) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (C3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3))) (= (tptp.aa_set4883462369968598652at_nat _let_1 (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat B3) C3)) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat (tptp.aa_set4883462369968598652at_nat _let_1 B3)) (tptp.aa_set4883462369968598652at_nat _let_1 C3))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C3 tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3))) (= (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat B3) C3)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.aa_set_nat_set_nat _let_1 B3)) (tptp.aa_set_nat_set_nat _let_1 C3))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3))) (= (tptp.aa_set8868280134176360700at_nat _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat B3) C3)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat (tptp.aa_set8868280134176360700at_nat _let_1 B3)) (tptp.aa_set8868280134176360700at_nat _let_1 C3))))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (C3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat A3))) (= (tptp.aa_set5535132180132642428at_nat _let_1 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat B3) C3)) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat (tptp.aa_set5535132180132642428at_nat _let_1 B3)) (tptp.aa_set5535132180132642428at_nat _let_1 C3))))) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (C3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat A3))) (= (tptp.aa_set6734554978791863420at_nat _let_1 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat B3) C3)) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat (tptp.aa_set6734554978791863420at_nat _let_1 B3)) (tptp.aa_set6734554978791863420at_nat _let_1 C3))))) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (C3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat A3))) (= (tptp.aa_set4883462369968598652at_nat _let_1 (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat B3) C3)) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat (tptp.aa_set4883462369968598652at_nat _let_1 B3)) (tptp.aa_set4883462369968598652at_nat _let_1 C3))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C3 tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3))) (= (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat B3) C3)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.aa_set_nat_set_nat _let_1 B3)) (tptp.aa_set_nat_set_nat _let_1 C3))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat B3) C3))) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat C3) A3)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat A3) B3)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat B3) C3))) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat C3) A3)))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (C3 tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat A3) B3)) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat B3) C3))) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat C3) A3)) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3) B3)) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat B3) C3))) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat C3) A3)))) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (C3 tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat A3) B3)) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat B3) C3))) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat C3) A3)) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3) B3)) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat B3) C3))) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat C3) A3)))) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (C3 tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat A3) B3)) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat B3) C3))) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat C3) A3)) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3) B3)) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat B3) C3))) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat C3) A3)))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C3 tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat B3) C3))) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat C3) A3)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat B3) C3))) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat C3) A3)))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn X))) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn (tptp.aa_assn_assn _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn Y) Z))) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn (tptp.aa_assn_assn _let_1 Y)) (tptp.aa_assn_assn _let_1 Z)))))) (forall ((X tptp.product_unit) (Y tptp.product_unit) (Z tptp.product_unit)) (let ((_let_1 (tptp.aa_Pro1375803928533059540t_unit tptp.sup_sup_Product_unit X))) (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit (tptp.aa_Pro8294289767544744956t_unit _let_1 (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit Y) Z))) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit (tptp.aa_Pro8294289767544744956t_unit _let_1 Y)) (tptp.aa_Pro8294289767544744956t_unit _let_1 Z)))))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat Y) Z))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat (tptp.aa_rat_rat _let_1 Y)) (tptp.aa_rat_rat _let_1 Z)))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat Y) Z))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat (tptp.aa_nat_nat _let_1 Y)) (tptp.aa_nat_nat _let_1 Z)))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.sup_sup_int X))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int Y) Z))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int (tptp.aa_int_int _let_1 Y)) (tptp.aa_int_int _let_1 Z)))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat X))) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat Y) Z))) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.aa_set_nat_set_nat _let_1 Y)) (tptp.aa_set_nat_set_nat _let_1 Z)))))) (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int X))) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int Y) Z))) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int (tptp.aa_set_int_set_int _let_1 Y)) (tptp.aa_set_int_set_int _let_1 Z)))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat X))) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat (tptp.aa_set8868280134176360700at_nat _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat Y) Z))) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.aa_set8868280134176360700at_nat _let_1 Y)) (tptp.aa_set8868280134176360700at_nat _let_1 Z)))))) (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat X))) (tptp.ord_le3000389064537975527at_nat (tptp.aa_set5535132180132642428at_nat _let_1 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat Y) Z)) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat (tptp.aa_set5535132180132642428at_nat _let_1 Y)) (tptp.aa_set5535132180132642428at_nat _let_1 Z))))) (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat X))) (tptp.ord_le8081472938463900775at_nat (tptp.aa_set6734554978791863420at_nat _let_1 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat Y) Z)) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat (tptp.aa_set6734554978791863420at_nat _let_1 Y)) (tptp.aa_set6734554978791863420at_nat _let_1 Z))))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X))) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn (tptp.aa_assn_assn _let_1 Y)) (tptp.aa_assn_assn _let_1 Z))) (tptp.aa_assn_assn _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn Y) Z)))))) (forall ((X tptp.product_unit) (Y tptp.product_unit) (Z tptp.product_unit)) (let ((_let_1 (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X))) (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.sup_sup_Product_unit (tptp.aa_Pro8294289767544744956t_unit _let_1 Y)) (tptp.aa_Pro8294289767544744956t_unit _let_1 Z))) (tptp.aa_Pro8294289767544744956t_unit _let_1 (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.sup_sup_Product_unit Y) Z)))))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat (tptp.aa_rat_rat _let_1 Y)) (tptp.aa_rat_rat _let_1 Z))) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat Y) Z)))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat (tptp.aa_nat_nat _let_1 Y)) (tptp.aa_nat_nat _let_1 Z))) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat Y) Z)))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.inf_inf_int X))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int (tptp.aa_int_int _let_1 Y)) (tptp.aa_int_int _let_1 Z))) (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int Y) Z)))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X))) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.aa_set_nat_set_nat _let_1 Y)) (tptp.aa_set_nat_set_nat _let_1 Z))) (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat Y) Z)))))) (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int X))) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int (tptp.aa_set_int_set_int _let_1 Y)) (tptp.aa_set_int_set_int _let_1 Z))) (tptp.aa_set_int_set_int _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int Y) Z)))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X))) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat (tptp.aa_set8868280134176360700at_nat _let_1 Y)) (tptp.aa_set8868280134176360700at_nat _let_1 Z))) (tptp.aa_set8868280134176360700at_nat _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat Y) Z)))))) (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat X))) (tptp.ord_le3000389064537975527at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat (tptp.aa_set5535132180132642428at_nat _let_1 Y)) (tptp.aa_set5535132180132642428at_nat _let_1 Z)) (tptp.aa_set5535132180132642428at_nat _let_1 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat Y) Z))))) (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat X))) (tptp.ord_le8081472938463900775at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat (tptp.aa_set6734554978791863420at_nat _let_1 Y)) (tptp.aa_set6734554978791863420at_nat _let_1 Z)) (tptp.aa_set6734554978791863420at_nat _let_1 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat Y) Z))))) (forall ((X tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X) tptp.bot_bot_assn) tptp.bot_bot_assn)) (forall ((X tptp.product_unit)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X) tptp.bot_bot_Product_unit) tptp.bot_bot_Product_unit)) (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X) tptp.bot_bo2099793752762293965at_nat) tptp.bot_bo2099793752762293965at_nat)) (forall ((X tptp.set_bool)) (= (tptp.inf_inf_set_bool X tptp.bot_bot_set_bool) tptp.bot_bot_set_bool)) (forall ((X tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X) tptp.bot_bot_set_nat) tptp.bot_bot_set_nat)) (forall ((X tptp.set_int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int X) tptp.bot_bot_set_int) tptp.bot_bot_set_int)) (forall ((X tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn tptp.bot_bot_assn) X) tptp.bot_bot_assn)) (forall ((X tptp.product_unit)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit tptp.bot_bot_Product_unit) X) tptp.bot_bot_Product_unit)) (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat tptp.bot_bo2099793752762293965at_nat) X) tptp.bot_bo2099793752762293965at_nat)) (forall ((X tptp.set_bool)) (= (tptp.inf_inf_set_bool tptp.bot_bot_set_bool X) tptp.bot_bot_set_bool)) (forall ((X tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat tptp.bot_bot_set_nat) X) tptp.bot_bot_set_nat)) (forall ((X tptp.set_int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int tptp.bot_bot_set_int) X) tptp.bot_bot_set_int)) (= (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a tptp.c) tptp.h2) (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat tptp.r2) (tptp.produc584006145561248582it_nat tptp.h tptp.t)))) (forall ((X tptp.fun_Pr6001797050664311790t_bool) (Xa2 tptp.fun_Pr6001797050664311790t_bool) (Xb tptp.produc3658429121746597890et_nat)) (=> (not (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.aa_fun6808777976510360636t_bool (tptp.times_assn_raw X) Xa2) Xb))) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (=> (= Xb (tptp.produc7507926704131184380et_nat H4 As4)) (exists ((As13 tptp.set_nat) (As23 tptp.set_nat)) (and (= As4 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat As13) As23)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat As13) As23) tptp.bot_bot_set_nat) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool X (tptp.produc7507926704131184380et_nat H4 As13))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool Xa2 (tptp.produc7507926704131184380et_nat H4 As23)))))))))) (forall ((X tptp.fun_Pr6001797050664311790t_bool) (Xa2 tptp.fun_Pr6001797050664311790t_bool) (Xb tptp.produc3658429121746597890et_nat)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.aa_fun6808777976510360636t_bool (tptp.times_assn_raw X) Xa2) Xb)) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (=> (= Xb (tptp.produc7507926704131184380et_nat H4 As4)) (not (exists ((As1 tptp.set_nat) (As2 tptp.set_nat)) (and (= As4 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat As1) As2)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat As1) As2) tptp.bot_bot_set_nat) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool X (tptp.produc7507926704131184380et_nat H4 As1))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool Xa2 (tptp.produc7507926704131184380et_nat H4 As2))))))))))) (forall ((X tptp.fun_Pr6001797050664311790t_bool) (Xa2 tptp.fun_Pr6001797050664311790t_bool) (Xb tptp.produc3658429121746597890et_nat) (Y tptp.bool)) (=> (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.aa_fun6808777976510360636t_bool (tptp.times_assn_raw X) Xa2) Xb)) (tptp.pp Y)) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (=> (= Xb (tptp.produc7507926704131184380et_nat H4 As4)) (= (tptp.pp Y) (not (exists ((As12 tptp.set_nat) (As22 tptp.set_nat)) (and (= As4 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat As12) As22)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat As12) As22) tptp.bot_bot_set_nat) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool X (tptp.produc7507926704131184380et_nat H4 As12))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool Xa2 (tptp.produc7507926704131184380et_nat H4 As22)))))))))))) (forall ((P tptp.fun_Pr6001797050664311790t_bool) (Q tptp.fun_Pr6001797050664311790t_bool) (H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.aa_fun6808777976510360636t_bool (tptp.times_assn_raw P) Q) (tptp.produc7507926704131184380et_nat H As))) (exists ((As12 tptp.set_nat) (As22 tptp.set_nat)) (and (= As (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat As12) As22)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat As12) As22) tptp.bot_bot_set_nat) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool P (tptp.produc7507926704131184380et_nat H As12))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool Q (tptp.produc7507926704131184380et_nat H As22))))))) (forall ((A tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) A))) (forall ((A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) A))) (forall ((A tptp.num)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) A))) (forall ((A tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) A))) (forall ((A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) A))) (forall ((X tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X) X))) (forall ((X tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) X))) (forall ((X tptp.num)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) X))) (forall ((X tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) X))) (forall ((X tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) X))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A3) tptp.bot_bo2099793752762293965at_nat)) (= A3 tptp.bot_bo2099793752762293965at_nat))) (forall ((A3 tptp.set_bool)) (= (tptp.ord_less_eq_set_bool A3 tptp.bot_bot_set_bool) (= A3 tptp.bot_bot_set_bool))) (forall ((A3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) tptp.bot_bot_set_nat)) (= A3 tptp.bot_bot_set_nat))) (forall ((A3 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) tptp.bot_bot_set_int)) (= A3 tptp.bot_bot_set_int))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat tptp.bot_bo2099793752762293965at_nat) A3))) (forall ((A3 tptp.set_bool)) (tptp.ord_less_eq_set_bool tptp.bot_bot_set_bool A3)) (forall ((A3 tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A3))) (forall ((A3 tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A3))) (forall ((C3 tptp.set_nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat C3))) (= (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3))) (and (tptp.pp (tptp.aa_set_nat_bool _let_1 A3)) (tptp.pp (tptp.aa_set_nat_bool _let_1 B3)))))) (forall ((C3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat C3))) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3))) (and (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 A3)) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 B3)))))) (forall ((C3 tptp.set_int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int C3))) (= (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))) (and (tptp.pp (tptp.aa_set_int_bool _let_1 A3)) (tptp.pp (tptp.aa_set_int_bool _let_1 B3)))))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (C3 tptp.set_Pr8693737435421807431at_nat)) (= (tptp.ord_le3000389064537975527at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3) B3) C3) (and (tptp.ord_le3000389064537975527at_nat A3 C3) (tptp.ord_le3000389064537975527at_nat B3 C3)))) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (C3 tptp.set_Pr8551490117392284871at_nat)) (= (tptp.ord_le8081472938463900775at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3) B3) C3) (and (tptp.ord_le8081472938463900775at_nat A3 C3) (tptp.ord_le8081472938463900775at_nat B3 C3)))) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (C3 tptp.set_Pr4329608150637261639at_nat)) (= (tptp.ord_le1268244103169919719at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3) B3) C3) (and (tptp.ord_le1268244103169919719at_nat A3 C3) (tptp.ord_le1268244103169919719at_nat B3 C3)))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)) C3)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) C3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B3) C3))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (C3 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3)) C3)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) C3)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) C3))))) (forall ((A tptp.assn) (B tptp.assn)) (= (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn A) B)) (= A (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A) B)))) (forall ((A3 tptp.set_nat) (C3 tptp.set_nat) (B3 tptp.set_nat) (D3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) C3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B3) D3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat C3) D3)))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (C3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (D3 tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A3) C3)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat B3) D3)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat C3) D3)))))) (forall ((A3 tptp.set_int) (C3 tptp.set_int) (B3 tptp.set_int) (D3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) C3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) D3)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3)) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int C3) D3)))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3)) A3))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3)) A3))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3)) A3))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3)) B3))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3)) B3))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3)) B3))) (forall ((B3 tptp.set_nat) (A3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B3) A3)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3) B3))) (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat B3) A3)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3) B3))) (forall ((B3 tptp.set_int) (A3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) A3)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3) B3))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) B3)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3) A3))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A3) B3)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3) A3))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3) A3))) (forall ((C3 tptp.set_nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat C3))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A3)) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 B3)) (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3))))))) (forall ((C3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat C3))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 A3)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 B3)) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3))))))) (forall ((C3 tptp.set_int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int C3))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 A3)) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 B3)) (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))))))) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool) (P tptp.fun_bool_bool) (Q tptp.fun_bool_bool)) (=> (tptp.ord_less_eq_set_bool A3 B3) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 A3)) (=> (tptp.pp (tptp.aa_bool_bool P X3)) (tptp.pp (tptp.aa_bool_bool Q X3))))) (tptp.ord_less_eq_set_bool (tptp.inf_inf_set_bool A3 (tptp.collect_bool P)) (tptp.inf_inf_set_bool B3 (tptp.collect_bool Q)))))) (forall ((A3 tptp.set_Pr958786334691620121nt_int) (B3 tptp.set_Pr958786334691620121nt_int) (P tptp.fun_Pr803113274115125473t_bool) (Q tptp.fun_Pr803113274115125473t_bool)) (=> (tptp.ord_le2843351958646193337nt_int A3 B3) (=> (forall ((X3 tptp.product_prod_int_int)) (=> (tptp.member5262025264175285858nt_int X3 A3) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool P X3)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool Q X3))))) (tptp.ord_le2843351958646193337nt_int (tptp.inf_in2269163501485487111nt_int A3 (tptp.collec213857154873943460nt_int P)) (tptp.inf_in2269163501485487111nt_int B3 (tptp.collec213857154873943460nt_int Q)))))) (forall ((A3 tptp.set_list_nat) (B3 tptp.set_list_nat) (P tptp.fun_list_nat_bool) (Q tptp.fun_list_nat_bool)) (=> (tptp.ord_le6045566169113846134st_nat A3 B3) (=> (forall ((X3 tptp.list_nat)) (=> (tptp.member_list_nat X3 A3) (=> (tptp.pp (tptp.aa_list_nat_bool P X3)) (tptp.pp (tptp.aa_list_nat_bool Q X3))))) (tptp.ord_le6045566169113846134st_nat (tptp.inf_inf_set_list_nat A3 (tptp.collect_list_nat P)) (tptp.inf_inf_set_list_nat B3 (tptp.collect_list_nat Q)))))) (forall ((A3 tptp.set_set_nat) (B3 tptp.set_set_nat) (P tptp.fun_set_nat_bool) (Q tptp.fun_set_nat_bool)) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat A3) B3)) (=> (forall ((X3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat X3) A3)) (=> (tptp.pp (tptp.aa_set_nat_bool P X3)) (tptp.pp (tptp.aa_set_nat_bool Q X3))))) (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat (tptp.inf_inf_set_set_nat A3 (tptp.collect_set_nat P))) (tptp.inf_inf_set_set_nat B3 (tptp.collect_set_nat Q))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (P tptp.fun_nat_bool) (Q tptp.fun_nat_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) B3)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (=> (tptp.pp (tptp.aa_nat_bool P X3)) (tptp.pp (tptp.aa_nat_bool Q X3))))) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) (tptp.collect_nat P))) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat B3) (tptp.collect_nat Q))))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (P tptp.fun_Pr7757163693017731481t_bool) (Q tptp.fun_Pr7757163693017731481t_bool)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A3) B3)) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat X3) A3)) (=> (tptp.pp (tptp.aa_Pro2232559814647311250t_bool P X3)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool Q X3))))) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) (tptp.collec3392354462482085612at_nat P))) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat B3) (tptp.collec3392354462482085612at_nat Q))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (P tptp.fun_int_bool) (Q tptp.fun_int_bool)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (=> (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool Q X3))))) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) (tptp.collect_int P))) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int B3) (tptp.collect_int Q))))))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (C3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (D3 tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.ord_le3000389064537975527at_nat A3 C3) (=> (tptp.ord_le3000389064537975527at_nat B3 D3) (tptp.ord_le3000389064537975527at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3) B3) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat C3) D3))))) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (C3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (D3 tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.ord_le8081472938463900775at_nat A3 C3) (=> (tptp.ord_le8081472938463900775at_nat B3 D3) (tptp.ord_le8081472938463900775at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3) B3) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat C3) D3))))) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (C3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (D3 tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.ord_le1268244103169919719at_nat A3 C3) (=> (tptp.ord_le1268244103169919719at_nat B3 D3) (tptp.ord_le1268244103169919719at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3) B3) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat C3) D3))))) (forall ((A3 tptp.set_nat) (C3 tptp.set_nat) (B3 tptp.set_nat) (D3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) C3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B3) D3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat C3) D3)))))) (forall ((A3 tptp.set_int) (C3 tptp.set_int) (B3 tptp.set_int) (D3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) C3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) D3)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3)) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int C3) D3)))))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (C3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.ord_le3000389064537975527at_nat A3 C3) (=> (tptp.ord_le3000389064537975527at_nat B3 C3) (tptp.ord_le3000389064537975527at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3) B3) C3)))) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (C3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.ord_le8081472938463900775at_nat A3 C3) (=> (tptp.ord_le8081472938463900775at_nat B3 C3) (tptp.ord_le8081472938463900775at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3) B3) C3)))) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (C3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.ord_le1268244103169919719at_nat A3 C3) (=> (tptp.ord_le1268244103169919719at_nat B3 C3) (tptp.ord_le1268244103169919719at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3) B3) C3)))) (forall ((A3 tptp.set_nat) (C3 tptp.set_nat) (B3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) C3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B3) C3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)) C3))))) (forall ((A3 tptp.set_int) (C3 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) C3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) C3)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3)) C3))))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (tptp.ord_le3000389064537975527at_nat A3 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3) B3))) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (tptp.ord_le8081472938463900775at_nat A3 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3) B3))) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (tptp.ord_le1268244103169919719at_nat A3 (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3) B3))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3)))) (forall ((B3 tptp.set_Pr8693737435421807431at_nat) (A3 tptp.set_Pr8693737435421807431at_nat)) (tptp.ord_le3000389064537975527at_nat B3 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3) B3))) (forall ((B3 tptp.set_Pr8551490117392284871at_nat) (A3 tptp.set_Pr8551490117392284871at_nat)) (tptp.ord_le8081472938463900775at_nat B3 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3) B3))) (forall ((B3 tptp.set_Pr4329608150637261639at_nat) (A3 tptp.set_Pr4329608150637261639at_nat)) (tptp.ord_le1268244103169919719at_nat B3 (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3) B3))) (forall ((B3 tptp.set_nat) (A3 tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)))) (forall ((B3 tptp.set_int) (A3 tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3)))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.ord_le3000389064537975527at_nat A3 B3) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3) B3) B3))) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.ord_le8081472938463900775at_nat A3 B3) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3) B3) B3))) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.ord_le1268244103169919719at_nat A3 B3) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3) B3) B3))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) B3)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3) B3))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3) B3))) (forall ((B3 tptp.set_Pr8693737435421807431at_nat) (A3 tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.ord_le3000389064537975527at_nat B3 A3) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3) B3) A3))) (forall ((B3 tptp.set_Pr8551490117392284871at_nat) (A3 tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.ord_le8081472938463900775at_nat B3 A3) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3) B3) A3))) (forall ((B3 tptp.set_Pr4329608150637261639at_nat) (A3 tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.ord_le1268244103169919719at_nat B3 A3) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3) B3) A3))) (forall ((B3 tptp.set_nat) (A3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B3) A3)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3) A3))) (forall ((B3 tptp.set_int) (A3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) A3)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3) A3))) (forall ((C3 tptp.set_Pr8693737435421807431at_nat) (A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.ord_le3000389064537975527at_nat C3 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3) B3)) (not (forall ((A5 tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.ord_le3000389064537975527at_nat A5 A3) (forall ((B5 tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.ord_le3000389064537975527at_nat B5 B3) (not (= C3 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A5) B5)))))))))) (forall ((C3 tptp.set_Pr8551490117392284871at_nat) (A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.ord_le8081472938463900775at_nat C3 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3) B3)) (not (forall ((A5 tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.ord_le8081472938463900775at_nat A5 A3) (forall ((B5 tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.ord_le8081472938463900775at_nat B5 B3) (not (= C3 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A5) B5)))))))))) (forall ((C3 tptp.set_Pr4329608150637261639at_nat) (A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.ord_le1268244103169919719at_nat C3 (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3) B3)) (not (forall ((A5 tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.ord_le1268244103169919719at_nat A5 A3) (forall ((B5 tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.ord_le1268244103169919719at_nat B5 B3) (not (= C3 (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A5) B5)))))))))) (forall ((C3 tptp.set_nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat C3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3))) (not (forall ((A5 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A5) A3)) (forall ((B5 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B5) B3)) (not (= C3 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A5) B5)))))))))) (forall ((C3 tptp.set_int) (A3 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int C3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3))) (not (forall ((A5 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A5) A3)) (forall ((B5 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B5) B3)) (not (= C3 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A5) B5)))))))))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (= (tptp.ord_le3000389064537975527at_nat A3 B3) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3) B3) B3))) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (= (tptp.ord_le8081472938463900775at_nat A3 B3) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3) B3) B3))) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (= (tptp.ord_le1268244103169919719at_nat A3 B3) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3) B3) B3))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) B3)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3) B3))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3) B3))) (forall ((Bs tptp.set_nat) (H tptp.heap_e7401611519738050253t_unit) (H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.relH Bs H) H3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat As) Bs)) (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.relH As H) H3))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3))) (= (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat (tptp.aa_set8868280134176360700at_nat _let_1 B3)) C3) (tptp.aa_set8868280134176360700at_nat _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat B3) C3))) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat C3) A3))))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (C3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat A3))) (= (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat (tptp.aa_set5535132180132642428at_nat _let_1 B3)) C3) (tptp.aa_set5535132180132642428at_nat _let_1 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat B3) C3))) (tptp.ord_le3000389064537975527at_nat C3 A3)))) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (C3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat A3))) (= (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat (tptp.aa_set6734554978791863420at_nat _let_1 B3)) C3) (tptp.aa_set6734554978791863420at_nat _let_1 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat B3) C3))) (tptp.ord_le8081472938463900775at_nat C3 A3)))) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (C3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat A3))) (= (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat (tptp.aa_set4883462369968598652at_nat _let_1 B3)) C3) (tptp.aa_set4883462369968598652at_nat _let_1 (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat B3) C3))) (tptp.ord_le1268244103169919719at_nat C3 A3)))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C3 tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3))) (= (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.aa_set_nat_set_nat _let_1 B3)) C3) (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat B3) C3))) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat C3) A3))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (C3 tptp.set_int)) (let ((_let_1 (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3))) (= (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int (tptp.aa_set_int_set_int _let_1 B3)) C3) (tptp.aa_set_int_set_int _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int B3) C3))) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int C3) A3))))) (forall ((A tptp.rat) (B tptp.rat)) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (not (= B A))))) (forall ((A tptp.num) (B tptp.num)) (= (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B))) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (not (= B A))))) (forall ((A tptp.nat) (B tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (not (= B A))))) (forall ((A tptp.int) (B tptp.int)) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (not (= B A))))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool _let_1 Y)))) (let ((_let_3 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Z))) (let ((_let_4 (tptp.pp (tptp.aa_rat_bool _let_3 X)))) (let ((_let_5 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y))) (let ((_let_6 (tptp.pp (tptp.aa_rat_bool _let_5 Z)))) (let ((_let_7 (tptp.pp (tptp.aa_rat_bool _let_5 X)))) (let ((_let_8 (tptp.pp (tptp.aa_rat_bool _let_3 Y)))) (let ((_let_9 (tptp.pp (tptp.aa_rat_bool _let_1 Z)))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))) (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X))) (let ((_let_2 (tptp.pp (tptp.aa_num_bool _let_1 Y)))) (let ((_let_3 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Z))) (let ((_let_4 (tptp.pp (tptp.aa_num_bool _let_3 X)))) (let ((_let_5 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y))) (let ((_let_6 (tptp.pp (tptp.aa_num_bool _let_5 Z)))) (let ((_let_7 (tptp.pp (tptp.aa_num_bool _let_5 X)))) (let ((_let_8 (tptp.pp (tptp.aa_num_bool _let_3 Y)))) (let ((_let_9 (tptp.pp (tptp.aa_num_bool _let_1 Z)))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool _let_1 Y)))) (let ((_let_3 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Z))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool _let_3 X)))) (let ((_let_5 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y))) (let ((_let_6 (tptp.pp (tptp.aa_nat_bool _let_5 Z)))) (let ((_let_7 (tptp.pp (tptp.aa_nat_bool _let_5 X)))) (let ((_let_8 (tptp.pp (tptp.aa_nat_bool _let_3 Y)))) (let ((_let_9 (tptp.pp (tptp.aa_nat_bool _let_1 Z)))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool _let_1 Y)))) (let ((_let_3 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z))) (let ((_let_4 (tptp.pp (tptp.aa_int_bool _let_3 X)))) (let ((_let_5 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y))) (let ((_let_6 (tptp.pp (tptp.aa_int_bool _let_5 Z)))) (let ((_let_7 (tptp.pp (tptp.aa_int_bool _let_5 X)))) (let ((_let_8 (tptp.pp (tptp.aa_int_bool _let_3 Y)))) (let ((_let_9 (tptp.pp (tptp.aa_int_bool _let_1 Z)))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (= X Y) (and (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X) Y)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int Y) X))))) (forall ((X tptp.rat) (Y tptp.rat)) (= (= X Y) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X))))) (forall ((X tptp.num) (Y tptp.num)) (= (= X Y) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) X))))) (forall ((X tptp.nat) (Y tptp.nat)) (= (= X Y) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X))))) (forall ((X tptp.int) (Y tptp.int)) (= (= X Y) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X))))) (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (=> (= A B) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) C)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) C))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (= A B) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) C))))) (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (=> (= A B) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (= A B) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) C))))) (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (let ((_let_1 (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 B)) (=> (= B C) (tptp.pp (tptp.aa_set_int_bool _let_1 C)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (=> (= B C) (tptp.pp (tptp.aa_rat_bool _let_1 C)))))) (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A))) (=> (tptp.pp (tptp.aa_num_bool _let_1 B)) (=> (= B C) (tptp.pp (tptp.aa_num_bool _let_1 C)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (=> (= B C) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (=> (= B C) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X) Y)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int Y) X)) (= X Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X)) (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) X)) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)) (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X)) (= X Y)))) (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (let ((_let_1 (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 B)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) C)) (tptp.pp (tptp.aa_set_int_bool _let_1 C)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (tptp.pp (tptp.aa_rat_bool _let_1 C)))))) (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A))) (=> (tptp.pp (tptp.aa_num_bool _let_1 B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (tptp.pp (tptp.aa_num_bool _let_1 C)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) C)) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) C)) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int Y) Z)) (tptp.pp (tptp.aa_set_int_bool _let_1 Z)))))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) Z)) (tptp.pp (tptp.aa_rat_bool _let_1 Z)))))) (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X))) (=> (tptp.pp (tptp.aa_num_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) Z)) (tptp.pp (tptp.aa_num_bool _let_1 Z)))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) Z)) (tptp.pp (tptp.aa_nat_bool _let_1 Z)))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X))) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) Z)) (tptp.pp (tptp.aa_int_bool _let_1 Z)))))) (forall ((P tptp.fun_rat_fun_rat_bool) (A tptp.rat) (B tptp.rat)) (=> (forall ((A4 tptp.rat) (B4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A4) B4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P A4) B4)))) (=> (forall ((A4 tptp.rat) (B4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P B4) A4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P A4) B4)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P A) B))))) (forall ((P tptp.fun_num_fun_num_bool) (A tptp.num) (B tptp.num)) (=> (forall ((A4 tptp.num) (B4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A4) B4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P A4) B4)))) (=> (forall ((A4 tptp.num) (B4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P B4) A4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P A4) B4)))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P A) B))))) (forall ((P tptp.fun_nat_fun_nat_bool) (A tptp.nat) (B tptp.nat)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A4) B4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A4) B4)))) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P B4) A4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A4) B4)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A) B))))) (forall ((P tptp.fun_int_fun_int_bool) (A tptp.int) (B tptp.int)) (=> (forall ((A4 tptp.int) (B4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A4) B4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A4) B4)))) (=> (forall ((A4 tptp.int) (B4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P B4) A4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A4) B4)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A) B))))) (forall ((A tptp.set_int) (B tptp.set_int)) (= (= A B) (and (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) A)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) B))))) (forall ((A tptp.rat) (B tptp.rat)) (= (= A B) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))))) (forall ((A tptp.num) (B tptp.num)) (= (= A B) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B))))) (forall ((A tptp.nat) (B tptp.nat)) (= (= A B) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B))))) (forall ((A tptp.int) (B tptp.int)) (= (= A B) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B))))) (forall ((B tptp.set_int) (A tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) A)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) B)) (= A B)))) (forall ((B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (= A B)))) (forall ((B tptp.num) (A tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (= A B)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= A B)))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (= A B)))) (forall ((B tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (let ((_let_1 (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int C))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) A)) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 B)) (tptp.pp (tptp.aa_set_int_bool _let_1 A)))))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (tptp.pp (tptp.aa_rat_bool _let_1 A)))))) (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num C))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (=> (tptp.pp (tptp.aa_num_bool _let_1 B)) (tptp.pp (tptp.aa_num_bool _let_1 A)))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (tptp.pp (tptp.aa_nat_bool _let_1 A)))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (tptp.pp (tptp.aa_int_bool _let_1 A)))))) (forall ((A tptp.set_int) (B tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) B)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) A)) (= A B)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (= A B)))) (forall ((A tptp.num) (B tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (= A B)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (= A B)))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (= A B)))) (forall ((A tptp.set_int) (B tptp.set_int)) (= (= A B) (and (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) B)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) A))))) (forall ((A tptp.rat) (B tptp.rat)) (= (= A B) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A))))) (forall ((A tptp.num) (B tptp.num)) (= (= A B) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A))))) (forall ((A tptp.nat) (B tptp.nat)) (= (= A B) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A))))) (forall ((A tptp.int) (B tptp.int)) (= (= A B) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A))))) (forall ((A tptp.rat) (F tptp.fun_rat_rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat F B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat F C)))))))) (forall ((A tptp.rat) (F tptp.fun_num_rat) (B tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_num_rat F B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F X3)) (tptp.aa_num_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_num_rat F C)))))))) (forall ((A tptp.rat) (F tptp.fun_nat_rat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat F B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) C)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F X3)) (tptp.aa_nat_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat F C)))))))) (forall ((A tptp.rat) (F tptp.fun_int_rat) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_int_rat F B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) C)) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat F X3)) (tptp.aa_int_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_int_rat F C)))))))) (forall ((A tptp.num) (F tptp.fun_rat_num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A))) (=> (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_rat_num F B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y3)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F X3)) (tptp.aa_rat_num F Y3))))) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_rat_num F C)))))))) (forall ((A tptp.num) (F tptp.fun_num_num) (B tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A))) (=> (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_num_num F B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y3)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F X3)) (tptp.aa_num_num F Y3))))) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_num_num F C)))))))) (forall ((A tptp.num) (F tptp.fun_nat_num) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A))) (=> (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_nat_num F B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) C)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) Y3)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F X3)) (tptp.aa_nat_num F Y3))))) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_nat_num F C)))))))) (forall ((A tptp.num) (F tptp.fun_int_num) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A))) (=> (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_int_num F B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) C)) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X3) Y3)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_int_num F X3)) (tptp.aa_int_num F Y3))))) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_int_num F C)))))))) (forall ((A tptp.nat) (F tptp.fun_rat_nat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_rat_nat F B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_rat_nat F X3)) (tptp.aa_rat_nat F Y3))))) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_rat_nat F C)))))))) (forall ((A tptp.nat) (F tptp.fun_num_nat) (B tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_num_nat F B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat F X3)) (tptp.aa_num_nat F Y3))))) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_num_nat F C)))))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F B)) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F B)) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y3)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F X3)) (tptp.aa_rat_num F Y3))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_rat_nat F B)) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_rat_nat F X3)) (tptp.aa_rat_nat F Y3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_rat_nat F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_int) (C tptp.int)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int F B)) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int F X3)) (tptp.aa_rat_int F Y3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int F A)) C)))))) (forall ((A tptp.num) (B tptp.num) (F tptp.fun_num_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F B)) C)) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F X3)) (tptp.aa_num_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F A)) C)))))) (forall ((A tptp.num) (B tptp.num) (F tptp.fun_num_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F B)) C)) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y3)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F X3)) (tptp.aa_num_num F Y3))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F A)) C)))))) (forall ((A tptp.num) (B tptp.num) (F tptp.fun_num_nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat F B)) C)) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat F X3)) (tptp.aa_num_nat F Y3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat F A)) C)))))) (forall ((A tptp.num) (B tptp.num) (F tptp.fun_num_int) (C tptp.int)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int F B)) C)) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int F X3)) (tptp.aa_num_int F Y3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int F A)) C)))))) (forall ((A tptp.nat) (B tptp.nat) (F tptp.fun_nat_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F B)) C)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F X3)) (tptp.aa_nat_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F A)) C)))))) (forall ((A tptp.nat) (B tptp.nat) (F tptp.fun_nat_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F B)) C)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) Y3)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F X3)) (tptp.aa_nat_num F Y3))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F A)) C)))))) (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (= X Y) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (= X Y) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (= X Y) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (= X Y) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (= X Y) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X)))) (forall ((X tptp.num) (Y tptp.num)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X)))) (forall ((A tptp.rat) (F tptp.fun_rat_rat) (B tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_rat F B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat F C))))))) (forall ((A tptp.num) (F tptp.fun_rat_num) (B tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_num F B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y3)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F X3)) (tptp.aa_rat_num F Y3))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) (tptp.aa_rat_num F C))))))) (forall ((A tptp.nat) (F tptp.fun_rat_nat) (B tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_nat F B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_rat_nat F X3)) (tptp.aa_rat_nat F Y3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) (tptp.aa_rat_nat F C))))))) (forall ((A tptp.int) (F tptp.fun_rat_int) (B tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_int F B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int F X3)) (tptp.aa_rat_int F Y3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) (tptp.aa_rat_int F C))))))) (forall ((A tptp.rat) (F tptp.fun_num_rat) (B tptp.num) (C tptp.num)) (=> (= A (tptp.aa_num_rat F B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F X3)) (tptp.aa_num_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_num_rat F C))))))) (forall ((A tptp.num) (F tptp.fun_num_num) (B tptp.num) (C tptp.num)) (=> (= A (tptp.aa_num_num F B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y3)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F X3)) (tptp.aa_num_num F Y3))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) (tptp.aa_num_num F C))))))) (forall ((A tptp.nat) (F tptp.fun_num_nat) (B tptp.num) (C tptp.num)) (=> (= A (tptp.aa_num_nat F B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat F X3)) (tptp.aa_num_nat F Y3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) (tptp.aa_num_nat F C))))))) (forall ((A tptp.int) (F tptp.fun_num_int) (B tptp.num) (C tptp.num)) (=> (= A (tptp.aa_num_int F B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int F X3)) (tptp.aa_num_int F Y3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) (tptp.aa_num_int F C))))))) (forall ((A tptp.rat) (F tptp.fun_nat_rat) (B tptp.nat) (C tptp.nat)) (=> (= A (tptp.aa_nat_rat F B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) C)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F X3)) (tptp.aa_nat_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_nat_rat F C))))))) (forall ((A tptp.num) (F tptp.fun_nat_num) (B tptp.nat) (C tptp.nat)) (=> (= A (tptp.aa_nat_num F B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) C)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) Y3)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F X3)) (tptp.aa_nat_num F Y3))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) (tptp.aa_nat_num F C))))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (= (tptp.aa_rat_rat F B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (= (tptp.aa_rat_num F B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y3)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F X3)) (tptp.aa_rat_num F Y3))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (= (tptp.aa_rat_nat F B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_rat_nat F X3)) (tptp.aa_rat_nat F Y3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_rat_nat F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_int) (C tptp.int)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (= (tptp.aa_rat_int F B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int F X3)) (tptp.aa_rat_int F Y3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int F A)) C)))))) (forall ((A tptp.num) (B tptp.num) (F tptp.fun_num_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (= (tptp.aa_num_rat F B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F X3)) (tptp.aa_num_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F A)) C)))))) (forall ((A tptp.num) (B tptp.num) (F tptp.fun_num_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (= (tptp.aa_num_num F B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y3)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F X3)) (tptp.aa_num_num F Y3))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F A)) C)))))) (forall ((A tptp.num) (B tptp.num) (F tptp.fun_num_nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (= (tptp.aa_num_nat F B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat F X3)) (tptp.aa_num_nat F Y3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat F A)) C)))))) (forall ((A tptp.num) (B tptp.num) (F tptp.fun_num_int) (C tptp.int)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (= (tptp.aa_num_int F B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int F X3)) (tptp.aa_num_int F Y3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int F A)) C)))))) (forall ((A tptp.nat) (B tptp.nat) (F tptp.fun_nat_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (= (tptp.aa_nat_rat F B) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F X3)) (tptp.aa_nat_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F A)) C)))))) (forall ((A tptp.nat) (B tptp.nat) (F tptp.fun_nat_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (= (tptp.aa_nat_num F B) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) Y3)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F X3)) (tptp.aa_nat_num F Y3))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F A)) C)))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X)))) (forall ((X tptp.num) (Y tptp.num)) (=> (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X)))) (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int Y) X)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X) Y)) (= X Y)))) (forall ((Y tptp.rat) (X tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (= X Y)))) (forall ((Y tptp.num) (X tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) X)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (= X Y)))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (= X Y)))) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (= X Y)))) (forall ((A3 tptp.set_nat) (K tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat K))) (=> (= A3 (tptp.aa_set_nat_set_nat _let_1 A)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B) (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A) B)))))) (forall ((A3 tptp.assn) (K tptp.assn) (A tptp.assn) (B tptp.assn)) (let ((_let_1 (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn K))) (=> (= A3 (tptp.aa_assn_assn _let_1 A)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A3) B) (tptp.aa_assn_assn _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A) B)))))) (forall ((A3 tptp.nat) (K tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat K))) (=> (= A3 (tptp.aa_nat_nat _let_1 A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat A3) B) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat A) B)))))) (forall ((A3 tptp.product_unit) (K tptp.product_unit) (A tptp.product_unit) (B tptp.product_unit)) (let ((_let_1 (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit K))) (=> (= A3 (tptp.aa_Pro8294289767544744956t_unit _let_1 A)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit A3) B) (tptp.aa_Pro8294289767544744956t_unit _let_1 (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit A) B)))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (K tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat K))) (=> (= A3 (tptp.aa_set8868280134176360700at_nat _let_1 A)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B) (tptp.aa_set8868280134176360700at_nat _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A) B)))))) (forall ((B3 tptp.set_nat) (K tptp.set_nat) (B tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A))) (let ((_let_2 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat K))) (=> (= B3 (tptp.aa_set_nat_set_nat _let_2 B)) (= (tptp.aa_set_nat_set_nat _let_1 B3) (tptp.aa_set_nat_set_nat _let_2 (tptp.aa_set_nat_set_nat _let_1 B))))))) (forall ((B3 tptp.assn) (K tptp.assn) (B tptp.assn) (A tptp.assn)) (let ((_let_1 (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A))) (let ((_let_2 (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn K))) (=> (= B3 (tptp.aa_assn_assn _let_2 B)) (= (tptp.aa_assn_assn _let_1 B3) (tptp.aa_assn_assn _let_2 (tptp.aa_assn_assn _let_1 B))))))) (forall ((B3 tptp.nat) (K tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat A))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat K))) (=> (= B3 (tptp.aa_nat_nat _let_2 B)) (= (tptp.aa_nat_nat _let_1 B3) (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat _let_1 B))))))) (forall ((B3 tptp.product_unit) (K tptp.product_unit) (B tptp.product_unit) (A tptp.product_unit)) (let ((_let_1 (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit A))) (let ((_let_2 (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit K))) (=> (= B3 (tptp.aa_Pro8294289767544744956t_unit _let_2 B)) (= (tptp.aa_Pro8294289767544744956t_unit _let_1 B3) (tptp.aa_Pro8294289767544744956t_unit _let_2 (tptp.aa_Pro8294289767544744956t_unit _let_1 B))))))) (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (K tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A))) (let ((_let_2 (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat K))) (=> (= B3 (tptp.aa_set8868280134176360700at_nat _let_2 B)) (= (tptp.aa_set8868280134176360700at_nat _let_1 B3) (tptp.aa_set8868280134176360700at_nat _let_2 (tptp.aa_set8868280134176360700at_nat _let_1 B))))))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (K tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat K))) (=> (= A3 (tptp.aa_set5535132180132642428at_nat _let_1 A)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3) B) (tptp.aa_set5535132180132642428at_nat _let_1 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A) B)))))) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (K tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat K))) (=> (= A3 (tptp.aa_set6734554978791863420at_nat _let_1 A)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3) B) (tptp.aa_set6734554978791863420at_nat _let_1 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A) B)))))) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (K tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat K))) (=> (= A3 (tptp.aa_set4883462369968598652at_nat _let_1 A)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3) B) (tptp.aa_set4883462369968598652at_nat _let_1 (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A) B)))))) (forall ((A3 tptp.set_nat) (K tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat K))) (=> (= A3 (tptp.aa_set_nat_set_nat _let_1 A)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B) (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A) B)))))) (forall ((A3 tptp.nat) (K tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat K))) (=> (= A3 (tptp.aa_nat_nat _let_1 A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat A3) B) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat A) B)))))) (forall ((B3 tptp.set_Pr8693737435421807431at_nat) (K tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A))) (let ((_let_2 (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat K))) (=> (= B3 (tptp.aa_set5535132180132642428at_nat _let_2 B)) (= (tptp.aa_set5535132180132642428at_nat _let_1 B3) (tptp.aa_set5535132180132642428at_nat _let_2 (tptp.aa_set5535132180132642428at_nat _let_1 B))))))) (forall ((B3 tptp.set_Pr8551490117392284871at_nat) (K tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A))) (let ((_let_2 (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat K))) (=> (= B3 (tptp.aa_set6734554978791863420at_nat _let_2 B)) (= (tptp.aa_set6734554978791863420at_nat _let_1 B3) (tptp.aa_set6734554978791863420at_nat _let_2 (tptp.aa_set6734554978791863420at_nat _let_1 B))))))) (forall ((B3 tptp.set_Pr4329608150637261639at_nat) (K tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A))) (let ((_let_2 (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat K))) (=> (= B3 (tptp.aa_set4883462369968598652at_nat _let_2 B)) (= (tptp.aa_set4883462369968598652at_nat _let_1 B3) (tptp.aa_set4883462369968598652at_nat _let_2 (tptp.aa_set4883462369968598652at_nat _let_1 B))))))) (forall ((B3 tptp.set_nat) (K tptp.set_nat) (B tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A))) (let ((_let_2 (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat K))) (=> (= B3 (tptp.aa_set_nat_set_nat _let_2 B)) (= (tptp.aa_set_nat_set_nat _let_1 B3) (tptp.aa_set_nat_set_nat _let_2 (tptp.aa_set_nat_set_nat _let_1 B))))))) (forall ((B3 tptp.nat) (K tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat A))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat K))) (=> (= B3 (tptp.aa_nat_nat _let_2 B)) (= (tptp.aa_nat_nat _let_1 B3) (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat _let_1 B))))))) (forall ((A tptp.set_Pr1261947904930325089at_nat)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat tptp.bot_bo2099793752762293965at_nat) A))) (forall ((A tptp.set_bool)) (tptp.ord_less_eq_set_bool tptp.bot_bot_set_bool A)) (forall ((A tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A))) (forall ((A tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A))) (forall ((A tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.bot_bot_nat) A))) (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A) tptp.bot_bo2099793752762293965at_nat)) (= A tptp.bot_bo2099793752762293965at_nat))) (forall ((A tptp.set_bool)) (= (tptp.ord_less_eq_set_bool A tptp.bot_bot_set_bool) (= A tptp.bot_bot_set_bool))) (forall ((A tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat)) (= A tptp.bot_bot_set_nat))) (forall ((A tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int)) (= A tptp.bot_bot_set_int))) (forall ((A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.bot_bot_nat)) (= A tptp.bot_bot_nat))) (forall ((A tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A) tptp.bot_bo2099793752762293965at_nat)) (= A tptp.bot_bo2099793752762293965at_nat))) (forall ((A tptp.set_bool)) (=> (tptp.ord_less_eq_set_bool A tptp.bot_bot_set_bool) (= A tptp.bot_bot_set_bool))) (forall ((A tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat)) (= A tptp.bot_bot_set_nat))) (forall ((A tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int)) (= A tptp.bot_bot_set_int))) (forall ((A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.bot_bot_nat)) (= A tptp.bot_bot_nat))) (forall ((X tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat X) tptp.bot_bo5327735625951526323at_nat) X)) (forall ((X tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat X) tptp.bot_bo8422036546324065075at_nat) X)) (forall ((X tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat X) tptp.bot_bo228742789529271731at_nat) X)) (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat X) tptp.bot_bo2099793752762293965at_nat) X)) (forall ((X tptp.set_bool)) (= (tptp.aa_set_bool_set_bool (tptp.aa_set4734229006438377534t_bool tptp.sup_sup_set_bool X) tptp.bot_bot_set_bool) X)) (forall ((X tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat X) tptp.bot_bot_set_nat) X)) (forall ((X tptp.set_int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int X) tptp.bot_bot_set_int) X)) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X))) (= (tptp.aa_assn_assn _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn Y) Z)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn (tptp.aa_assn_assn _let_1 Y)) (tptp.aa_assn_assn _let_1 Z))))) (forall ((X tptp.product_unit) (Y tptp.product_unit) (Z tptp.product_unit)) (let ((_let_1 (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X))) (= (tptp.aa_Pro8294289767544744956t_unit _let_1 (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.sup_sup_Product_unit Y) Z)) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.sup_sup_Product_unit (tptp.aa_Pro8294289767544744956t_unit _let_1 Y)) (tptp.aa_Pro8294289767544744956t_unit _let_1 Z))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X))) (= (tptp.aa_set8868280134176360700at_nat _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat Y) Z)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat (tptp.aa_set8868280134176360700at_nat _let_1 Y)) (tptp.aa_set8868280134176360700at_nat _let_1 Z))))) (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat X))) (= (tptp.aa_set5535132180132642428at_nat _let_1 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat Y) Z)) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat (tptp.aa_set5535132180132642428at_nat _let_1 Y)) (tptp.aa_set5535132180132642428at_nat _let_1 Z))))) (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat X))) (= (tptp.aa_set6734554978791863420at_nat _let_1 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat Y) Z)) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat (tptp.aa_set6734554978791863420at_nat _let_1 Y)) (tptp.aa_set6734554978791863420at_nat _let_1 Z))))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat X))) (= (tptp.aa_set4883462369968598652at_nat _let_1 (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat Y) Z)) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat (tptp.aa_set4883462369968598652at_nat _let_1 Y)) (tptp.aa_set4883462369968598652at_nat _let_1 Z))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X))) (= (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat Y) Z)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.aa_set_nat_set_nat _let_1 Y)) (tptp.aa_set_nat_set_nat _let_1 Z))))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn X))) (= (tptp.aa_assn_assn _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn Y) Z)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn (tptp.aa_assn_assn _let_1 Y)) (tptp.aa_assn_assn _let_1 Z))))) (forall ((X tptp.product_unit) (Y tptp.product_unit) (Z tptp.product_unit)) (let ((_let_1 (tptp.aa_Pro1375803928533059540t_unit tptp.sup_sup_Product_unit X))) (= (tptp.aa_Pro8294289767544744956t_unit _let_1 (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit Y) Z)) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit (tptp.aa_Pro8294289767544744956t_unit _let_1 Y)) (tptp.aa_Pro8294289767544744956t_unit _let_1 Z))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat X))) (= (tptp.aa_set8868280134176360700at_nat _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat Y) Z)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.aa_set8868280134176360700at_nat _let_1 Y)) (tptp.aa_set8868280134176360700at_nat _let_1 Z))))) (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat X))) (= (tptp.aa_set5535132180132642428at_nat _let_1 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat Y) Z)) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat (tptp.aa_set5535132180132642428at_nat _let_1 Y)) (tptp.aa_set5535132180132642428at_nat _let_1 Z))))) (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat X))) (= (tptp.aa_set6734554978791863420at_nat _let_1 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat Y) Z)) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat (tptp.aa_set6734554978791863420at_nat _let_1 Y)) (tptp.aa_set6734554978791863420at_nat _let_1 Z))))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat X))) (= (tptp.aa_set4883462369968598652at_nat _let_1 (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat Y) Z)) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat (tptp.aa_set4883462369968598652at_nat _let_1 Y)) (tptp.aa_set4883462369968598652at_nat _let_1 Z))))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat X))) (= (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat Y) Z)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.aa_set_nat_set_nat _let_1 Y)) (tptp.aa_set_nat_set_nat _let_1 Z))))) (forall ((Y tptp.assn) (Z tptp.assn) (X tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn Y) Z)) X) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn Y) X)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn Z) X)))) (forall ((Y tptp.product_unit) (Z tptp.product_unit) (X tptp.product_unit)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.sup_sup_Product_unit Y) Z)) X) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.sup_sup_Product_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit Y) X)) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit Z) X)))) (forall ((Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat Y) Z)) X) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat Y) X)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat Z) X)))) (forall ((Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat) (X tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat Y) Z)) X) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat Y) X)) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat Z) X)))) (forall ((Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat) (X tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat Y) Z)) X) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat Y) X)) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat Z) X)))) (forall ((Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat Y) Z)) X) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat Y) X)) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat Z) X)))) (forall ((Y tptp.set_nat) (Z tptp.set_nat) (X tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat Y) Z)) X) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat Y) X)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat Z) X)))) (forall ((Y tptp.assn) (Z tptp.assn) (X tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn Y) Z)) X) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn Y) X)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn Z) X)))) (forall ((Y tptp.product_unit) (Z tptp.product_unit) (X tptp.product_unit)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.sup_sup_Product_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit Y) Z)) X) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.sup_sup_Product_unit Y) X)) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.sup_sup_Product_unit Z) X)))) (forall ((Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat Y) Z)) X) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat Y) X)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat Z) X)))) (forall ((Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat) (X tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat Y) Z)) X) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat Y) X)) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat Z) X)))) (forall ((Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat) (X tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat Y) Z)) X) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat Y) X)) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat Z) X)))) (forall ((Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat Y) Z)) X) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat Y) X)) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat Z) X)))) (forall ((Y tptp.set_nat) (Z tptp.set_nat) (X tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat Y) Z)) X) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat Y) X)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat Z) X)))) (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat)) (= (tptp.sup_su1419176701018045153at_nat (tptp.some_s579751585967276588at_nat X) (tptp.some_s579751585967276588at_nat Y)) (tptp.some_s579751585967276588at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat X) Y)))) (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat)) (= (tptp.sup_su5873096292857799009at_nat (tptp.some_s287724117700012716at_nat X) (tptp.some_s287724117700012716at_nat Y)) (tptp.some_s287724117700012716at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat X) Y)))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (= (tptp.sup_su2273273666271716065at_nat (tptp.some_s5890477192898017836at_nat X) (tptp.some_s5890477192898017836at_nat Y)) (tptp.some_s5890477192898017836at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat X) Y)))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (tptp.sup_su3598758113090618626et_nat (tptp.some_set_nat X) (tptp.some_set_nat Y)) (tptp.some_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat X) Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.sup_sup_option_nat (tptp.aa_nat_option_nat tptp.some_nat X) (tptp.aa_nat_option_nat tptp.some_nat Y)) (tptp.aa_nat_option_nat tptp.some_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat X) Y)))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (tptp.inf_in7812914138253463912et_nat (tptp.some_set_nat X) (tptp.some_set_nat Y)) (tptp.some_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X) Y)))) (forall ((X tptp.assn) (Y tptp.assn)) (= (tptp.inf_inf_option_assn (tptp.some_assn X) (tptp.some_assn Y)) (tptp.some_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X) Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.inf_inf_option_nat (tptp.aa_nat_option_nat tptp.some_nat X) (tptp.aa_nat_option_nat tptp.some_nat Y)) (tptp.aa_nat_option_nat tptp.some_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat X) Y)))) (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (tptp.inf_in5800606384722953409t_unit (tptp.some_Product_unit X) (tptp.some_Product_unit Y)) (tptp.some_Product_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X) Y)))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (tptp.inf_in777885744494410645at_nat (tptp.some_s147305329494351046at_nat X) (tptp.some_s147305329494351046at_nat Y)) (tptp.some_s147305329494351046at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X) Y)))) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (tptp.ord_le353528952715127954et_int (tptp.some_set_int X) (tptp.some_set_int Y)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.ord_le2406147912482264968on_rat (tptp.some_rat X) (tptp.some_rat Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.pp (tptp.aa_option_num_bool (tptp.aa_opt4409681509335781342m_bool tptp.ord_le6622620407824499402on_num (tptp.aa_num_option_num tptp.some_num X)) (tptp.aa_num_option_num tptp.some_num Y))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.ord_le5914376470875661696on_nat (tptp.aa_nat_option_nat tptp.some_nat X) (tptp.aa_nat_option_nat tptp.some_nat Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.ord_le1736525451366464988on_int (tptp.aa_int_option_int tptp.some_int X) (tptp.aa_int_option_int tptp.some_int Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)))) (not (forall ((R2 tptp.a) (H5 tptp.heap_e7401611519738050253t_unit)) (=> (exists ((T2 tptp.nat)) (= (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a tptp.c) tptp.h2) (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat R2) (tptp.produc584006145561248582it_nat H5 T2))))) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn (tptp.aa_a_assn tptp.q R2)) (tptp.produc7507926704131184380et_nat H5 (tptp.hoare_new_addrs tptp.h2 tptp.as1 H5)))) (=> (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.relH (tptp.collect_nat tptp.aTP_Lamm_ag) tptp.h2) H5)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.lim_Product_unit tptp.h2)) (tptp.lim_Product_unit H5))))))))) (forall ((X2 tptp.produc3260487557148687353it_nat) (Y2 tptp.produc3260487557148687353it_nat)) (= (= (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat X2) (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat Y2)) (= X2 Y2))) (forall ((X2 tptp.num) (Y2 tptp.num)) (= (= (tptp.aa_num_option_num tptp.some_num X2) (tptp.aa_num_option_num tptp.some_num Y2)) (= X2 Y2))) (forall ((X2 tptp.produc8664842809031399944it_nat) (Y2 tptp.produc8664842809031399944it_nat)) (= (= (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat X2) (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat Y2)) (= X2 Y2))) (forall ((X5 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool tptp.bot_bo8343409700046576086t_bool X5)) (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat X5) tptp.bot_bot_set_set_nat)))) (forall ((X5 tptp.product_prod_nat_nat)) (= (tptp.pp (tptp.aa_Pro2232559814647311250t_bool tptp.bot_bo3782518310583830573t_bool X5)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat X5) tptp.bot_bo2099793752762293965at_nat)))) (forall ((X5 tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool tptp.bot_bo4756488196683355415l_bool X5)) (tptp.pp (tptp.member_bool X5 tptp.bot_bot_set_bool)))) (forall ((X5 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool tptp.bot_bot_fun_nat_bool X5)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X5) tptp.bot_bot_set_nat)))) (forall ((X5 tptp.int)) (= (tptp.pp (tptp.aa_int_bool tptp.bot_bot_fun_int_bool X5)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X5) tptp.bot_bot_set_int)))) (forall ((P tptp.fun_Pr803113274115125473t_bool)) (= (= (tptp.collec213857154873943460nt_int P) tptp.bot_bo1796632182523588997nt_int) (= P tptp.bot_bo6051839928536000373t_bool))) (forall ((P tptp.fun_list_nat_bool)) (= (= (tptp.collect_list_nat P) tptp.bot_bot_set_list_nat) (= P tptp.bot_bo6469247547558333820t_bool))) (forall ((P tptp.fun_set_nat_bool)) (= (= (tptp.collect_set_nat P) tptp.bot_bot_set_set_nat) (= P tptp.bot_bo8343409700046576086t_bool))) (forall ((P tptp.fun_Pr7757163693017731481t_bool)) (= (= (tptp.collec3392354462482085612at_nat P) tptp.bot_bo2099793752762293965at_nat) (= P tptp.bot_bo3782518310583830573t_bool))) (forall ((P tptp.fun_bool_bool)) (= (= (tptp.collect_bool P) tptp.bot_bot_set_bool) (= P tptp.bot_bo4756488196683355415l_bool))) (forall ((P tptp.fun_nat_bool)) (= (= (tptp.collect_nat P) tptp.bot_bot_set_nat) (= P tptp.bot_bot_fun_nat_bool))) (forall ((P tptp.fun_int_bool)) (= (= (tptp.collect_int P) tptp.bot_bot_set_int) (= P tptp.bot_bot_fun_int_bool))) (forall ((X tptp.produc6768802789813714928nt_int)) (not (forall ((F2 tptp.fun_in6429348457993719614e_term) (A4 tptp.int) (B4 tptp.int)) (not (= X (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int F2) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A4) B4))))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A) A2)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat B) B2)) (=> (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A2) B2) tptp.bot_bo2099793752762293965at_nat) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A) B) tptp.bot_bo2099793752762293965at_nat))))) (forall ((A tptp.set_bool) (A2 tptp.set_bool) (B tptp.set_bool) (B2 tptp.set_bool)) (=> (tptp.ord_less_eq_set_bool A A2) (=> (tptp.ord_less_eq_set_bool B B2) (=> (= (tptp.inf_inf_set_bool A2 B2) tptp.bot_bot_set_bool) (= (tptp.inf_inf_set_bool A B) tptp.bot_bot_set_bool))))) (forall ((A tptp.set_nat) (A2 tptp.set_nat) (B tptp.set_nat) (B2 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A) A2)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B) B2)) (=> (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A2) B2) tptp.bot_bot_set_nat) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A) B) tptp.bot_bot_set_nat))))) (forall ((A tptp.set_int) (A2 tptp.set_int) (B tptp.set_int) (B2 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) A2)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) B2)) (=> (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A2) B2) tptp.bot_bot_set_int) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A) B) tptp.bot_bot_set_int))))) (forall ((A tptp.set_set_nat) (B tptp.set_set_nat)) (=> (forall ((X3 tptp.set_nat)) (let ((_let_1 (tptp.member_set_nat X3))) (=> (tptp.pp (tptp.aa_set_set_nat_bool _let_1 A)) (not (tptp.pp (tptp.aa_set_set_nat_bool _let_1 B)))))) (= (tptp.inf_inf_set_set_nat A B) tptp.bot_bot_set_set_nat))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.product_prod_nat_nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat X3))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 A)) (not (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 B)))))) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A) B) tptp.bot_bo2099793752762293965at_nat))) (forall ((A tptp.set_bool) (B tptp.set_bool)) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 A)) (not (tptp.pp (tptp.member_bool X3 B))))) (= (tptp.inf_inf_set_bool A B) tptp.bot_bot_set_bool))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (tptp.member_nat X3))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A)) (not (tptp.pp (tptp.aa_set_nat_bool _let_1 B)))))) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A) B) tptp.bot_bot_set_nat))) (forall ((A tptp.set_int) (B tptp.set_int)) (=> (forall ((X3 tptp.int)) (let ((_let_1 (tptp.member_int X3))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 A)) (not (tptp.pp (tptp.aa_set_int_bool _let_1 B)))))) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A) B) tptp.bot_bot_set_int))) (forall ((M tptp.set_int) (X tptp.option_set_int)) (=> (tptp.ord_le353528952715127954et_int (tptp.some_set_int M) X) (not (forall ((M2 tptp.set_int)) (=> (= X (tptp.some_set_int M2)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int M) M2)))))))) (forall ((M tptp.rat) (X tptp.option_rat)) (=> (tptp.ord_le2406147912482264968on_rat (tptp.some_rat M) X) (not (forall ((M2 tptp.rat)) (=> (= X (tptp.some_rat M2)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat M) M2)))))))) (forall ((M tptp.num) (X tptp.option_num)) (=> (tptp.pp (tptp.aa_option_num_bool (tptp.aa_opt4409681509335781342m_bool tptp.ord_le6622620407824499402on_num (tptp.aa_num_option_num tptp.some_num M)) X)) (not (forall ((M2 tptp.num)) (=> (= X (tptp.aa_num_option_num tptp.some_num M2)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) M2)))))))) (forall ((M tptp.nat) (X tptp.option_nat)) (=> (tptp.ord_le5914376470875661696on_nat (tptp.aa_nat_option_nat tptp.some_nat M) X) (not (forall ((M2 tptp.nat)) (=> (= X (tptp.aa_nat_option_nat tptp.some_nat M2)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) M2)))))))) (forall ((M tptp.int) (X tptp.option_int)) (=> (tptp.ord_le1736525451366464988on_int (tptp.aa_int_option_int tptp.some_int M) X) (not (forall ((M2 tptp.int)) (=> (= X (tptp.aa_int_option_int tptp.some_int M2)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int M) M2)))))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.product_prod_nat_nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat X3))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 A3)) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 B3))))) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A3) B3)))) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool)) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 A3)) (tptp.pp (tptp.member_bool X3 B3)))) (tptp.ord_less_eq_set_bool A3 B3))) (forall ((A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (=> (forall ((X3 tptp.set_nat)) (let ((_let_1 (tptp.member_set_nat X3))) (=> (tptp.pp (tptp.aa_set_set_nat_bool _let_1 A3)) (tptp.pp (tptp.aa_set_set_nat_bool _let_1 B3))))) (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat A3) B3)))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (tptp.member_nat X3))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A3)) (tptp.pp (tptp.aa_set_nat_bool _let_1 B3))))) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) B3)))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (forall ((X3 tptp.int)) (let ((_let_1 (tptp.member_int X3))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 A3)) (tptp.pp (tptp.aa_set_int_bool _let_1 B3))))) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) A3)) (= A3 B3)))) (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.relH _let_75 tptp.h2) tptp.h)) (forall ((X tptp.assn) (Y tptp.assn)) (= (tptp.ord_less_option_assn (tptp.some_assn X) (tptp.some_assn Y)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.ord_less_option_rat (tptp.some_rat X) (tptp.some_rat Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.pp (tptp.aa_option_num_bool (tptp.aa_opt4409681509335781342m_bool tptp.ord_less_option_num (tptp.aa_num_option_num tptp.some_num X)) (tptp.aa_num_option_num tptp.some_num Y))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.ord_less_option_nat (tptp.aa_nat_option_nat tptp.some_nat X) (tptp.aa_nat_option_nat tptp.some_nat Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.ord_less_option_int (tptp.aa_int_option_int tptp.some_int X) (tptp.aa_int_option_int tptp.some_int Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)))) (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.relH _let_76 tptp.h2) tptp.h)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat tptp.as2) _let_75)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat _let_76) _let_75)) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat X))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A3) B3)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 A3)) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 B3)))))) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool) (X tptp.bool)) (=> (tptp.ord_less_eq_set_bool A3 B3) (=> (tptp.pp (tptp.member_bool X A3)) (tptp.pp (tptp.member_bool X B3))))) (forall ((A3 tptp.set_set_nat) (B3 tptp.set_set_nat) (X tptp.set_nat)) (let ((_let_1 (tptp.member_set_nat X))) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat A3) B3)) (=> (tptp.pp (tptp.aa_set_set_nat_bool _let_1 A3)) (tptp.pp (tptp.aa_set_set_nat_bool _let_1 B3)))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (X tptp.nat)) (let ((_let_1 (tptp.member_nat X))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) B3)) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A3)) (tptp.pp (tptp.aa_set_nat_bool _let_1 B3)))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (X tptp.int)) (let ((_let_1 (tptp.member_int X))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 A3)) (tptp.pp (tptp.aa_set_int_bool _let_1 B3)))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C tptp.product_prod_nat_nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat C))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A3) B3)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 A3)) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 B3)))))) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool) (C tptp.bool)) (=> (tptp.ord_less_eq_set_bool A3 B3) (=> (tptp.pp (tptp.member_bool C A3)) (tptp.pp (tptp.member_bool C B3))))) (forall ((A3 tptp.set_set_nat) (B3 tptp.set_set_nat) (C tptp.set_nat)) (let ((_let_1 (tptp.member_set_nat C))) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat A3) B3)) (=> (tptp.pp (tptp.aa_set_set_nat_bool _let_1 A3)) (tptp.pp (tptp.aa_set_set_nat_bool _let_1 B3)))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C tptp.nat)) (let ((_let_1 (tptp.member_nat C))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) B3)) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A3)) (tptp.pp (tptp.aa_set_nat_bool _let_1 B3)))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (C tptp.int)) (let ((_let_1 (tptp.member_int C))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 A3)) (tptp.pp (tptp.aa_set_int_bool _let_1 B3)))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (= A3 B3) (not (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) A3))))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A3) B3)) (forall ((X4 tptp.product_prod_nat_nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat X4))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 A3)) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 B3))))))) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool)) (= (tptp.ord_less_eq_set_bool A3 B3) (forall ((X4 tptp.bool)) (=> (tptp.pp (tptp.member_bool X4 A3)) (tptp.pp (tptp.member_bool X4 B3)))))) (forall ((A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (= (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat A3) B3)) (forall ((X4 tptp.set_nat)) (let ((_let_1 (tptp.member_set_nat X4))) (=> (tptp.pp (tptp.aa_set_set_nat_bool _let_1 A3)) (tptp.pp (tptp.aa_set_set_nat_bool _let_1 B3))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) B3)) (forall ((X4 tptp.nat)) (let ((_let_1 (tptp.member_nat X4))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A3)) (tptp.pp (tptp.aa_set_nat_bool _let_1 B3))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (forall ((X4 tptp.int)) (let ((_let_1 (tptp.member_int X4))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 A3)) (tptp.pp (tptp.aa_set_int_bool _let_1 B3))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (= A3 B3) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (= A3 B3) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) A3)))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A3) B3)) (forall ((T3 tptp.product_prod_nat_nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat T3))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 A3)) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 B3))))))) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool)) (= (tptp.ord_less_eq_set_bool A3 B3) (forall ((T3 tptp.bool)) (=> (tptp.pp (tptp.member_bool T3 A3)) (tptp.pp (tptp.member_bool T3 B3)))))) (forall ((A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (= (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat A3) B3)) (forall ((T3 tptp.set_nat)) (let ((_let_1 (tptp.member_set_nat T3))) (=> (tptp.pp (tptp.aa_set_set_nat_bool _let_1 A3)) (tptp.pp (tptp.aa_set_set_nat_bool _let_1 B3))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) B3)) (forall ((T3 tptp.nat)) (let ((_let_1 (tptp.member_nat T3))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A3)) (tptp.pp (tptp.aa_set_nat_bool _let_1 B3))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (forall ((T3 tptp.int)) (let ((_let_1 (tptp.member_int T3))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 A3)) (tptp.pp (tptp.aa_set_int_bool _let_1 B3))))))) (forall ((A3 tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) A3))) (forall ((P tptp.fun_Pr803113274115125473t_bool) (Q tptp.fun_Pr803113274115125473t_bool)) (=> (forall ((X3 tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool P X3)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool Q X3)))) (tptp.ord_le2843351958646193337nt_int (tptp.collec213857154873943460nt_int P) (tptp.collec213857154873943460nt_int Q)))) (forall ((P tptp.fun_list_nat_bool) (Q tptp.fun_list_nat_bool)) (=> (forall ((X3 tptp.list_nat)) (=> (tptp.pp (tptp.aa_list_nat_bool P X3)) (tptp.pp (tptp.aa_list_nat_bool Q X3)))) (tptp.ord_le6045566169113846134st_nat (tptp.collect_list_nat P) (tptp.collect_list_nat Q)))) (forall ((P tptp.fun_set_nat_bool) (Q tptp.fun_set_nat_bool)) (=> (forall ((X3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool P X3)) (tptp.pp (tptp.aa_set_nat_bool Q X3)))) (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat (tptp.collect_set_nat P)) (tptp.collect_set_nat Q))))) (forall ((P tptp.fun_nat_bool) (Q tptp.fun_nat_bool)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P X3)) (tptp.pp (tptp.aa_nat_bool Q X3)))) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.collect_nat P)) (tptp.collect_nat Q))))) (forall ((P tptp.fun_int_bool) (Q tptp.fun_int_bool)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool Q X3)))) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.collect_int P)) (tptp.collect_int Q))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (C3 tptp.set_int)) (let ((_let_1 (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 B3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) C3)) (tptp.pp (tptp.aa_set_int_bool _let_1 C3)))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (= A3 B3) (and (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) A3))))) (forall ((R tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat) (X5 tptp.product_prod_nat_nat)) (= (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_fun830836278467416944t_bool (tptp.sup_su5674415786711694021t_bool (tptp.aTP_Lamm_a R)) (tptp.aTP_Lamm_a S)) X5)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat X5) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat R) S))))) (forall ((R tptp.set_bool) (S tptp.set_bool) (X5 tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.sup_su2675241097686107055l_bool (tptp.aTP_Lamm_aa R) (tptp.aTP_Lamm_aa S)) X5)) (tptp.pp (tptp.member_bool X5 (tptp.aa_set_bool_set_bool (tptp.aa_set4734229006438377534t_bool tptp.sup_sup_set_bool R) S))))) (forall ((R tptp.set_set_nat) (S tptp.set_set_nat) (X5 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.sup_su7038862894554899774t_bool (tptp.aTP_Lamm_ad R) (tptp.aTP_Lamm_ad S)) X5)) (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat X5) (tptp.sup_sup_set_set_nat R S))))) (forall ((R tptp.set_int) (S tptp.set_int) (X5 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.sup_sup_fun_int_bool (tptp.aTP_Lamm_af R) (tptp.aTP_Lamm_af S)) X5)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X5) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int R) S))))) (forall ((R tptp.set_Pr8693737435421807431at_nat) (S tptp.set_Pr8693737435421807431at_nat) (X5 tptp.produc859450856879609959at_nat)) (= (tptp.pp (tptp.aa_Pro6098352494050694700t_bool (tptp.sup_su3901408610078580575t_bool (tptp.aTP_Lamm_ai R) (tptp.aTP_Lamm_ai S)) X5)) (tptp.member8206827879206165904at_nat X5 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat R) S)))) (forall ((R tptp.set_Pr8551490117392284871at_nat) (S tptp.set_Pr8551490117392284871at_nat) (X5 tptp.produc4166570645942440679at_nat)) (= (tptp.pp (tptp.aa_Pro5063669228512387756t_bool (tptp.sup_su2357402678989182943t_bool (tptp.aTP_Lamm_aj R) (tptp.aTP_Lamm_aj S)) X5)) (tptp.member6689249552917799696at_nat X5 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat R) S)))) (forall ((R tptp.set_Pr4329608150637261639at_nat) (S tptp.set_Pr4329608150637261639at_nat) (X5 tptp.produc3843707927480180839at_nat)) (= (tptp.pp (tptp.aa_Pro1809015098595223084t_bool (tptp.sup_su5834520091132235615t_bool (tptp.aTP_Lamm_ak R) (tptp.aTP_Lamm_ak S)) X5)) (tptp.member8757157785044589968at_nat X5 (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat R) S)))) (forall ((R tptp.set_nat) (S tptp.set_nat) (X5 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.sup_sup_fun_nat_bool (tptp.aTP_Lamm_ae R) (tptp.aTP_Lamm_ae S)) X5)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X5) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat R) S))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (P tptp.fun_Pr7757163693017731481t_bool)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat (tptp.collec3392354462482085612at_nat (tptp.aa_fun830836278467416944t_bool (tptp.aTP_Lamm_al A3) P))) A3))) (forall ((A3 tptp.set_bool) (P tptp.fun_bool_bool)) (tptp.ord_less_eq_set_bool (tptp.collect_bool (tptp.aa_fun8098540714523660868l_bool (tptp.aTP_Lamm_am A3) P)) A3)) (forall ((A3 tptp.set_Pr958786334691620121nt_int) (P tptp.fun_Pr803113274115125473t_bool)) (tptp.ord_le2843351958646193337nt_int (tptp.collec213857154873943460nt_int (tptp.aa_fun8917503761599146496t_bool (tptp.aTP_Lamm_an A3) P)) A3)) (forall ((A3 tptp.set_list_nat) (P tptp.fun_list_nat_bool)) (tptp.ord_le6045566169113846134st_nat (tptp.collect_list_nat (tptp.aa_fun6009467934925565500t_bool (tptp.aTP_Lamm_ao A3) P)) A3)) (forall ((A3 tptp.set_set_nat) (P tptp.fun_set_nat_bool)) (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat (tptp.collect_set_nat (tptp.aa_fun3565389549526402364t_bool (tptp.aTP_Lamm_ap A3) P))) A3))) (forall ((A3 tptp.set_nat) (P tptp.fun_nat_bool)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.collect_nat (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_aq A3) P))) A3))) (forall ((A3 tptp.set_int) (P tptp.fun_int_bool)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.collect_int (tptp.aa_fun5146555767781538748t_bool (tptp.aTP_Lamm_ar A3) P))) A3))) (forall ((R tptp.set_bool) (S tptp.set_bool) (X5 tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.inf_in9217375510005350933l_bool (tptp.aTP_Lamm_aa R) (tptp.aTP_Lamm_aa S)) X5)) (tptp.pp (tptp.member_bool X5 (tptp.inf_inf_set_bool R S))))) (forall ((R tptp.set_set_nat) (S tptp.set_set_nat) (X5 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.inf_in6168126700042863960t_bool (tptp.aTP_Lamm_ad R) (tptp.aTP_Lamm_ad S)) X5)) (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat X5) (tptp.inf_inf_set_set_nat R S))))) (forall ((R tptp.set_int) (S tptp.set_int) (X5 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.inf_inf_fun_int_bool (tptp.aTP_Lamm_af R) (tptp.aTP_Lamm_af S)) X5)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X5) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int R) S))))) (forall ((R tptp.set_nat) (S tptp.set_nat) (X5 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.inf_inf_fun_nat_bool (tptp.aTP_Lamm_ae R) (tptp.aTP_Lamm_ae S)) X5)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X5) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat R) S))))) (forall ((R tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat) (X5 tptp.product_prod_nat_nat)) (= (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_fun830836278467416944t_bool (tptp.inf_in2244499300375407147t_bool (tptp.aTP_Lamm_a R)) (tptp.aTP_Lamm_a S)) X5)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat X5) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat R) S))))) (forall ((R tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat) (X5 tptp.nat) (Xa3 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.sup_su8404041055355318397t_bool (tptp.aTP_Lamm_as R) (tptp.aTP_Lamm_as S)) X5) Xa3)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat X5) Xa3)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat R) S))))) (forall ((R tptp.set_Pr1106803562331729365et_nat) (S tptp.set_Pr1106803562331729365et_nat) (X5 tptp.fun_Pr6001797050664311790t_bool) (Xa3 tptp.produc3658429121746597890et_nat)) (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.aa_fun6808777976510360636t_bool (tptp.sup_su8473734197704899055t_bool (tptp.aTP_Lamm_at R) (tptp.aTP_Lamm_at S)) X5) Xa3)) (tptp.member8615881266069945910et_nat (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat X5) Xa3) (tptp.sup_su5640057190298842881et_nat R S)))) (forall ((R tptp.set_Pr9222568342844664434et_nat) (S tptp.set_Pr9222568342844664434et_nat) (X5 tptp.fun_Pr6001797050664311790t_bool) (Xa3 tptp.produc6108883039684432031et_nat)) (= (tptp.pp (tptp.aa_Pro7454463142485379962t_bool (tptp.aa_fun1003322038264691679t_bool (tptp.sup_su7193092575417274386t_bool (tptp.aTP_Lamm_au R) (tptp.aTP_Lamm_au S)) X5) Xa3)) (tptp.member2818932950976722259et_nat (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat X5) Xa3) (tptp.sup_su2440191842239582110et_nat R S)))) (forall ((R tptp.set_Pr233528076387193594nt_int) (S tptp.set_Pr233528076387193594nt_int) (X5 tptp.fun_Pr9164807099015279978e_term) (Xa3 tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun5300525129335604105t_bool (tptp.sup_su8737265340369414900t_bool (tptp.aTP_Lamm_av R) (tptp.aTP_Lamm_av S)) X5) Xa3)) (tptp.member690604328116145115nt_int (tptp.aa_Pro3513184699142849729nt_int (tptp.aa_fun1388719692539776744nt_int tptp.produc1560874099174258678nt_int X5) Xa3) (tptp.sup_su3143671203043873318nt_int R S)))) (forall ((R tptp.set_Pr5033440245338114598nt_int) (S tptp.set_Pr5033440245338114598nt_int) (X5 tptp.fun_in6429348457993719614e_term) (Xa3 tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun4446166836006121821t_bool (tptp.sup_su8464148172981958856t_bool (tptp.aTP_Lamm_aw R) (tptp.aTP_Lamm_aw S)) X5) Xa3)) (tptp.member500491123954006279nt_int (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int X5) Xa3) (tptp.sup_su1426507467619248466nt_int R S)))) (forall ((R tptp.set_Pr7098220151150636591it_nat) (S tptp.set_Pr7098220151150636591it_nat) (X5 tptp.a) (Xa3 tptp.produc6653097349344004940it_nat)) (= (tptp.pp (tptp.aa_Pro3182513528956304653t_bool (tptp.aa_a_f736957945511644770t_bool (tptp.sup_su496982905583290645t_bool (tptp.aTP_Lamm_ax R) (tptp.aTP_Lamm_ax S)) X5) Xa3)) (tptp.member4554412811331277712it_nat (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat X5) Xa3) (tptp.sup_su3211442154794319707it_nat R S)))) (forall ((R tptp.set_Pr8693737435421807431at_nat) (S tptp.set_Pr8693737435421807431at_nat) (X5 tptp.product_prod_nat_nat) (Xa3 tptp.product_prod_nat_nat)) (= (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool (tptp.sup_su8812873402214772865t_bool (tptp.aTP_Lamm_ay R) (tptp.aTP_Lamm_ay S)) X5) Xa3)) (tptp.member8206827879206165904at_nat (tptp.produc6161850002892822231at_nat X5 Xa3) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat R) S)))) (forall ((R tptp.set_Pr8551490117392284871at_nat) (S tptp.set_Pr8551490117392284871at_nat) (X5 tptp.multis2468970476368604999at_nat) (Xa3 tptp.multis2468970476368604999at_nat)) (= (tptp.pp (tptp.aa_mul7406001252470835788t_bool (tptp.aa_mul6531253083629095518t_bool (tptp.sup_su4244330202147125633t_bool (tptp.aTP_Lamm_az R) (tptp.aTP_Lamm_az S)) X5) Xa3)) (tptp.member6689249552917799696at_nat (tptp.produc4348348721325984599at_nat X5 Xa3) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat R) S)))) (forall ((R tptp.set_Pr4329608150637261639at_nat) (S tptp.set_Pr4329608150637261639at_nat) (X5 tptp.set_Pr1261947904930325089at_nat) (Xa3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool (tptp.sup_su794791877260760193t_bool (tptp.aTP_Lamm_ba R) (tptp.aTP_Lamm_ba S)) X5) Xa3)) (tptp.member8757157785044589968at_nat (tptp.produc2922128104949294807at_nat X5 Xa3) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat R) S)))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A3) B3)) (tptp.pp (tptp.aa_fun8663595511526100224l_bool (tptp.ord_le2468614981408567801t_bool (tptp.aTP_Lamm_a A3)) (tptp.aTP_Lamm_a B3))))) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool)) (= (tptp.ord_less_eq_set_bool A3 B3) (tptp.ord_le2902245940885495011l_bool (tptp.aTP_Lamm_aa A3) (tptp.aTP_Lamm_aa B3)))) (forall ((A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (= (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat A3) B3)) (tptp.ord_le1461730252015488778t_bool (tptp.aTP_Lamm_ad A3) (tptp.aTP_Lamm_ad B3)))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) B3)) (tptp.ord_le8840051076831633728t_bool (tptp.aTP_Lamm_ae A3) (tptp.aTP_Lamm_ae B3)))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (tptp.ord_le5715760110363009508t_bool (tptp.aTP_Lamm_af A3) (tptp.aTP_Lamm_af B3)))) (forall ((R tptp.set_Pr1106803562331729365et_nat) (S tptp.set_Pr1106803562331729365et_nat) (X5 tptp.fun_Pr6001797050664311790t_bool) (Xa3 tptp.produc3658429121746597890et_nat)) (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.aa_fun6808777976510360636t_bool (tptp.inf_in1653871643881371733t_bool (tptp.aTP_Lamm_at R) (tptp.aTP_Lamm_at S)) X5) Xa3)) (tptp.member8615881266069945910et_nat (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat X5) Xa3) (tptp.inf_in3597378546985178727et_nat R S)))) (forall ((R tptp.set_Pr9222568342844664434et_nat) (S tptp.set_Pr9222568342844664434et_nat) (X5 tptp.fun_Pr6001797050664311790t_bool) (Xa3 tptp.produc6108883039684432031et_nat)) (= (tptp.pp (tptp.aa_Pro7454463142485379962t_bool (tptp.aa_fun1003322038264691679t_bool (tptp.inf_in1990189605607894136t_bool (tptp.aTP_Lamm_au R) (tptp.aTP_Lamm_au S)) X5) Xa3)) (tptp.member2818932950976722259et_nat (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat X5) Xa3) (tptp.inf_in2726514487731080452et_nat R S)))) (forall ((R tptp.set_Pr233528076387193594nt_int) (S tptp.set_Pr233528076387193594nt_int) (X5 tptp.fun_Pr9164807099015279978e_term) (Xa3 tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun5300525129335604105t_bool (tptp.inf_in1149571566421838938t_bool (tptp.aTP_Lamm_av R) (tptp.aTP_Lamm_av S)) X5) Xa3)) (tptp.member690604328116145115nt_int (tptp.aa_Pro3513184699142849729nt_int (tptp.aa_fun1388719692539776744nt_int tptp.produc1560874099174258678nt_int X5) Xa3) (tptp.inf_in2887154609111356556nt_int R S)))) (forall ((R tptp.set_Pr5033440245338114598nt_int) (S tptp.set_Pr5033440245338114598nt_int) (X5 tptp.fun_in6429348457993719614e_term) (Xa3 tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun4446166836006121821t_bool (tptp.inf_in276823688150084142t_bool (tptp.aTP_Lamm_aw R) (tptp.aTP_Lamm_aw S)) X5) Xa3)) (tptp.member500491123954006279nt_int (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int X5) Xa3) (tptp.inf_in6211236335575333816nt_int R S)))) (forall ((R tptp.set_Pr7098220151150636591it_nat) (S tptp.set_Pr7098220151150636591it_nat) (X5 tptp.a) (Xa3 tptp.produc6653097349344004940it_nat)) (= (tptp.pp (tptp.aa_Pro3182513528956304653t_bool (tptp.aa_a_f736957945511644770t_bool (tptp.inf_in1512249387717995387t_bool (tptp.aTP_Lamm_ax R) (tptp.aTP_Lamm_ax S)) X5) Xa3)) (tptp.member4554412811331277712it_nat (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat X5) Xa3) (tptp.inf_in3493107508024165057it_nat R S)))) (forall ((R tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat) (X5 tptp.nat) (Xa3 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.inf_in183157752877997207t_bool (tptp.aTP_Lamm_as R) (tptp.aTP_Lamm_as S)) X5) Xa3)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat X5) Xa3)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat R) S))))) (forall ((P tptp.fun_Pr803113274115125473t_bool) (Q tptp.fun_Pr803113274115125473t_bool)) (= (tptp.ord_le2843351958646193337nt_int (tptp.collec213857154873943460nt_int P) (tptp.collec213857154873943460nt_int Q)) (forall ((X4 tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool P X4)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool Q X4)))))) (forall ((P tptp.fun_list_nat_bool) (Q tptp.fun_list_nat_bool)) (= (tptp.ord_le6045566169113846134st_nat (tptp.collect_list_nat P) (tptp.collect_list_nat Q)) (forall ((X4 tptp.list_nat)) (=> (tptp.pp (tptp.aa_list_nat_bool P X4)) (tptp.pp (tptp.aa_list_nat_bool Q X4)))))) (forall ((P tptp.fun_set_nat_bool) (Q tptp.fun_set_nat_bool)) (= (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat (tptp.collect_set_nat P)) (tptp.collect_set_nat Q))) (forall ((X4 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool P X4)) (tptp.pp (tptp.aa_set_nat_bool Q X4)))))) (forall ((P tptp.fun_nat_bool) (Q tptp.fun_nat_bool)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.collect_nat P)) (tptp.collect_nat Q))) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P X4)) (tptp.pp (tptp.aa_nat_bool Q X4)))))) (forall ((P tptp.fun_int_bool) (Q tptp.fun_int_bool)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.collect_int P)) (tptp.collect_int Q))) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P X4)) (tptp.pp (tptp.aa_int_bool Q X4)))))) (forall ((X5 tptp.fun_Pr6001797050664311790t_bool) (Xa3 tptp.produc3658429121746597890et_nat)) (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.aa_fun6808777976510360636t_bool tptp.bot_bo7579426410670377815t_bool X5) Xa3)) (tptp.member8615881266069945910et_nat (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat X5) Xa3) tptp.bot_bo4581812875773903977et_nat))) (forall ((X5 tptp.fun_Pr6001797050664311790t_bool) (Xa3 tptp.produc6108883039684432031et_nat)) (= (tptp.pp (tptp.aa_Pro7454463142485379962t_bool (tptp.aa_fun1003322038264691679t_bool tptp.bot_bo6981864666715171194t_bool X5) Xa3)) (tptp.member2818932950976722259et_nat (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat X5) Xa3) tptp.bot_bo2330764134935536902et_nat))) (forall ((X5 tptp.fun_Pr9164807099015279978e_term) (Xa3 tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun5300525129335604105t_bool tptp.bot_bo9220524098407837788t_bool X5) Xa3)) (tptp.member690604328116145115nt_int (tptp.aa_Pro3513184699142849729nt_int (tptp.aa_fun1388719692539776744nt_int tptp.produc1560874099174258678nt_int X5) Xa3) tptp.bot_bo5853814528170464142nt_int))) (forall ((X5 tptp.fun_in6429348457993719614e_term) (Xa3 tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun4446166836006121821t_bool tptp.bot_bo6140462223577857584t_bool X5) Xa3)) (tptp.member500491123954006279nt_int (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int X5) Xa3) tptp.bot_bo1891714543702108858nt_int))) (forall ((X5 tptp.a) (Xa3 tptp.produc6653097349344004940it_nat)) (= (tptp.pp (tptp.aa_Pro3182513528956304653t_bool (tptp.aa_a_f736957945511644770t_bool tptp.bot_bo457101921447070333t_bool X5) Xa3)) (tptp.member4554412811331277712it_nat (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat X5) Xa3) tptp.bot_bo8480459777671986371it_nat))) (forall ((X5 tptp.nat) (Xa3 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bot_bo6560894463593755925t_bool X5) Xa3)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat X5) Xa3)) tptp.bot_bo2099793752762293965at_nat)))) (forall ((R tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat)) (= (forall ((X4 tptp.nat) (Xa tptp.nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat X4) Xa)))) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 R)) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 S))))) (= R S))) (forall ((R tptp.set_Pr1106803562331729365et_nat) (S tptp.set_Pr1106803562331729365et_nat)) (= (forall ((X4 tptp.fun_Pr6001797050664311790t_bool) (Xa tptp.produc3658429121746597890et_nat)) (let ((_let_1 (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat X4) Xa))) (= (tptp.member8615881266069945910et_nat _let_1 R) (tptp.member8615881266069945910et_nat _let_1 S)))) (= R S))) (forall ((R tptp.set_Pr9222568342844664434et_nat) (S tptp.set_Pr9222568342844664434et_nat)) (= (forall ((X4 tptp.fun_Pr6001797050664311790t_bool) (Xa tptp.produc6108883039684432031et_nat)) (let ((_let_1 (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat X4) Xa))) (= (tptp.member2818932950976722259et_nat _let_1 R) (tptp.member2818932950976722259et_nat _let_1 S)))) (= R S))) (forall ((R tptp.set_Pr233528076387193594nt_int) (S tptp.set_Pr233528076387193594nt_int)) (= (forall ((X4 tptp.fun_Pr9164807099015279978e_term) (Xa tptp.product_prod_int_int)) (let ((_let_1 (tptp.aa_Pro3513184699142849729nt_int (tptp.aa_fun1388719692539776744nt_int tptp.produc1560874099174258678nt_int X4) Xa))) (= (tptp.member690604328116145115nt_int _let_1 R) (tptp.member690604328116145115nt_int _let_1 S)))) (= R S))) (forall ((R tptp.set_Pr5033440245338114598nt_int) (S tptp.set_Pr5033440245338114598nt_int)) (= (forall ((X4 tptp.fun_in6429348457993719614e_term) (Xa tptp.product_prod_int_int)) (let ((_let_1 (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int X4) Xa))) (= (tptp.member500491123954006279nt_int _let_1 R) (tptp.member500491123954006279nt_int _let_1 S)))) (= R S))) (forall ((R tptp.set_Pr7098220151150636591it_nat) (S tptp.set_Pr7098220151150636591it_nat)) (= (forall ((X4 tptp.a) (Xa tptp.produc6653097349344004940it_nat)) (let ((_let_1 (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat X4) Xa))) (= (tptp.member4554412811331277712it_nat _let_1 R) (tptp.member4554412811331277712it_nat _let_1 S)))) (= R S))) (forall ((R tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat)) (= (tptp.ord_le4899916226251588169t_bool (tptp.aTP_Lamm_as R) (tptp.aTP_Lamm_as S)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat R) S)))) (forall ((R tptp.set_Pr1106803562331729365et_nat) (S tptp.set_Pr1106803562331729365et_nat)) (= (tptp.ord_le782085092667036451t_bool (tptp.aTP_Lamm_at R) (tptp.aTP_Lamm_at S)) (tptp.ord_le8271263703964716597et_nat R S))) (forall ((R tptp.set_Pr9222568342844664434et_nat) (S tptp.set_Pr9222568342844664434et_nat)) (= (tptp.ord_le6285654293108895046t_bool (tptp.aTP_Lamm_au R) (tptp.aTP_Lamm_au S)) (tptp.ord_le4695037514429983442et_nat R S))) (forall ((R tptp.set_Pr233528076387193594nt_int) (S tptp.set_Pr233528076387193594nt_int)) (= (tptp.ord_le1486933126236225064t_bool (tptp.aTP_Lamm_av R) (tptp.aTP_Lamm_av S)) (tptp.ord_le5172437211506631514nt_int R S))) (forall ((R tptp.set_Pr5033440245338114598nt_int) (S tptp.set_Pr5033440245338114598nt_int)) (= (tptp.ord_le4148652360786930684t_bool (tptp.aTP_Lamm_aw R) (tptp.aTP_Lamm_aw S)) (tptp.ord_le172202941055982214nt_int R S))) (forall ((R tptp.set_Pr7098220151150636591it_nat) (S tptp.set_Pr7098220151150636591it_nat)) (= (tptp.ord_le3021217390550374985t_bool (tptp.aTP_Lamm_ax R) (tptp.aTP_Lamm_ax S)) (tptp.ord_le4478181985103859343it_nat R S))) (forall ((X tptp.rat)) (exists ((Y3 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y3) X)))) (forall ((X tptp.int)) (exists ((Y3 tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y3) X)))) (forall ((X tptp.rat)) (exists ((X_1 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) X_1)))) (forall ((X tptp.nat)) (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) X_1)))) (forall ((X tptp.int)) (exists ((X_1 tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) X_1)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (exists ((Z2 tptp.rat)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Z2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z2) Y)))))) (forall ((X tptp.assn) (Y tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X) Y)) (not (= X Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (not (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (not (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (not (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (not (= X Y)))) (forall ((A tptp.assn) (B tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) B)) (not (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn B) A))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A))))) (forall ((A tptp.num) (B tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) A))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A))))) (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (=> (= A B) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn B) C)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) C))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (= A B) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) C))))) (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (=> (= A B) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) C)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (= A B) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) C))))) (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A))) (=> (tptp.pp (tptp.aa_assn_bool _let_1 B)) (=> (= B C) (tptp.pp (tptp.aa_assn_bool _let_1 C)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (=> (= B C) (tptp.pp (tptp.aa_rat_bool _let_1 C)))))) (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num A))) (=> (tptp.pp (tptp.aa_num_bool _let_1 B)) (=> (= B C) (tptp.pp (tptp.aa_num_bool _let_1 C)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (=> (= B C) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (=> (= B C) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((P tptp.fun_nat_bool) (A tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (forall ((Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y4) X3)) (tptp.pp (tptp.aa_nat_bool P Y4)))) (tptp.pp (tptp.aa_nat_bool P X3)))) (tptp.pp (tptp.aa_nat_bool P A)))) (forall ((Y tptp.rat) (X tptp.rat)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X))) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y))) (= X Y)))) (forall ((Y tptp.num) (X tptp.num)) (=> (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X))) (= (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y))) (= X Y)))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X))) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y))) (= X Y)))) (forall ((Y tptp.int) (X tptp.int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X))) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y))) (= X Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y))) (=> (not (= X Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X))))) (forall ((X tptp.num) (Y tptp.num)) (=> (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y))) (=> (not (= X Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y))) (=> (not (= X Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X))))) (forall ((X tptp.int) (Y tptp.int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y))) (=> (not (= X Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X))))) (forall ((B tptp.assn) (A tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn B) A)) (not (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) B))))) (forall ((B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))))) (forall ((B tptp.num) (A tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) A)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B))))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B))))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B))))) (forall ((A tptp.assn)) (not (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) A)))) (forall ((A tptp.rat)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) A)))) (forall ((A tptp.num)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) A)))) (forall ((A tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) A)))) (forall ((A tptp.int)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) A)))) (forall ((P tptp.fun_nat_bool)) (= (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool P X_12))) (exists ((N tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool P N)) (forall ((M3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M3) N)) (not (tptp.pp (tptp.aa_nat_bool P M3))))))))) (forall ((P tptp.fun_rat_fun_rat_bool) (A tptp.rat) (B tptp.rat)) (=> (forall ((A4 tptp.rat) (B4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A4) B4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P A4) B4)))) (=> (forall ((A4 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P A4) A4))) (=> (forall ((A4 tptp.rat) (B4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P B4) A4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P A4) B4)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P A) B)))))) (forall ((P tptp.fun_num_fun_num_bool) (A tptp.num) (B tptp.num)) (=> (forall ((A4 tptp.num) (B4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A4) B4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P A4) B4)))) (=> (forall ((A4 tptp.num)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P A4) A4))) (=> (forall ((A4 tptp.num) (B4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P B4) A4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P A4) B4)))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P A) B)))))) (forall ((P tptp.fun_nat_fun_nat_bool) (A tptp.nat) (B tptp.nat)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A4) B4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A4) B4)))) (=> (forall ((A4 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A4) A4))) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P B4) A4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A4) B4)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A) B)))))) (forall ((P tptp.fun_int_fun_int_bool) (A tptp.int) (B tptp.int)) (=> (forall ((A4 tptp.int) (B4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A4) B4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A4) B4)))) (=> (forall ((A4 tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A4) A4))) (=> (forall ((A4 tptp.int) (B4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P B4) A4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A4) B4)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A) B)))))) (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A))) (=> (tptp.pp (tptp.aa_assn_bool _let_1 B)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn B) C)) (tptp.pp (tptp.aa_assn_bool _let_1 C)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (tptp.pp (tptp.aa_rat_bool _let_1 C)))))) (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num A))) (=> (tptp.pp (tptp.aa_num_bool _let_1 B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) C)) (tptp.pp (tptp.aa_num_bool _let_1 C)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) C)) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) C)) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((X tptp.rat) (Y tptp.rat)) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y))) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X)) (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (= (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y))) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X)) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y))) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X)) (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y))) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X)) (= X Y)))) (forall ((B tptp.assn) (A tptp.assn) (C tptp.assn)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn C))) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn B) A)) (=> (tptp.pp (tptp.aa_assn_bool _let_1 B)) (tptp.pp (tptp.aa_assn_bool _let_1 A)))))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (tptp.pp (tptp.aa_rat_bool _let_1 A)))))) (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num C))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) A)) (=> (tptp.pp (tptp.aa_num_bool _let_1 B)) (tptp.pp (tptp.aa_num_bool _let_1 A)))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (tptp.pp (tptp.aa_nat_bool _let_1 A)))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (tptp.pp (tptp.aa_int_bool _let_1 A)))))) (forall ((A tptp.assn) (B tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) B)) (not (= A B)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (not (= A B)))) (forall ((A tptp.num) (B tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B)) (not (= A B)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (not (= A B)))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (not (= A B)))) (forall ((B tptp.assn) (A tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn B) A)) (not (= A B)))) (forall ((B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (not (= A B)))) (forall ((B tptp.num) (A tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) A)) (not (= A B)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A)) (not (= A B)))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)) (not (= A B)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (= X Y)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X))))) (forall ((X tptp.num) (Y tptp.num)) (=> (not (= X Y)) (=> (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X))))) (forall ((X tptp.int) (Y tptp.int)) (=> (not (= X Y)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X))))) (forall ((X tptp.assn) (Y tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X) Y)) (not (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn Y) X))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X))))) (forall ((X tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X))))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X))))) (forall ((X tptp.rat) (Y tptp.rat)) (= (not (= X Y)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X))))) (forall ((X tptp.num) (Y tptp.num)) (= (not (= X Y)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X))))) (forall ((X tptp.nat) (Y tptp.nat)) (= (not (= X Y)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X))))) (forall ((X tptp.int) (Y tptp.int)) (= (not (= X Y)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X))))) (forall ((A tptp.assn) (B tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) B)) (not (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn B) A))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A))))) (forall ((A tptp.num) (B tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) A))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A))))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X))) (=> (tptp.pp (tptp.aa_assn_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn Y) Z)) (tptp.pp (tptp.aa_assn_bool _let_1 Z)))))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) Z)) (tptp.pp (tptp.aa_rat_bool _let_1 Z)))))) (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num X))) (=> (tptp.pp (tptp.aa_num_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) Z)) (tptp.pp (tptp.aa_num_bool _let_1 Z)))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) Z)) (tptp.pp (tptp.aa_nat_bool _let_1 Z)))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int X))) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) Z)) (tptp.pp (tptp.aa_int_bool _let_1 Z)))))) (forall ((A tptp.assn) (F tptp.fun_assn_assn) (B tptp.assn) (C tptp.assn)) (=> (= A (tptp.aa_assn_assn F B)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn B) C)) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X3) Y3)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_assn_assn F X3)) (tptp.aa_assn_assn F Y3))))) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) (tptp.aa_assn_assn F C))))))) (forall ((A tptp.rat) (F tptp.fun_assn_rat) (B tptp.assn) (C tptp.assn)) (=> (= A (tptp.aa_assn_rat F B)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn B) C)) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_assn_rat F X3)) (tptp.aa_assn_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_assn_rat F C))))))) (forall ((A tptp.num) (F tptp.fun_assn_num) (B tptp.assn) (C tptp.assn)) (=> (= A (tptp.aa_assn_num F B)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn B) C)) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X3) Y3)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_assn_num F X3)) (tptp.aa_assn_num F Y3))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) (tptp.aa_assn_num F C))))))) (forall ((A tptp.nat) (F tptp.fun_assn_nat) (B tptp.assn) (C tptp.assn)) (=> (= A (tptp.aa_assn_nat F B)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn B) C)) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X3) Y3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_assn_nat F X3)) (tptp.aa_assn_nat F Y3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) (tptp.aa_assn_nat F C))))))) (forall ((A tptp.int) (F tptp.fun_assn_int) (B tptp.assn) (C tptp.assn)) (=> (= A (tptp.aa_assn_int F B)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn B) C)) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X3) Y3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_assn_int F X3)) (tptp.aa_assn_int F Y3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) (tptp.aa_assn_int F C))))))) (forall ((A tptp.assn) (F tptp.fun_rat_assn) (B tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_assn F B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y3)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_rat_assn F X3)) (tptp.aa_rat_assn F Y3))))) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) (tptp.aa_rat_assn F C))))))) (forall ((A tptp.rat) (F tptp.fun_rat_rat) (B tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_rat F B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat F C))))))) (forall ((A tptp.num) (F tptp.fun_rat_num) (B tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_num F B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y3)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_rat_num F X3)) (tptp.aa_rat_num F Y3))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) (tptp.aa_rat_num F C))))))) (forall ((A tptp.nat) (F tptp.fun_rat_nat) (B tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_nat F B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_rat_nat F X3)) (tptp.aa_rat_nat F Y3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) (tptp.aa_rat_nat F C))))))) (forall ((A tptp.int) (F tptp.fun_rat_int) (B tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_int F B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int F X3)) (tptp.aa_rat_int F Y3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) (tptp.aa_rat_int F C))))))) (forall ((A tptp.assn) (B tptp.assn) (F tptp.fun_assn_assn) (C tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) B)) (=> (= (tptp.aa_assn_assn F B) C) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X3) Y3)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_assn_assn F X3)) (tptp.aa_assn_assn F Y3))))) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_assn_assn F A)) C)))))) (forall ((A tptp.assn) (B tptp.assn) (F tptp.fun_assn_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) B)) (=> (= (tptp.aa_assn_rat F B) C) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_assn_rat F X3)) (tptp.aa_assn_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_assn_rat F A)) C)))))) (forall ((A tptp.assn) (B tptp.assn) (F tptp.fun_assn_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) B)) (=> (= (tptp.aa_assn_num F B) C) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X3) Y3)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_assn_num F X3)) (tptp.aa_assn_num F Y3))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_assn_num F A)) C)))))) (forall ((A tptp.assn) (B tptp.assn) (F tptp.fun_assn_nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) B)) (=> (= (tptp.aa_assn_nat F B) C) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X3) Y3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_assn_nat F X3)) (tptp.aa_assn_nat F Y3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_assn_nat F A)) C)))))) (forall ((A tptp.assn) (B tptp.assn) (F tptp.fun_assn_int) (C tptp.int)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) B)) (=> (= (tptp.aa_assn_int F B) C) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X3) Y3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_assn_int F X3)) (tptp.aa_assn_int F Y3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_assn_int F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_assn) (C tptp.assn)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (= (tptp.aa_rat_assn F B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y3)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_rat_assn F X3)) (tptp.aa_rat_assn F Y3))))) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_rat_assn F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (= (tptp.aa_rat_rat F B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (= (tptp.aa_rat_num F B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y3)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_rat_num F X3)) (tptp.aa_rat_num F Y3))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_rat_num F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (= (tptp.aa_rat_nat F B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_rat_nat F X3)) (tptp.aa_rat_nat F Y3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_rat_nat F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_int) (C tptp.int)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (= (tptp.aa_rat_int F B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int F X3)) (tptp.aa_rat_int F Y3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int F A)) C)))))) (forall ((X tptp.assn)) (not (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X) X)))) (forall ((X tptp.rat)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) X)))) (forall ((X tptp.num)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) X)))) (forall ((X tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) X)))) (forall ((X tptp.int)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) X)))) (forall ((A tptp.assn) (F tptp.fun_assn_assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A))) (=> (tptp.pp (tptp.aa_assn_bool _let_1 (tptp.aa_assn_assn F B))) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn B) C)) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X3) Y3)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_assn_assn F X3)) (tptp.aa_assn_assn F Y3))))) (tptp.pp (tptp.aa_assn_bool _let_1 (tptp.aa_assn_assn F C)))))))) (forall ((A tptp.assn) (F tptp.fun_rat_assn) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A))) (=> (tptp.pp (tptp.aa_assn_bool _let_1 (tptp.aa_rat_assn F B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y3)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_rat_assn F X3)) (tptp.aa_rat_assn F Y3))))) (tptp.pp (tptp.aa_assn_bool _let_1 (tptp.aa_rat_assn F C)))))))) (forall ((A tptp.assn) (F tptp.fun_num_assn) (B tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A))) (=> (tptp.pp (tptp.aa_assn_bool _let_1 (tptp.aa_num_assn F B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) C)) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X3) Y3)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_num_assn F X3)) (tptp.aa_num_assn F Y3))))) (tptp.pp (tptp.aa_assn_bool _let_1 (tptp.aa_num_assn F C)))))))) (forall ((A tptp.assn) (F tptp.fun_nat_assn) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A))) (=> (tptp.pp (tptp.aa_assn_bool _let_1 (tptp.aa_nat_assn F B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) C)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) Y3)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_nat_assn F X3)) (tptp.aa_nat_assn F Y3))))) (tptp.pp (tptp.aa_assn_bool _let_1 (tptp.aa_nat_assn F C)))))))) (forall ((A tptp.assn) (F tptp.fun_int_assn) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A))) (=> (tptp.pp (tptp.aa_assn_bool _let_1 (tptp.aa_int_assn F B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) C)) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) Y3)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_int_assn F X3)) (tptp.aa_int_assn F Y3))))) (tptp.pp (tptp.aa_assn_bool _let_1 (tptp.aa_int_assn F C)))))))) (forall ((A tptp.rat) (F tptp.fun_assn_rat) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_assn_rat F B))) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn B) C)) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_assn_rat F X3)) (tptp.aa_assn_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_assn_rat F C)))))))) (forall ((A tptp.rat) (F tptp.fun_rat_rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat F B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat F C)))))))) (forall ((A tptp.rat) (F tptp.fun_num_rat) (B tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_num_rat F B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) C)) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat F X3)) (tptp.aa_num_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_num_rat F C)))))))) (forall ((A tptp.rat) (F tptp.fun_nat_rat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat F B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) C)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat F X3)) (tptp.aa_nat_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat F C)))))))) (forall ((A tptp.rat) (F tptp.fun_int_rat) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_int_rat F B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) C)) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat F X3)) (tptp.aa_int_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_int_rat F C)))))))) (forall ((A tptp.assn) (B tptp.assn) (F tptp.fun_assn_assn) (C tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) B)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_assn_assn F B)) C)) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X3) Y3)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_assn_assn F X3)) (tptp.aa_assn_assn F Y3))))) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_assn_assn F A)) C)))))) (forall ((A tptp.assn) (B tptp.assn) (F tptp.fun_assn_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_assn_rat F B)) C)) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_assn_rat F X3)) (tptp.aa_assn_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_assn_rat F A)) C)))))) (forall ((A tptp.assn) (B tptp.assn) (F tptp.fun_assn_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_assn_num F B)) C)) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X3) Y3)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_assn_num F X3)) (tptp.aa_assn_num F Y3))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_assn_num F A)) C)))))) (forall ((A tptp.assn) (B tptp.assn) (F tptp.fun_assn_nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_assn_nat F B)) C)) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X3) Y3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_assn_nat F X3)) (tptp.aa_assn_nat F Y3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_assn_nat F A)) C)))))) (forall ((A tptp.assn) (B tptp.assn) (F tptp.fun_assn_int) (C tptp.int)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_assn_int F B)) C)) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X3) Y3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_assn_int F X3)) (tptp.aa_assn_int F Y3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_assn_int F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_assn) (C tptp.assn)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_rat_assn F B)) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y3)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_rat_assn F X3)) (tptp.aa_rat_assn F Y3))))) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_rat_assn F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F B)) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_rat_num F B)) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y3)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_rat_num F X3)) (tptp.aa_rat_num F Y3))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_rat_num F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_rat_nat F B)) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_rat_nat F X3)) (tptp.aa_rat_nat F Y3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_rat_nat F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_int) (C tptp.int)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int F B)) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int F X3)) (tptp.aa_rat_int F Y3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int F A)) C)))))) (forall ((X tptp.assn) (Y tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X) Y)) (not (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn Y) X))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X))))) (forall ((X tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X))))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X))))) (forall ((X tptp.assn) (Y tptp.assn) (P tptp.bool)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X) Y)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn Y) X)) (tptp.pp P)))) (forall ((X tptp.rat) (Y tptp.rat) (P tptp.bool)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X)) (tptp.pp P)))) (forall ((X tptp.num) (Y tptp.num) (P tptp.bool)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X)) (tptp.pp P)))) (forall ((X tptp.nat) (Y tptp.nat) (P tptp.bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X)) (tptp.pp P)))) (forall ((X tptp.int) (Y tptp.int) (P tptp.bool)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X)) (tptp.pp P)))) (forall ((X tptp.rat) (Y tptp.rat)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (= X Y) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X)))) (forall ((X tptp.num) (Y tptp.num)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (= X Y) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (= X Y) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (= X Y) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X)))) (forall ((X tptp.assn) (Y tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X) Y)) (not (= X Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (not (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (not (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (not (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (not (= X Y)))) (forall ((X tptp.assn) (Y tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X) Y)) (not (= Y X)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (not (= Y X)))) (forall ((X tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (not (= Y X)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (not (= Y X)))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (not (= Y X)))) (forall ((X tptp.assn) (Y tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X) Y)) (not (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn Y) X))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X))))) (forall ((X tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X))))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X))))) (forall ((S tptp.set_Pr958786334691620121nt_int) (P tptp.fun_Pr803113274115125473t_bool)) (= (tptp.ord_le2843351958646193337nt_int S (tptp.collec213857154873943460nt_int P)) (forall ((X4 tptp.product_prod_int_int)) (=> (tptp.member5262025264175285858nt_int X4 S) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool P X4)))))) (forall ((S tptp.set_list_nat) (P tptp.fun_list_nat_bool)) (= (tptp.ord_le6045566169113846134st_nat S (tptp.collect_list_nat P)) (forall ((X4 tptp.list_nat)) (=> (tptp.member_list_nat X4 S) (tptp.pp (tptp.aa_list_nat_bool P X4)))))) (forall ((S tptp.set_set_nat) (P tptp.fun_set_nat_bool)) (= (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat S) (tptp.collect_set_nat P))) (forall ((X4 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat X4) S)) (tptp.pp (tptp.aa_set_nat_bool P X4)))))) (forall ((S tptp.set_nat) (P tptp.fun_nat_bool)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat S) (tptp.collect_nat P))) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) S)) (tptp.pp (tptp.aa_nat_bool P X4)))))) (forall ((S tptp.set_int) (P tptp.fun_int_bool)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int S) (tptp.collect_int P))) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) S)) (tptp.pp (tptp.aa_int_bool P X4)))))) (forall ((R tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat)) (= (tptp.pp (tptp.aa_fun8663595511526100224l_bool (tptp.ord_le2468614981408567801t_bool (tptp.aTP_Lamm_a R)) (tptp.aTP_Lamm_a S))) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat R) S)))) (forall ((R tptp.set_bool) (S tptp.set_bool)) (= (tptp.ord_le2902245940885495011l_bool (tptp.aTP_Lamm_aa R) (tptp.aTP_Lamm_aa S)) (tptp.ord_less_eq_set_bool R S))) (forall ((R tptp.set_set_nat) (S tptp.set_set_nat)) (= (tptp.ord_le1461730252015488778t_bool (tptp.aTP_Lamm_ad R) (tptp.aTP_Lamm_ad S)) (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat R) S)))) (forall ((R tptp.set_nat) (S tptp.set_nat)) (= (tptp.ord_le8840051076831633728t_bool (tptp.aTP_Lamm_ae R) (tptp.aTP_Lamm_ae S)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat R) S)))) (forall ((R tptp.set_int) (S tptp.set_int)) (= (tptp.ord_le5715760110363009508t_bool (tptp.aTP_Lamm_af R) (tptp.aTP_Lamm_af S)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int R) S)))) (= tptp.bot_bo1796632182523588997nt_int (tptp.collec213857154873943460nt_int tptp.aTP_Lamm_bb)) (= tptp.bot_bot_set_list_nat (tptp.collect_list_nat tptp.aTP_Lamm_bc)) (= tptp.bot_bot_set_set_nat (tptp.collect_set_nat tptp.aTP_Lamm_bd)) (= tptp.bot_bo2099793752762293965at_nat (tptp.collec3392354462482085612at_nat tptp.aTP_Lamm_be)) (= tptp.bot_bot_set_bool (tptp.collect_bool tptp.aTP_Lamm_bf)) (= tptp.bot_bot_set_nat (tptp.collect_nat tptp.aTP_Lamm_bg)) (= tptp.bot_bot_set_int (tptp.collect_int tptp.aTP_Lamm_bh)) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool)) (= (tptp.inf_inf_set_bool A3 B3) (tptp.collect_bool (tptp.aa_set6670506438128111678l_bool (tptp.aTP_Lamm_bi A3) B3)))) (forall ((A3 tptp.set_Pr958786334691620121nt_int) (B3 tptp.set_Pr958786334691620121nt_int)) (= (tptp.inf_in2269163501485487111nt_int A3 B3) (tptp.collec213857154873943460nt_int (tptp.aa_set1381271197253378494t_bool (tptp.aTP_Lamm_bj A3) B3)))) (forall ((A3 tptp.set_list_nat) (B3 tptp.set_list_nat)) (= (tptp.inf_inf_set_list_nat A3 B3) (tptp.collect_list_nat (tptp.aa_set257547205302447420t_bool (tptp.aTP_Lamm_bk A3) B3)))) (forall ((A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (= (tptp.inf_inf_set_set_nat A3 B3) (tptp.collect_set_nat (tptp.aa_set9121396911425987952t_bool (tptp.aTP_Lamm_bl A3) B3)))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3) (tptp.collect_int (tptp.aa_set7012339369581096484t_bool (tptp.aTP_Lamm_bm A3) B3)))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3) (tptp.collect_nat (tptp.aa_set3744802623701456604t_bool (tptp.aTP_Lamm_bn A3) B3)))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3) (tptp.collec3392354462482085612at_nat (tptp.aa_set5223363028666124222t_bool (tptp.aTP_Lamm_bo A3) B3)))) (forall ((X tptp.bool) (A3 tptp.set_bool) (P tptp.fun_bool_bool)) (= (tptp.pp (tptp.member_bool X (tptp.inf_inf_set_bool A3 (tptp.collect_bool P)))) (and (tptp.pp (tptp.member_bool X A3)) (tptp.pp (tptp.aa_bool_bool P X))))) (forall ((X tptp.product_prod_int_int) (A3 tptp.set_Pr958786334691620121nt_int) (P tptp.fun_Pr803113274115125473t_bool)) (= (tptp.member5262025264175285858nt_int X (tptp.inf_in2269163501485487111nt_int A3 (tptp.collec213857154873943460nt_int P))) (and (tptp.member5262025264175285858nt_int X A3) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool P X))))) (forall ((X tptp.list_nat) (A3 tptp.set_list_nat) (P tptp.fun_list_nat_bool)) (= (tptp.member_list_nat X (tptp.inf_inf_set_list_nat A3 (tptp.collect_list_nat P))) (and (tptp.member_list_nat X A3) (tptp.pp (tptp.aa_list_nat_bool P X))))) (forall ((X tptp.set_nat) (A3 tptp.set_set_nat) (P tptp.fun_set_nat_bool)) (let ((_let_1 (tptp.member_set_nat X))) (= (tptp.pp (tptp.aa_set_set_nat_bool _let_1 (tptp.inf_inf_set_set_nat A3 (tptp.collect_set_nat P)))) (and (tptp.pp (tptp.aa_set_set_nat_bool _let_1 A3)) (tptp.pp (tptp.aa_set_nat_bool P X)))))) (forall ((X tptp.int) (A3 tptp.set_int) (P tptp.fun_int_bool)) (let ((_let_1 (tptp.member_int X))) (= (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) (tptp.collect_int P)))) (and (tptp.pp (tptp.aa_set_int_bool _let_1 A3)) (tptp.pp (tptp.aa_int_bool P X)))))) (forall ((X tptp.nat) (A3 tptp.set_nat) (P tptp.fun_nat_bool)) (let ((_let_1 (tptp.member_nat X))) (= (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) (tptp.collect_nat P)))) (and (tptp.pp (tptp.aa_set_nat_bool _let_1 A3)) (tptp.pp (tptp.aa_nat_bool P X)))))) (forall ((X tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (P tptp.fun_Pr7757163693017731481t_bool)) (let ((_let_1 (tptp.member8440522571783428010at_nat X))) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) (tptp.collec3392354462482085612at_nat P)))) (and (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 A3)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool P X)))))) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool)) (= (tptp.inf_inf_set_bool A3 B3) (tptp.collect_bool (tptp.inf_in9217375510005350933l_bool (tptp.aTP_Lamm_aa A3) (tptp.aTP_Lamm_aa B3))))) (forall ((A3 tptp.set_Pr958786334691620121nt_int) (B3 tptp.set_Pr958786334691620121nt_int)) (= (tptp.inf_in2269163501485487111nt_int A3 B3) (tptp.collec213857154873943460nt_int (tptp.inf_in4513820918327576947t_bool (tptp.aTP_Lamm_ab A3) (tptp.aTP_Lamm_ab B3))))) (forall ((A3 tptp.set_list_nat) (B3 tptp.set_list_nat)) (= (tptp.inf_inf_set_list_nat A3 B3) (tptp.collect_list_nat (tptp.inf_in7940471347505502206t_bool (tptp.aTP_Lamm_ac A3) (tptp.aTP_Lamm_ac B3))))) (forall ((A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (= (tptp.inf_inf_set_set_nat A3 B3) (tptp.collect_set_nat (tptp.inf_in6168126700042863960t_bool (tptp.aTP_Lamm_ad A3) (tptp.aTP_Lamm_ad B3))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3) (tptp.collect_int (tptp.inf_inf_fun_int_bool (tptp.aTP_Lamm_af A3) (tptp.aTP_Lamm_af B3))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3) (tptp.collect_nat (tptp.inf_inf_fun_nat_bool (tptp.aTP_Lamm_ae A3) (tptp.aTP_Lamm_ae B3))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3) (tptp.collec3392354462482085612at_nat (tptp.aa_fun830836278467416944t_bool (tptp.inf_in2244499300375407147t_bool (tptp.aTP_Lamm_a A3)) (tptp.aTP_Lamm_a B3))))) (forall ((P tptp.fun_Pr803113274115125473t_bool) (Q tptp.fun_Pr803113274115125473t_bool)) (= (tptp.collec213857154873943460nt_int (tptp.aa_fun8917503761599146496t_bool (tptp.aTP_Lamm_bp P) Q)) (tptp.inf_in2269163501485487111nt_int (tptp.collec213857154873943460nt_int P) (tptp.collec213857154873943460nt_int Q)))) (forall ((P tptp.fun_list_nat_bool) (Q tptp.fun_list_nat_bool)) (= (tptp.collect_list_nat (tptp.aa_fun6009467934925565500t_bool (tptp.aTP_Lamm_bq P) Q)) (tptp.inf_inf_set_list_nat (tptp.collect_list_nat P) (tptp.collect_list_nat Q)))) (forall ((P tptp.fun_set_nat_bool) (Q tptp.fun_set_nat_bool)) (= (tptp.collect_set_nat (tptp.aa_fun3565389549526402364t_bool (tptp.aTP_Lamm_br P) Q)) (tptp.inf_inf_set_set_nat (tptp.collect_set_nat P) (tptp.collect_set_nat Q)))) (forall ((P tptp.fun_int_bool) (Q tptp.fun_int_bool)) (= (tptp.collect_int (tptp.aa_fun5146555767781538748t_bool (tptp.aTP_Lamm_bs P) Q)) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int (tptp.collect_int P)) (tptp.collect_int Q)))) (forall ((P tptp.fun_nat_bool) (Q tptp.fun_nat_bool)) (= (tptp.collect_nat (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_bt P) Q)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.collect_nat P)) (tptp.collect_nat Q)))) (forall ((P tptp.fun_Pr7757163693017731481t_bool) (Q tptp.fun_Pr7757163693017731481t_bool)) (= (tptp.collec3392354462482085612at_nat (tptp.aa_fun830836278467416944t_bool (tptp.aTP_Lamm_bu P) Q)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.collec3392354462482085612at_nat P)) (tptp.collec3392354462482085612at_nat Q)))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat A3) B3) (tptp.collec3392354462482085612at_nat (tptp.aa_set5223363028666124222t_bool (tptp.aTP_Lamm_bv A3) B3)))) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool)) (= (tptp.aa_set_bool_set_bool (tptp.aa_set4734229006438377534t_bool tptp.sup_sup_set_bool A3) B3) (tptp.collect_bool (tptp.aa_set6670506438128111678l_bool (tptp.aTP_Lamm_bw A3) B3)))) (forall ((A3 tptp.set_Pr958786334691620121nt_int) (B3 tptp.set_Pr958786334691620121nt_int)) (= (tptp.sup_su6024340866399070445nt_int A3 B3) (tptp.collec213857154873943460nt_int (tptp.aa_set1381271197253378494t_bool (tptp.aTP_Lamm_bx A3) B3)))) (forall ((A3 tptp.set_list_nat) (B3 tptp.set_list_nat)) (= (tptp.sup_sup_set_list_nat A3 B3) (tptp.collect_list_nat (tptp.aa_set257547205302447420t_bool (tptp.aTP_Lamm_by A3) B3)))) (forall ((A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (= (tptp.sup_sup_set_set_nat A3 B3) (tptp.collect_set_nat (tptp.aa_set9121396911425987952t_bool (tptp.aTP_Lamm_bz A3) B3)))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3) (tptp.collect_int (tptp.aa_set7012339369581096484t_bool (tptp.aTP_Lamm_ca A3) B3)))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3) B3) (tptp.collec7088162979684241874at_nat (tptp.aa_set6997699984206591038t_bool (tptp.aTP_Lamm_cb A3) B3)))) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3) B3) (tptp.collec5204685387357076818at_nat (tptp.aa_set5968938463291210814t_bool (tptp.aTP_Lamm_cc A3) B3)))) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3) B3) (tptp.collec6321179662152712658at_nat (tptp.aa_set377272637606474814t_bool (tptp.aTP_Lamm_cd A3) B3)))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3) (tptp.collect_nat (tptp.aa_set3744802623701456604t_bool (tptp.aTP_Lamm_ce A3) B3)))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat A3) B3) (tptp.collec3392354462482085612at_nat (tptp.aa_fun830836278467416944t_bool (tptp.sup_su5674415786711694021t_bool (tptp.aTP_Lamm_a A3)) (tptp.aTP_Lamm_a B3))))) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool)) (= (tptp.aa_set_bool_set_bool (tptp.aa_set4734229006438377534t_bool tptp.sup_sup_set_bool A3) B3) (tptp.collect_bool (tptp.sup_su2675241097686107055l_bool (tptp.aTP_Lamm_aa A3) (tptp.aTP_Lamm_aa B3))))) (forall ((A3 tptp.set_Pr958786334691620121nt_int) (B3 tptp.set_Pr958786334691620121nt_int)) (= (tptp.sup_su6024340866399070445nt_int A3 B3) (tptp.collec213857154873943460nt_int (tptp.sup_su7943737404663863821t_bool (tptp.aTP_Lamm_ab A3) (tptp.aTP_Lamm_ab B3))))) (forall ((A3 tptp.set_list_nat) (B3 tptp.set_list_nat)) (= (tptp.sup_sup_set_list_nat A3 B3) (tptp.collect_list_nat (tptp.sup_su7820324534880642276t_bool (tptp.aTP_Lamm_ac A3) (tptp.aTP_Lamm_ac B3))))) (forall ((A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (= (tptp.sup_sup_set_set_nat A3 B3) (tptp.collect_set_nat (tptp.sup_su7038862894554899774t_bool (tptp.aTP_Lamm_ad A3) (tptp.aTP_Lamm_ad B3))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3) (tptp.collect_int (tptp.sup_sup_fun_int_bool (tptp.aTP_Lamm_af A3) (tptp.aTP_Lamm_af B3))))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3) B3) (tptp.collec7088162979684241874at_nat (tptp.sup_su3901408610078580575t_bool (tptp.aTP_Lamm_ai A3) (tptp.aTP_Lamm_ai B3))))) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3) B3) (tptp.collec5204685387357076818at_nat (tptp.sup_su2357402678989182943t_bool (tptp.aTP_Lamm_aj A3) (tptp.aTP_Lamm_aj B3))))) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3) B3) (tptp.collec6321179662152712658at_nat (tptp.sup_su5834520091132235615t_bool (tptp.aTP_Lamm_ak A3) (tptp.aTP_Lamm_ak B3))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3) (tptp.collect_nat (tptp.sup_sup_fun_nat_bool (tptp.aTP_Lamm_ae A3) (tptp.aTP_Lamm_ae B3))))) (forall ((P tptp.fun_Pr803113274115125473t_bool) (Q tptp.fun_Pr803113274115125473t_bool)) (= (tptp.collec213857154873943460nt_int (tptp.aa_fun8917503761599146496t_bool (tptp.aTP_Lamm_cf P) Q)) (tptp.sup_su6024340866399070445nt_int (tptp.collec213857154873943460nt_int P) (tptp.collec213857154873943460nt_int Q)))) (forall ((P tptp.fun_list_nat_bool) (Q tptp.fun_list_nat_bool)) (= (tptp.collect_list_nat (tptp.aa_fun6009467934925565500t_bool (tptp.aTP_Lamm_cg P) Q)) (tptp.sup_sup_set_list_nat (tptp.collect_list_nat P) (tptp.collect_list_nat Q)))) (forall ((P tptp.fun_set_nat_bool) (Q tptp.fun_set_nat_bool)) (= (tptp.collect_set_nat (tptp.aa_fun3565389549526402364t_bool (tptp.aTP_Lamm_ch P) Q)) (tptp.sup_sup_set_set_nat (tptp.collect_set_nat P) (tptp.collect_set_nat Q)))) (forall ((P tptp.fun_int_bool) (Q tptp.fun_int_bool)) (= (tptp.collect_int (tptp.aa_fun5146555767781538748t_bool (tptp.aTP_Lamm_ci P) Q)) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int (tptp.collect_int P)) (tptp.collect_int Q)))) (forall ((P tptp.fun_Pr446604468264085555t_bool) (Q tptp.fun_Pr446604468264085555t_bool)) (= (tptp.collec7088162979684241874at_nat (tptp.aa_fun3665199231186260388t_bool (tptp.aTP_Lamm_cj P) Q)) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat (tptp.collec7088162979684241874at_nat P)) (tptp.collec7088162979684241874at_nat Q)))) (forall ((P tptp.fun_Pr3976602594631769267t_bool) (Q tptp.fun_Pr3976602594631769267t_bool)) (= (tptp.collec5204685387357076818at_nat (tptp.aa_fun3556822901603992740t_bool (tptp.aTP_Lamm_ck P) Q)) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat (tptp.collec5204685387357076818at_nat P)) (tptp.collec5204685387357076818at_nat Q)))) (forall ((P tptp.fun_Pr1607443439640623155t_bool) (Q tptp.fun_Pr1607443439640623155t_bool)) (= (tptp.collec6321179662152712658at_nat (tptp.aa_fun5022828243006652836t_bool (tptp.aTP_Lamm_cl P) Q)) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat (tptp.collec6321179662152712658at_nat P)) (tptp.collec6321179662152712658at_nat Q)))) (forall ((P tptp.fun_nat_bool) (Q tptp.fun_nat_bool)) (= (tptp.collect_nat (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_cm P) Q)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.collect_nat P)) (tptp.collect_nat Q)))) (forall ((N2 tptp.nat) (P tptp.fun_nat_bool)) (=> (=> (forall ((N3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N3) N2)) (not (tptp.pp (tptp.aa_nat_bool P N3))))) (tptp.pp (tptp.aa_nat_bool P N2))) (exists ((N4 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N4) N2)) (tptp.pp (tptp.aa_nat_bool P N4)))))) (forall ((X tptp.assn) (Y tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn X) Y)) (or (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X) Y)) (= X Y)))) (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X) Y)) (or (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int X) Y)) (= X Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (= X Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X)))) (forall ((X tptp.num) (Y tptp.num)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X)))) (forall ((A tptp.assn) (B tptp.assn) (F tptp.fun_assn_assn) (C tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) B)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn (tptp.aa_assn_assn F B)) C)) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X3) Y3)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_assn_assn F X3)) (tptp.aa_assn_assn F Y3))))) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_assn_assn F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_assn) (C tptp.assn)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn (tptp.aa_rat_assn F B)) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y3)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_rat_assn F X3)) (tptp.aa_rat_assn F Y3))))) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_rat_assn F A)) C)))))) (forall ((A tptp.num) (B tptp.num) (F tptp.fun_num_assn) (C tptp.assn)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn (tptp.aa_num_assn F B)) C)) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X3) Y3)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_num_assn F X3)) (tptp.aa_num_assn F Y3))))) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_num_assn F A)) C)))))) (forall ((A tptp.nat) (B tptp.nat) (F tptp.fun_nat_assn) (C tptp.assn)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn (tptp.aa_nat_assn F B)) C)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) Y3)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_nat_assn F X3)) (tptp.aa_nat_assn F Y3))))) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_nat_assn F A)) C)))))) (forall ((A tptp.int) (B tptp.int) (F tptp.fun_int_assn) (C tptp.assn)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn (tptp.aa_int_assn F B)) C)) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) Y3)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_int_assn F X3)) (tptp.aa_int_assn F Y3))))) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_int_assn F A)) C)))))) (forall ((A tptp.assn) (B tptp.assn) (F tptp.fun_assn_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_assn_rat F B)) C)) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_assn_rat F X3)) (tptp.aa_assn_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_assn_rat F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F B)) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F A)) C)))))) (forall ((A tptp.num) (B tptp.num) (F tptp.fun_num_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F B)) C)) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat F X3)) (tptp.aa_num_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat F A)) C)))))) (forall ((A tptp.nat) (B tptp.nat) (F tptp.fun_nat_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F B)) C)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat F X3)) (tptp.aa_nat_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat F A)) C)))))) (forall ((A tptp.int) (B tptp.int) (F tptp.fun_int_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat F B)) C)) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat F X3)) (tptp.aa_int_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat F A)) C)))))) (forall ((A tptp.assn) (F tptp.fun_rat_assn) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A))) (=> (tptp.pp (tptp.aa_assn_bool _let_1 (tptp.aa_rat_assn F B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y3)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn (tptp.aa_rat_assn F X3)) (tptp.aa_rat_assn F Y3))))) (tptp.pp (tptp.aa_assn_bool _let_1 (tptp.aa_rat_assn F C)))))))) (forall ((A tptp.rat) (F tptp.fun_rat_rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat F B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat F C)))))))) (forall ((A tptp.num) (F tptp.fun_rat_num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num A))) (=> (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_rat_num F B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y3)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F X3)) (tptp.aa_rat_num F Y3))))) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_rat_num F C)))))))) (forall ((A tptp.nat) (F tptp.fun_rat_nat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_rat_nat F B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_rat_nat F X3)) (tptp.aa_rat_nat F Y3))))) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_rat_nat F C)))))))) (forall ((A tptp.int) (F tptp.fun_rat_int) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_rat_int F B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int F X3)) (tptp.aa_rat_int F Y3))))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_rat_int F C)))))))) (forall ((A tptp.assn) (F tptp.fun_num_assn) (B tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A))) (=> (tptp.pp (tptp.aa_assn_bool _let_1 (tptp.aa_num_assn F B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y3)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn (tptp.aa_num_assn F X3)) (tptp.aa_num_assn F Y3))))) (tptp.pp (tptp.aa_assn_bool _let_1 (tptp.aa_num_assn F C)))))))) (forall ((A tptp.rat) (F tptp.fun_num_rat) (B tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_num_rat F B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F X3)) (tptp.aa_num_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_num_rat F C)))))))) (forall ((A tptp.num) (F tptp.fun_num_num) (B tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num A))) (=> (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_num_num F B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y3)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F X3)) (tptp.aa_num_num F Y3))))) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_num_num F C)))))))) (forall ((A tptp.nat) (F tptp.fun_num_nat) (B tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_num_nat F B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat F X3)) (tptp.aa_num_nat F Y3))))) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_num_nat F C)))))))) (forall ((A tptp.int) (F tptp.fun_num_int) (B tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_num_int F B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int F X3)) (tptp.aa_num_int F Y3))))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_num_int F C)))))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_assn) (C tptp.assn)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_rat_assn F B)) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y3)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn (tptp.aa_rat_assn F X3)) (tptp.aa_rat_assn F Y3))))) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_rat_assn F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F B)) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_rat_num F B)) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y3)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F X3)) (tptp.aa_rat_num F Y3))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_rat_num F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_rat_nat F B)) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_rat_nat F X3)) (tptp.aa_rat_nat F Y3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_rat_nat F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_int) (C tptp.int)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int F B)) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int F X3)) (tptp.aa_rat_int F Y3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int F A)) C)))))) (forall ((A tptp.num) (B tptp.num) (F tptp.fun_num_assn) (C tptp.assn)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_num_assn F B)) C)) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y3)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn (tptp.aa_num_assn F X3)) (tptp.aa_num_assn F Y3))))) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_num_assn F A)) C)))))) (forall ((A tptp.num) (B tptp.num) (F tptp.fun_num_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat F B)) C)) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F X3)) (tptp.aa_num_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat F A)) C)))))) (forall ((A tptp.num) (B tptp.num) (F tptp.fun_num_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_num_num F B)) C)) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y3)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F X3)) (tptp.aa_num_num F Y3))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_num_num F A)) C)))))) (forall ((A tptp.num) (B tptp.num) (F tptp.fun_num_nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_num_nat F B)) C)) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat F X3)) (tptp.aa_num_nat F Y3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_num_nat F A)) C)))))) (forall ((A tptp.num) (B tptp.num) (F tptp.fun_num_int) (C tptp.int)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_num_int F B)) C)) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int F X3)) (tptp.aa_num_int F Y3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_num_int F A)) C)))))) (forall ((A tptp.assn) (F tptp.fun_assn_assn) (B tptp.assn) (C tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn A) (tptp.aa_assn_assn F B))) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn B) C)) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X3) Y3)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_assn_assn F X3)) (tptp.aa_assn_assn F Y3))))) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) (tptp.aa_assn_assn F C))))))) (forall ((A tptp.assn) (F tptp.fun_rat_assn) (B tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn A) (tptp.aa_rat_assn F B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y3)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_rat_assn F X3)) (tptp.aa_rat_assn F Y3))))) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) (tptp.aa_rat_assn F C))))))) (forall ((A tptp.assn) (F tptp.fun_num_assn) (B tptp.num) (C tptp.num)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn A) (tptp.aa_num_assn F B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) C)) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X3) Y3)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_num_assn F X3)) (tptp.aa_num_assn F Y3))))) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) (tptp.aa_num_assn F C))))))) (forall ((A tptp.assn) (F tptp.fun_nat_assn) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn A) (tptp.aa_nat_assn F B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) C)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) Y3)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_nat_assn F X3)) (tptp.aa_nat_assn F Y3))))) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) (tptp.aa_nat_assn F C))))))) (forall ((A tptp.assn) (F tptp.fun_int_assn) (B tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn A) (tptp.aa_int_assn F B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) C)) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) Y3)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_int_assn F X3)) (tptp.aa_int_assn F Y3))))) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) (tptp.aa_int_assn F C))))))) (forall ((A tptp.rat) (F tptp.fun_assn_rat) (B tptp.assn) (C tptp.assn)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_assn_rat F B))) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn B) C)) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_assn_rat F X3)) (tptp.aa_assn_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_assn_rat F C))))))) (forall ((A tptp.rat) (F tptp.fun_rat_rat) (B tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat F B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat F C))))))) (forall ((A tptp.rat) (F tptp.fun_num_rat) (B tptp.num) (C tptp.num)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_num_rat F B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) C)) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat F X3)) (tptp.aa_num_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_num_rat F C))))))) (forall ((A tptp.rat) (F tptp.fun_nat_rat) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_nat_rat F B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) C)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat F X3)) (tptp.aa_nat_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_nat_rat F C))))))) (forall ((A tptp.rat) (F tptp.fun_int_rat) (B tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_int_rat F B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) C)) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) Y3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat F X3)) (tptp.aa_int_rat F Y3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_int_rat F C))))))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X))) (=> (tptp.pp (tptp.aa_assn_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn Y) Z)) (tptp.pp (tptp.aa_assn_bool _let_1 Z)))))) (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int X))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int Y) Z)) (tptp.pp (tptp.aa_set_int_bool _let_1 Z)))))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) Z)) (tptp.pp (tptp.aa_rat_bool _let_1 Z)))))) (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num X))) (=> (tptp.pp (tptp.aa_num_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) Z)) (tptp.pp (tptp.aa_num_bool _let_1 Z)))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) Z)) (tptp.pp (tptp.aa_nat_bool _let_1 Z)))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int X))) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) Z)) (tptp.pp (tptp.aa_int_bool _let_1 Z)))))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn X) Y)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn Y) Z)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X) Z))))) (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X) Y)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int Y) Z)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int X) Z))))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) Z)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Z))))) (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) Z)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Z))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) Z)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Z))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Z))))) (forall ((A tptp.assn) (B tptp.assn)) (=> (not (= A B)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn A) B)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) B))))) (forall ((A tptp.set_int) (B tptp.set_int)) (=> (not (= A B)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) B)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int A) B))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))))) (forall ((A tptp.num) (B tptp.num)) (=> (not (= A B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B))))) (forall ((A tptp.int) (B tptp.int)) (=> (not (= A B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B))))) (forall ((A tptp.assn) (B tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn A) B)) (=> (not (= A B)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) B))))) (forall ((A tptp.set_int) (B tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) B)) (=> (not (= A B)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int A) B))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (not (= A B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))))) (forall ((A tptp.num) (B tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (not (= A B)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (not (= A B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (=> (not (= A B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B))))) (forall ((X tptp.assn) (Y tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X) Y)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn X) Y)))) (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int X) Y)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X)))) (forall ((X tptp.num) (Y tptp.num)) (= (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X)))) (forall ((X tptp.num) (Y tptp.num)) (= (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X)))) (forall ((X tptp.assn) (Y tptp.assn)) (= (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X) Y)) (and (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn X) Y)) (not (= X Y))))) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int X) Y)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X) Y)) (not (= X Y))))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (not (= X Y))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (not (= X Y))))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (not (= X Y))))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (not (= X Y))))) (forall ((X tptp.assn) (Y tptp.assn)) (= (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn X) Y)) (or (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X) Y)) (= X Y)))) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X) Y)) (or (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int X) Y)) (= X Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (= X Y)))) (forall ((B tptp.assn) (A tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn B) A)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn B) A)))) (forall ((B tptp.set_int) (A tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int B) A)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) A)))) (forall ((B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)))) (forall ((B tptp.num) (A tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) A)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)))) (forall ((A tptp.assn) (B tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) B)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn A) B)))) (forall ((A tptp.set_int) (B tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int A) B)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) B)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)))) (forall ((A tptp.num) (B tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)))) (forall ((B tptp.assn) (A tptp.assn)) (= (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn B) A)) (and (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn B) A)) (not (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn A) B)))))) (forall ((B tptp.set_int) (A tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int B) A)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) A)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) B)))))) (forall ((B tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)))))) (forall ((B tptp.num) (A tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) A)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)))))) (forall ((B tptp.nat) (A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)))))) (forall ((B tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)))))) (forall ((B tptp.assn) (A tptp.assn) (C tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn B) A)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn C) B)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn C) A))))) (forall ((B tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int B) A)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int C) B)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int C) A))))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) A))))) (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) A)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num C) B)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num C) A))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C) A))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) A))))) (forall ((B tptp.assn) (A tptp.assn) (C tptp.assn)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn C))) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn B) A)) (=> (tptp.pp (tptp.aa_assn_bool _let_1 B)) (tptp.pp (tptp.aa_assn_bool _let_1 A)))))) (forall ((B tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (let ((_let_1 (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int C))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) A)) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 B)) (tptp.pp (tptp.aa_set_int_bool _let_1 A)))))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (tptp.pp (tptp.aa_rat_bool _let_1 A)))))) (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num C))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (=> (tptp.pp (tptp.aa_num_bool _let_1 B)) (tptp.pp (tptp.aa_num_bool _let_1 A)))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (tptp.pp (tptp.aa_nat_bool _let_1 A)))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (tptp.pp (tptp.aa_int_bool _let_1 A)))))) (forall ((B tptp.assn) (A tptp.assn)) (= (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn B) A)) (and (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn B) A)) (not (= A B))))) (forall ((B tptp.set_int) (A tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int B) A)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) A)) (not (= A B))))) (forall ((B tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (not (= A B))))) (forall ((B tptp.num) (A tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) A)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (not (= A B))))) (forall ((B tptp.nat) (A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (not (= A B))))) (forall ((B tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (not (= A B))))) (forall ((B tptp.assn) (A tptp.assn)) (= (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn B) A)) (or (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn B) A)) (= A B)))) (forall ((B tptp.set_int) (A tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) A)) (or (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int B) A)) (= A B)))) (forall ((B tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (= A B)))) (forall ((B tptp.num) (A tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) A)) (= A B)))) (forall ((B tptp.nat) (A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A)) (= A B)))) (forall ((B tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)) (= A B)))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (=> (forall ((W tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) W)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat W) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat W) Z))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) Z))))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z) X)) (=> (forall ((W tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z) W)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat W) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) W))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) Z))))) (forall ((A tptp.assn) (B tptp.assn)) (= (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) B)) (and (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn A) B)) (not (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn B) A)))))) (forall ((A tptp.set_int) (B tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int A) B)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) B)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) A)))))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)))))) (forall ((A tptp.num) (B tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)))))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)))))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)))))) (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A))) (=> (tptp.pp (tptp.aa_assn_bool _let_1 B)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn B) C)) (tptp.pp (tptp.aa_assn_bool _let_1 C)))))) (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (let ((_let_1 (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int A))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 B)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) C)) (tptp.pp (tptp.aa_set_int_bool _let_1 C)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (tptp.pp (tptp.aa_rat_bool _let_1 C)))))) (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num A))) (=> (tptp.pp (tptp.aa_num_bool _let_1 B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (tptp.pp (tptp.aa_num_bool _let_1 C)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) C)) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) C)) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn A) B)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn B) C)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) C))))) (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) B)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int B) C)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int A) C))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) C))))) (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) C)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) C))))) (forall ((A tptp.assn) (B tptp.assn)) (= (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) B)) (and (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn A) B)) (not (= A B))))) (forall ((A tptp.set_int) (B tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int A) B)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) B)) (not (= A B))))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (not (= A B))))) (forall ((A tptp.num) (B tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (not (= A B))))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (not (= A B))))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (not (= A B))))) (forall ((A tptp.assn) (B tptp.assn)) (= (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn A) B)) (or (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) B)) (= A B)))) (forall ((A tptp.set_int) (B tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) B)) (or (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int A) B)) (= A B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (= A B)))) (forall ((A tptp.num) (B tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B)) (= A B)))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (= A B)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (= A B)))) (forall ((Y tptp.rat) (X tptp.rat)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)))) (forall ((Y tptp.num) (X tptp.num)) (=> (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) X))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)))) (forall ((Y tptp.int) (X tptp.int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)))) (forall ((X tptp.assn) (Y tptp.assn)) (= (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X) Y)) (and (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn X) Y)) (not (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn Y) X)))))) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int X) Y)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X) Y)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int Y) X)))))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X)))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) X)))))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)))))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X)))))) (forall ((Y tptp.rat) (Z tptp.rat)) (=> (forall ((X3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Z)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) Z)))) (forall ((Z tptp.rat) (Y tptp.rat)) (=> (forall ((X3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z) X3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X3)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) Z)))) (forall ((X tptp.assn) (Y tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn X) Y)) (= (not (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X) Y))) (= X Y)))) (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X) Y)) (= (not (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int X) Y))) (= X Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y))) (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (= (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y))) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y))) (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y))) (= X Y)))) (forall ((X tptp.assn) (Y tptp.assn)) (=> (not (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X) Y))) (= (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn X) Y)) (= X Y)))) (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (not (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int X) Y))) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X) Y)) (= X Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y))) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (= X Y)))) (forall ((A tptp.assn) (B tptp.assn)) (= (not (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) B))) (or (not (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn A) B))) (= A B)))) (forall ((A tptp.set_int) (B tptp.set_int)) (= (not (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int A) B))) (or (not (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) B))) (= A B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))) (or (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))) (= A B)))) (forall ((A tptp.num) (B tptp.num)) (= (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B))) (or (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B))) (= A B)))) (forall ((A tptp.nat) (B tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B))) (or (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B))) (= A B)))) (forall ((A tptp.int) (B tptp.int)) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B))) (or (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B))) (= A B)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X)))) (forall ((X tptp.num) (Y tptp.num)) (=> (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X)))) (forall ((Y tptp.assn) (X tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn Y) X)) (not (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X) Y))))) (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int Y) X)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int X) Y))))) (forall ((Y tptp.rat) (X tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y))))) (forall ((Y tptp.num) (X tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) X)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y))))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y))))) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y))))) (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (not (= A tptp.bot_bo2099793752762293965at_nat)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le7866589430770878221at_nat tptp.bot_bo2099793752762293965at_nat) A)))) (forall ((A tptp.set_bool)) (= (not (= A tptp.bot_bot_set_bool)) (tptp.ord_less_set_bool tptp.bot_bot_set_bool A))) (forall ((A tptp.set_nat)) (= (not (= A tptp.bot_bot_set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat tptp.bot_bot_set_nat) A)))) (forall ((A tptp.set_int)) (= (not (= A tptp.bot_bot_set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int tptp.bot_bot_set_int) A)))) (forall ((A tptp.assn)) (= (not (= A tptp.bot_bot_assn)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn tptp.bot_bot_assn) A)))) (forall ((A tptp.nat)) (= (not (= A tptp.bot_bot_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.bot_bot_nat) A)))) (forall ((A tptp.set_Pr1261947904930325089at_nat)) (not (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le7866589430770878221at_nat A) tptp.bot_bo2099793752762293965at_nat)))) (forall ((A tptp.set_bool)) (not (tptp.ord_less_set_bool A tptp.bot_bot_set_bool))) (forall ((A tptp.set_nat)) (not (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat A) tptp.bot_bot_set_nat)))) (forall ((A tptp.set_int)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int A) tptp.bot_bot_set_int)))) (forall ((A tptp.assn)) (not (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) tptp.bot_bot_assn)))) (forall ((A tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) tptp.bot_bot_nat)))) (forall ((B tptp.set_nat) (C tptp.set_nat) (A tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat B) C)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A) B)) C)))) (forall ((B tptp.product_unit) (C tptp.product_unit) (A tptp.product_unit)) (=> (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le361264281704409273t_unit B) C)) (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le361264281704409273t_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit A) B)) C)))) (forall ((B tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le7866589430770878221at_nat B) C)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le7866589430770878221at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A) B)) C)))) (forall ((B tptp.assn) (C tptp.assn) (A tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn B) C)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A) B)) C)))) (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat A) B)) C)))) (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat A) B)) C)))) (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int A) B)) C)))) (forall ((A tptp.set_nat) (C tptp.set_nat) (B tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat A) C)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A) B)) C)))) (forall ((A tptp.product_unit) (C tptp.product_unit) (B tptp.product_unit)) (=> (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le361264281704409273t_unit A) C)) (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le361264281704409273t_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit A) B)) C)))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le7866589430770878221at_nat A) C)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le7866589430770878221at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A) B)) C)))) (forall ((A tptp.assn) (C tptp.assn) (B tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) C)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A) B)) C)))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat A) B)) C)))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat A) B)) C)))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int A) B)) C)))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat A) B)) (and (= A (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A) B)) (not (= A B))))) (forall ((A tptp.product_unit) (B tptp.product_unit)) (= (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le361264281704409273t_unit A) B)) (and (= A (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit A) B)) (not (= A B))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le7866589430770878221at_nat A) B)) (and (= A (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A) B)) (not (= A B))))) (forall ((A tptp.assn) (B tptp.assn)) (= (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) B)) (and (= A (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A) B)) (not (= A B))))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (and (= A (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat A) B)) (not (= A B))))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (and (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat A) B)) (not (= A B))))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (and (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int A) B)) (not (= A B))))) (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat A))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat B) C))) (not (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 B)) (not (tptp.pp (tptp.aa_set_nat_bool _let_1 C)))))))) (forall ((A tptp.product_unit) (B tptp.product_unit) (C tptp.product_unit)) (let ((_let_1 (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le361264281704409273t_unit A))) (=> (tptp.pp (tptp.aa_Product_unit_bool _let_1 (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit B) C))) (not (=> (tptp.pp (tptp.aa_Product_unit_bool _let_1 B)) (not (tptp.pp (tptp.aa_Product_unit_bool _let_1 C)))))))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set7594618562247239262t_bool tptp.ord_le7866589430770878221at_nat A))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat B) C))) (not (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 B)) (not (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 C)))))))) (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A))) (=> (tptp.pp (tptp.aa_assn_bool _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn B) C))) (not (=> (tptp.pp (tptp.aa_assn_bool _let_1 B)) (not (tptp.pp (tptp.aa_assn_bool _let_1 C)))))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat B) C))) (not (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (not (tptp.pp (tptp.aa_rat_bool _let_1 C)))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat B) C))) (not (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (not (tptp.pp (tptp.aa_nat_bool _let_1 C)))))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int B) C))) (not (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (not (tptp.pp (tptp.aa_int_bool _let_1 C)))))))) (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat B) A)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A) B) B))) (forall ((B tptp.product_unit) (A tptp.product_unit)) (=> (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le361264281704409273t_unit B) A)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit A) B) B))) (forall ((B tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le7866589430770878221at_nat B) A)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A) B) B))) (forall ((B tptp.assn) (A tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn B) A)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A) B) B))) (forall ((B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat A) B) B))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat A) B) B))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int A) B) B))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat A) B)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A) B) A))) (forall ((A tptp.product_unit) (B tptp.product_unit)) (=> (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le361264281704409273t_unit A) B)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit A) B) A))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le7866589430770878221at_nat A) B)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A) B) A))) (forall ((A tptp.assn) (B tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) B)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A) B) A))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat A) B) A))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat A) B) A))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int A) B) A))) (forall ((B tptp.set_nat) (X tptp.set_nat) (A tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat B) X)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A) B)) X)))) (forall ((B tptp.product_unit) (X tptp.product_unit) (A tptp.product_unit)) (=> (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le361264281704409273t_unit B) X)) (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le361264281704409273t_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit A) B)) X)))) (forall ((B tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le7866589430770878221at_nat B) X)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le7866589430770878221at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A) B)) X)))) (forall ((B tptp.assn) (X tptp.assn) (A tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn B) X)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A) B)) X)))) (forall ((B tptp.rat) (X tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat A) B)) X)))) (forall ((B tptp.nat) (X tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) X)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat A) B)) X)))) (forall ((B tptp.int) (X tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) X)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int A) B)) X)))) (forall ((A tptp.set_nat) (X tptp.set_nat) (B tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat A) X)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A) B)) X)))) (forall ((A tptp.product_unit) (X tptp.product_unit) (B tptp.product_unit)) (=> (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le361264281704409273t_unit A) X)) (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le361264281704409273t_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit A) B)) X)))) (forall ((A tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le7866589430770878221at_nat A) X)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le7866589430770878221at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A) B)) X)))) (forall ((A tptp.assn) (X tptp.assn) (B tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) X)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A) B)) X)))) (forall ((A tptp.rat) (X tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.inf_inf_rat A) B)) X)))) (forall ((A tptp.nat) (X tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) X)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat A) B)) X)))) (forall ((A tptp.int) (X tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) X)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.inf_inf_int A) B)) X)))) (forall ((C tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.ord_le6428140832669894131at_nat C B) (tptp.ord_le6428140832669894131at_nat C (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A) B)))) (forall ((C tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.ord_le7642048601412989811at_nat C B) (tptp.ord_le7642048601412989811at_nat C (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A) B)))) (forall ((C tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.ord_le2604355607129572851at_nat C B) (tptp.ord_le2604355607129572851at_nat C (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A) B)))) (forall ((C tptp.set_nat) (B tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat C))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 B)) (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A) B)))))) (forall ((C tptp.assn) (B tptp.assn) (A tptp.assn)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn C))) (=> (tptp.pp (tptp.aa_assn_bool _let_1 B)) (tptp.pp (tptp.aa_assn_bool _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn A) B)))))) (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat A) B)))))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat A) B)))))) (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int C))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int A) B)))))) (forall ((C tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.ord_le6428140832669894131at_nat C A) (tptp.ord_le6428140832669894131at_nat C (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A) B)))) (forall ((C tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.ord_le7642048601412989811at_nat C A) (tptp.ord_le7642048601412989811at_nat C (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A) B)))) (forall ((C tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.ord_le2604355607129572851at_nat C A) (tptp.ord_le2604355607129572851at_nat C (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A) B)))) (forall ((C tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat C))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A)) (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A) B)))))) (forall ((C tptp.assn) (A tptp.assn) (B tptp.assn)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn C))) (=> (tptp.pp (tptp.aa_assn_bool _let_1 A)) (tptp.pp (tptp.aa_assn_bool _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn A) B)))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat A) B)))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat A) B)))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int C))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int A) B)))))) (forall ((B tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat)) (= (tptp.ord_le6428140832669894131at_nat B A) (and (= A (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A) B)) (not (= A B))))) (forall ((B tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat)) (= (tptp.ord_le7642048601412989811at_nat B A) (and (= A (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A) B)) (not (= A B))))) (forall ((B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (= (tptp.ord_le2604355607129572851at_nat B A) (and (= A (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A) B)) (not (= A B))))) (forall ((B tptp.set_nat) (A tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat B) A)) (and (= A (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A) B)) (not (= A B))))) (forall ((B tptp.assn) (A tptp.assn)) (= (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn B) A)) (and (= A (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn A) B)) (not (= A B))))) (forall ((B tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (and (= A (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat A) B)) (not (= A B))))) (forall ((B tptp.nat) (A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A)) (and (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat A) B)) (not (= A B))))) (forall ((B tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)) (and (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int A) B)) (not (= A B))))) (forall ((B tptp.set_Pr8693737435421807431at_nat) (C tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.ord_le6428140832669894131at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat B) C) A) (not (=> (tptp.ord_le6428140832669894131at_nat B A) (not (tptp.ord_le6428140832669894131at_nat C A)))))) (forall ((B tptp.set_Pr8551490117392284871at_nat) (C tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.ord_le7642048601412989811at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat B) C) A) (not (=> (tptp.ord_le7642048601412989811at_nat B A) (not (tptp.ord_le7642048601412989811at_nat C A)))))) (forall ((B tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.ord_le2604355607129572851at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat B) C) A) (not (=> (tptp.ord_le2604355607129572851at_nat B A) (not (tptp.ord_le2604355607129572851at_nat C A)))))) (forall ((B tptp.set_nat) (C tptp.set_nat) (A tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat B) C)) A)) (not (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat B) A)) (not (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat C) A))))))) (forall ((B tptp.assn) (C tptp.assn) (A tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn B) C)) A)) (not (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn B) A)) (not (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn C) A))))))) (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat B) C)) A)) (not (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) A))))))) (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat B) C)) A)) (not (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C) A))))))) (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int B) C)) A)) (not (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) A))))))) (forall ((A tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.ord_le6428140832669894131at_nat A B) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A) B) B))) (forall ((A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.ord_le7642048601412989811at_nat A B) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A) B) B))) (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.ord_le2604355607129572851at_nat A B) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A) B) B))) (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat A) B)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A) B) B))) (forall ((A tptp.assn) (B tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) B)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn A) B) B))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat A) B) B))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat A) B) B))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int A) B) B))) (forall ((B tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.ord_le6428140832669894131at_nat B A) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A) B) A))) (forall ((B tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.ord_le7642048601412989811at_nat B A) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A) B) A))) (forall ((B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.ord_le2604355607129572851at_nat B A) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A) B) A))) (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat B) A)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A) B) A))) (forall ((B tptp.assn) (A tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn B) A)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn A) B) A))) (forall ((B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat A) B) A))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat A) B) A))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int A) B) A))) (forall ((X tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.ord_le6428140832669894131at_nat X B) (tptp.ord_le6428140832669894131at_nat X (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A) B)))) (forall ((X tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.ord_le7642048601412989811at_nat X B) (tptp.ord_le7642048601412989811at_nat X (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A) B)))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.ord_le2604355607129572851at_nat X B) (tptp.ord_le2604355607129572851at_nat X (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A) B)))) (forall ((X tptp.set_nat) (B tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat X))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 B)) (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A) B)))))) (forall ((X tptp.assn) (B tptp.assn) (A tptp.assn)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X))) (=> (tptp.pp (tptp.aa_assn_bool _let_1 B)) (tptp.pp (tptp.aa_assn_bool _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn A) B)))))) (forall ((X tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat A) B)))))) (forall ((X tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat A) B)))))) (forall ((X tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int X))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int A) B)))))) (forall ((X tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.ord_le6428140832669894131at_nat X A) (tptp.ord_le6428140832669894131at_nat X (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A) B)))) (forall ((X tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.ord_le7642048601412989811at_nat X A) (tptp.ord_le7642048601412989811at_nat X (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A) B)))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.ord_le2604355607129572851at_nat X A) (tptp.ord_le2604355607129572851at_nat X (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A) B)))) (forall ((X tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat X))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A)) (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A) B)))))) (forall ((X tptp.assn) (A tptp.assn) (B tptp.assn)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X))) (=> (tptp.pp (tptp.aa_assn_bool _let_1 A)) (tptp.pp (tptp.aa_assn_bool _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn A) B)))))) (forall ((X tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.sup_sup_rat A) B)))))) (forall ((X tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat A) B)))))) (forall ((X tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int X))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.sup_sup_int A) B)))))) (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat) (H3 tptp.heap_e7401611519738050253t_unit)) (= (tptp.hoare_new_addrs H As H3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat As) (tptp.collect_nat (tptp.aa_hea5076648075882977743t_bool (tptp.aTP_Lamm_cn H) H3))))) (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int) (D2 tptp.set_int)) (=> (= A B) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) C)) (=> (= C D2) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) D2)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (= A B) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (= C D2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) D2)))))) (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D2 tptp.num)) (=> (= A B) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (= C D2) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) D2)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (= A B) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) C)) (=> (= C D2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) D2)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= A B) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) C)) (=> (= C D2) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) D2)))))) (forall ((A tptp.nat) (B tptp.nat) (S tptp.set_Pr1261947904930325089at_nat) (P tptp.fun_nat_fun_nat_bool)) (let ((_let_1 (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat A) B)) S)))) (=> _let_1 (=> (=> _let_1 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A) B))) (exists ((A4 tptp.nat) (B4 tptp.nat)) (and (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat A4) B4)) S)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A4) B4)))))))) (forall ((A tptp.fun_Pr6001797050664311790t_bool) (B tptp.produc3658429121746597890et_nat) (S tptp.set_Pr1106803562331729365et_nat) (P tptp.fun_fu7398481913972163267t_bool)) (let ((_let_1 (tptp.member8615881266069945910et_nat (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat A) B) S))) (=> _let_1 (=> (=> _let_1 (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.aa_fun6808777976510360636t_bool P A) B))) (exists ((A4 tptp.fun_Pr6001797050664311790t_bool) (B4 tptp.produc3658429121746597890et_nat)) (and (tptp.member8615881266069945910et_nat (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat A4) B4) S) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.aa_fun6808777976510360636t_bool P A4) B4)))))))) (forall ((A tptp.fun_Pr6001797050664311790t_bool) (B tptp.produc6108883039684432031et_nat) (S tptp.set_Pr9222568342844664434et_nat) (P tptp.fun_fu5758690788630904038t_bool)) (let ((_let_1 (tptp.member2818932950976722259et_nat (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat A) B) S))) (=> _let_1 (=> (=> _let_1 (tptp.pp (tptp.aa_Pro7454463142485379962t_bool (tptp.aa_fun1003322038264691679t_bool P A) B))) (exists ((A4 tptp.fun_Pr6001797050664311790t_bool) (B4 tptp.produc6108883039684432031et_nat)) (and (tptp.member2818932950976722259et_nat (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat A4) B4) S) (tptp.pp (tptp.aa_Pro7454463142485379962t_bool (tptp.aa_fun1003322038264691679t_bool P A4) B4)))))))) (forall ((A tptp.fun_Pr9164807099015279978e_term) (B tptp.product_prod_int_int) (S tptp.set_Pr233528076387193594nt_int) (P tptp.fun_fu4196931294019812808t_bool)) (let ((_let_1 (tptp.member690604328116145115nt_int (tptp.aa_Pro3513184699142849729nt_int (tptp.aa_fun1388719692539776744nt_int tptp.produc1560874099174258678nt_int A) B) S))) (=> _let_1 (=> (=> _let_1 (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun5300525129335604105t_bool P A) B))) (exists ((A4 tptp.fun_Pr9164807099015279978e_term) (B4 tptp.product_prod_int_int)) (and (tptp.member690604328116145115nt_int (tptp.aa_Pro3513184699142849729nt_int (tptp.aa_fun1388719692539776744nt_int tptp.produc1560874099174258678nt_int A4) B4) S) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun5300525129335604105t_bool P A4) B4)))))))) (forall ((A tptp.fun_in6429348457993719614e_term) (B tptp.product_prod_int_int) (S tptp.set_Pr5033440245338114598nt_int) (P tptp.fun_fu5117548769634986908t_bool)) (let ((_let_1 (tptp.member500491123954006279nt_int (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int A) B) S))) (=> _let_1 (=> (=> _let_1 (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun4446166836006121821t_bool P A) B))) (exists ((A4 tptp.fun_in6429348457993719614e_term) (B4 tptp.product_prod_int_int)) (and (tptp.member500491123954006279nt_int (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int A4) B4) S) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun4446166836006121821t_bool P A4) B4)))))))) (forall ((A tptp.a) (B tptp.produc6653097349344004940it_nat) (S tptp.set_Pr7098220151150636591it_nat) (P tptp.fun_a_4602865052023851497t_bool)) (let ((_let_1 (tptp.member4554412811331277712it_nat (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat A) B) S))) (=> _let_1 (=> (=> _let_1 (tptp.pp (tptp.aa_Pro3182513528956304653t_bool (tptp.aa_a_f736957945511644770t_bool P A) B))) (exists ((A4 tptp.a) (B4 tptp.produc6653097349344004940it_nat)) (and (tptp.member4554412811331277712it_nat (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat A4) B4) S) (tptp.pp (tptp.aa_Pro3182513528956304653t_bool (tptp.aa_a_f736957945511644770t_bool P A4) B4)))))))) (forall ((R3 tptp.set_Pr1261947904930325089at_nat) (S2 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat X3) Y3)))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 R3)) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 S2))))) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat R3) S2)))) (forall ((R3 tptp.set_Pr1106803562331729365et_nat) (S2 tptp.set_Pr1106803562331729365et_nat)) (=> (forall ((X3 tptp.fun_Pr6001797050664311790t_bool) (Y3 tptp.produc3658429121746597890et_nat)) (let ((_let_1 (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat X3) Y3))) (=> (tptp.member8615881266069945910et_nat _let_1 R3) (tptp.member8615881266069945910et_nat _let_1 S2)))) (tptp.ord_le8271263703964716597et_nat R3 S2))) (forall ((R3 tptp.set_Pr9222568342844664434et_nat) (S2 tptp.set_Pr9222568342844664434et_nat)) (=> (forall ((X3 tptp.fun_Pr6001797050664311790t_bool) (Y3 tptp.produc6108883039684432031et_nat)) (let ((_let_1 (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat X3) Y3))) (=> (tptp.member2818932950976722259et_nat _let_1 R3) (tptp.member2818932950976722259et_nat _let_1 S2)))) (tptp.ord_le4695037514429983442et_nat R3 S2))) (forall ((R3 tptp.set_Pr233528076387193594nt_int) (S2 tptp.set_Pr233528076387193594nt_int)) (=> (forall ((X3 tptp.fun_Pr9164807099015279978e_term) (Y3 tptp.product_prod_int_int)) (let ((_let_1 (tptp.aa_Pro3513184699142849729nt_int (tptp.aa_fun1388719692539776744nt_int tptp.produc1560874099174258678nt_int X3) Y3))) (=> (tptp.member690604328116145115nt_int _let_1 R3) (tptp.member690604328116145115nt_int _let_1 S2)))) (tptp.ord_le5172437211506631514nt_int R3 S2))) (forall ((R3 tptp.set_Pr5033440245338114598nt_int) (S2 tptp.set_Pr5033440245338114598nt_int)) (=> (forall ((X3 tptp.fun_in6429348457993719614e_term) (Y3 tptp.product_prod_int_int)) (let ((_let_1 (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int X3) Y3))) (=> (tptp.member500491123954006279nt_int _let_1 R3) (tptp.member500491123954006279nt_int _let_1 S2)))) (tptp.ord_le172202941055982214nt_int R3 S2))) (forall ((R3 tptp.set_Pr7098220151150636591it_nat) (S2 tptp.set_Pr7098220151150636591it_nat)) (=> (forall ((X3 tptp.a) (Y3 tptp.produc6653097349344004940it_nat)) (let ((_let_1 (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat X3) Y3))) (=> (tptp.member4554412811331277712it_nat _let_1 R3) (tptp.member4554412811331277712it_nat _let_1 S2)))) (tptp.ord_le4478181985103859343it_nat R3 S2))) (forall ((X tptp.set_nat) (S tptp.set_set_nat)) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat X) S)) (not (= S tptp.bot_bot_set_set_nat)))) (forall ((X tptp.product_prod_nat_nat) (S tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat X) S)) (not (= S tptp.bot_bo2099793752762293965at_nat)))) (forall ((X tptp.bool) (S tptp.set_bool)) (=> (tptp.pp (tptp.member_bool X S)) (not (= S tptp.bot_bot_set_bool)))) (forall ((X tptp.nat) (S tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X) S)) (not (= S tptp.bot_bot_set_nat)))) (forall ((X tptp.int) (S tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X) S)) (not (= S tptp.bot_bot_set_int)))) (forall ((S tptp.set_set_nat)) (=> (not (= S tptp.bot_bot_set_set_nat)) (not (forall ((X3 tptp.set_nat)) (not (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat X3) S))))))) (forall ((S tptp.set_Pr1261947904930325089at_nat)) (=> (not (= S tptp.bot_bo2099793752762293965at_nat)) (not (forall ((X3 tptp.product_prod_nat_nat)) (not (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat X3) S))))))) (forall ((S tptp.set_bool)) (=> (not (= S tptp.bot_bot_set_bool)) (not (forall ((X3 tptp.bool)) (not (tptp.pp (tptp.member_bool X3 S))))))) (forall ((S tptp.set_nat)) (=> (not (= S tptp.bot_bot_set_nat)) (not (forall ((X3 tptp.nat)) (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) S))))))) (forall ((S tptp.set_int)) (=> (not (= S tptp.bot_bot_set_int)) (not (forall ((X3 tptp.int)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) S))))))) (forall ((S tptp.set_nat) (S3 tptp.set_nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat B3))) (let ((_let_2 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat S) S3)) (=> (= (tptp.aa_set_nat_set_nat _let_2 S3) (tptp.aa_set_nat_set_nat _let_1 S3)) (= (tptp.aa_set_nat_set_nat _let_2 S) (tptp.aa_set_nat_set_nat _let_1 S))))))) (forall ((S tptp.set_Pr1261947904930325089at_nat) (S3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat B3))) (let ((_let_2 (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat S) S3)) (=> (= (tptp.aa_set8868280134176360700at_nat _let_2 S3) (tptp.aa_set8868280134176360700at_nat _let_1 S3)) (= (tptp.aa_set8868280134176360700at_nat _let_2 S) (tptp.aa_set8868280134176360700at_nat _let_1 S))))))) (forall ((S tptp.set_int) (S3 tptp.set_int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int B3))) (let ((_let_2 (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int S) S3)) (=> (= (tptp.aa_set_int_set_int _let_2 S3) (tptp.aa_set_int_set_int _let_1 S3)) (= (tptp.aa_set_int_set_int _let_2 S) (tptp.aa_set_int_set_int _let_1 S))))))) (forall ((P tptp.assn) (C tptp.heap_T5738788834812785303t_unit) (Q tptp.fun_Pr6626665806141890376t_assn)) (= (tptp.hoare_8945653483474564448t_unit P C Q) (forall ((H6 tptp.heap_e7401611519738050253t_unit) (As5 tptp.set_nat)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn P) (tptp.produc7507926704131184380et_nat H6 As5))) (exists ((R4 tptp.product_unit) (H7 tptp.heap_e7401611519738050253t_unit)) (and (exists ((T3 tptp.nat)) (= (tptp.aa_hea684056619475940329it_nat (tptp.heap_T875086893843062177t_unit C) H6) (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat (tptp.produc7133225469290080770it_nat R4 (tptp.produc584006145561248582it_nat H7 T3))))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn (tptp.aa_Product_unit_assn Q R4)) (tptp.produc7507926704131184380et_nat H7 (tptp.hoare_new_addrs H6 As5 H7)))) (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.relH (tptp.collect_nat (tptp.aa_set3744802623701456604t_bool (tptp.aTP_Lamm_co H6) As5)) H6) H7)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.lim_Product_unit H6)) (tptp.lim_Product_unit H7))))))))) (forall ((P tptp.assn) (C tptp.heap_Time_Heap_a) (Q tptp.fun_a_assn)) (= (tptp.hoare_hoare_triple_a P C Q) (forall ((H6 tptp.heap_e7401611519738050253t_unit) (As5 tptp.set_nat)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn P) (tptp.produc7507926704131184380et_nat H6 As5))) (exists ((R4 tptp.a) (H7 tptp.heap_e7401611519738050253t_unit)) (and (exists ((T3 tptp.nat)) (= (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a C) H6) (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat R4) (tptp.produc584006145561248582it_nat H7 T3))))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn (tptp.aa_a_assn Q R4)) (tptp.produc7507926704131184380et_nat H7 (tptp.hoare_new_addrs H6 As5 H7)))) (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.relH (tptp.collect_nat (tptp.aa_set3744802623701456604t_bool (tptp.aTP_Lamm_co H6) As5)) H6) H7)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.lim_Product_unit H6)) (tptp.lim_Product_unit H7))))))))) (forall ((P tptp.assn) (C tptp.heap_T5738788834812785303t_unit) (Q tptp.fun_Pr6626665806141890376t_assn)) (=> (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn P) (tptp.produc7507926704131184380et_nat H4 As4))) (exists ((R5 tptp.product_unit) (H8 tptp.heap_e7401611519738050253t_unit) (T4 tptp.nat)) (and (= (tptp.aa_hea684056619475940329it_nat (tptp.heap_T875086893843062177t_unit C) H4) (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat (tptp.produc7133225469290080770it_nat R5 (tptp.produc584006145561248582it_nat H8 T4)))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn (tptp.aa_Product_unit_assn Q R5)) (tptp.produc7507926704131184380et_nat H8 (tptp.hoare_new_addrs H4 As4 H8)))) (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.relH (tptp.collect_nat (tptp.aa_set3744802623701456604t_bool (tptp.aTP_Lamm_co H4) As4)) H4) H8)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.lim_Product_unit H4)) (tptp.lim_Product_unit H8))))))) (tptp.hoare_8945653483474564448t_unit P C Q))) (forall ((P tptp.assn) (C tptp.heap_Time_Heap_a) (Q tptp.fun_a_assn)) (=> (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn P) (tptp.produc7507926704131184380et_nat H4 As4))) (exists ((R5 tptp.a) (H8 tptp.heap_e7401611519738050253t_unit) (T4 tptp.nat)) (and (= (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a C) H4) (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat R5) (tptp.produc584006145561248582it_nat H8 T4)))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn (tptp.aa_a_assn Q R5)) (tptp.produc7507926704131184380et_nat H8 (tptp.hoare_new_addrs H4 As4 H8)))) (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.relH (tptp.collect_nat (tptp.aa_set3744802623701456604t_bool (tptp.aTP_Lamm_co H4) As4)) H4) H8)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.lim_Product_unit H4)) (tptp.lim_Product_unit H8))))))) (tptp.hoare_hoare_triple_a P C Q))) (forall ((P tptp.assn) (C tptp.heap_T5738788834812785303t_unit) (Q tptp.fun_Pr6626665806141890376t_assn) (H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (tptp.hoare_8945653483474564448t_unit P C Q) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn P) (tptp.produc7507926704131184380et_nat H As))) (not (forall ((R2 tptp.product_unit) (H5 tptp.heap_e7401611519738050253t_unit)) (=> (exists ((T2 tptp.nat)) (= (tptp.aa_hea684056619475940329it_nat (tptp.heap_T875086893843062177t_unit C) H) (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat (tptp.produc7133225469290080770it_nat R2 (tptp.produc584006145561248582it_nat H5 T2))))) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn (tptp.aa_Product_unit_assn Q R2)) (tptp.produc7507926704131184380et_nat H5 (tptp.hoare_new_addrs H As H5)))) (=> (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.relH (tptp.collect_nat (tptp.aa_set3744802623701456604t_bool (tptp.aTP_Lamm_co H) As)) H) H5)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.lim_Product_unit H)) (tptp.lim_Product_unit H5)))))))))))) (forall ((P tptp.assn) (C tptp.heap_Time_Heap_a) (Q tptp.fun_a_assn) (H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (tptp.hoare_hoare_triple_a P C Q) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn P) (tptp.produc7507926704131184380et_nat H As))) (not (forall ((R2 tptp.a) (H5 tptp.heap_e7401611519738050253t_unit)) (=> (exists ((T2 tptp.nat)) (= (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a C) H) (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat R2) (tptp.produc584006145561248582it_nat H5 T2))))) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn (tptp.aa_a_assn Q R2)) (tptp.produc7507926704131184380et_nat H5 (tptp.hoare_new_addrs H As H5)))) (=> (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.relH (tptp.collect_nat (tptp.aa_set3744802623701456604t_bool (tptp.aTP_Lamm_co H) As)) H) H5)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.lim_Product_unit H)) (tptp.lim_Product_unit H5)))))))))))) (tptp.semila1307241728879085301at_nat tptp.sup_su718114333110466843at_nat tptp.bot_bo5327735625951526323at_nat tptp.aTP_Lamm_cp tptp.aTP_Lamm_cq) (tptp.semila5207306265035627125at_nat tptp.sup_su3035147773818789531at_nat tptp.bot_bo8422036546324065075at_nat tptp.aTP_Lamm_cr tptp.aTP_Lamm_cs) (tptp.semila6534579987270727413at_nat tptp.sup_su5525570899277871387at_nat tptp.bot_bo228742789529271731at_nat tptp.aTP_Lamm_ct tptp.aTP_Lamm_cu) (tptp.semila4918476307565957903at_nat tptp.sup_su6327502436637775413at_nat tptp.bot_bo2099793752762293965at_nat tptp.aTP_Lamm_cv tptp.aTP_Lamm_cw) (tptp.semila8830438993314920101t_bool tptp.sup_sup_set_bool tptp.bot_bot_set_bool tptp.aTP_Lamm_cx tptp.aTP_Lamm_cy) (tptp.semila1667268886620078168et_nat tptp.sup_sup_set_nat tptp.bot_bot_set_nat tptp.aTP_Lamm_cz tptp.aTP_Lamm_da) (tptp.semila8603258263270017530r_assn tptp.sup_sup_assn tptp.bot_bot_assn tptp.aTP_Lamm_db tptp.aTP_Lamm_dc) (tptp.semila6712789903965657268et_int tptp.sup_sup_set_int tptp.bot_bot_set_int tptp.aTP_Lamm_dd tptp.aTP_Lamm_de) (forall ((N2 tptp.nat) (P tptp.fun_nat_bool) (M tptp.nat)) (=> (forall ((K2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) K2)) (tptp.pp (tptp.aa_nat_bool P K2)))) (=> (forall ((K2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K2) N2)) (=> (forall ((I tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K2) I)) (tptp.pp (tptp.aa_nat_bool P I)))) (tptp.pp (tptp.aa_nat_bool P K2))))) (tptp.pp (tptp.aa_nat_bool P M))))) (forall ((F tptp.fun_nat_nat) (I2 tptp.nat) (J tptp.nat)) (=> (forall ((I3 tptp.nat) (J2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) J2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat F I3)) (tptp.aa_nat_nat F J2))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) J)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat F I2)) (tptp.aa_nat_nat F J)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (=> (not (= M N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (= M N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (= M N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (not (= M N2))))) (forall ((A3 tptp.set_set_nat)) (=> (forall ((X3 tptp.set_nat)) (not (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat X3) A3)))) (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat A3) tptp.bot_bot_set_set_nat)))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.product_prod_nat_nat)) (not (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat X3) A3)))) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A3) tptp.bot_bo2099793752762293965at_nat)))) (forall ((A3 tptp.set_bool)) (=> (forall ((X3 tptp.bool)) (not (tptp.pp (tptp.member_bool X3 A3)))) (tptp.ord_less_eq_set_bool A3 tptp.bot_bot_set_bool))) (forall ((A3 tptp.set_nat)) (=> (forall ((X3 tptp.nat)) (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)))) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) tptp.bot_bot_set_nat)))) (forall ((A3 tptp.set_int)) (=> (forall ((X3 tptp.int)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)))) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) tptp.bot_bot_set_int)))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (=> (not (= A3 B3)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int A3) B3))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (= A3 tptp.bot_bo2099793752762293965at_nat) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A3) B3)))) (forall ((F tptp.fun_nat_fun_nat_nat) (Z tptp.nat) (Less_eq tptp.fun_nat_fun_nat_bool) (Less tptp.fun_nat_fun_nat_bool) (A tptp.nat) (B tptp.nat)) (=> (tptp.semila1623282765462674594er_nat F Z Less_eq Less) (= (= Z (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat F A) B)) (and (= A Z) (= B Z))))) (forall ((F tptp.fun_nat_fun_nat_nat) (Z tptp.nat) (Less_eq tptp.fun_nat_fun_nat_bool) (Less tptp.fun_nat_fun_nat_bool) (A tptp.nat) (B tptp.nat)) (=> (tptp.semila1623282765462674594er_nat F Z Less_eq Less) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat F A) B) Z) (and (= A Z) (= B Z))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (not (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le7866589430770878221at_nat A3) tptp.bot_bo2099793752762293965at_nat)))) (forall ((A3 tptp.set_bool)) (not (tptp.ord_less_set_bool A3 tptp.bot_bot_set_bool))) (forall ((A3 tptp.set_nat)) (not (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat A3) tptp.bot_bot_set_nat)))) (forall ((A3 tptp.set_int)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int A3) tptp.bot_bot_set_int)))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (or (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int A3) B3)) (= A3 B3)))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (C3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int B3) C3)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int A3) C3))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int A3) B3)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) A3)))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (C3 tptp.set_int)) (let ((_let_1 (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int A3))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 B3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) C3)) (tptp.pp (tptp.aa_set_int_bool _let_1 C3)))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int A3) B3)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int A3) B3)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (not (= A3 B3))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int A3) B3)) (not (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) A3)))))) (forall ((A tptp.assn) (B tptp.assn)) (= (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) B)) (and (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn A) B)) (not (= A B))))) (forall ((R3 tptp.nat) (S2 tptp.nat) (R tptp.set_Pr1261947904930325089at_nat) (S4 tptp.nat)) (let ((_let_1 (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat R3))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat (tptp.aa_nat7603221163087113075at_nat _let_1 S2)) R)) (=> (= S4 S2) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat (tptp.aa_nat7603221163087113075at_nat _let_1 S4)) R)))))) (forall ((R3 tptp.fun_Pr6001797050664311790t_bool) (S2 tptp.produc3658429121746597890et_nat) (R tptp.set_Pr1106803562331729365et_nat) (S4 tptp.produc3658429121746597890et_nat)) (let ((_let_1 (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat R3))) (=> (tptp.member8615881266069945910et_nat (tptp.aa_Pro1252775905504286431et_nat _let_1 S2) R) (=> (= S4 S2) (tptp.member8615881266069945910et_nat (tptp.aa_Pro1252775905504286431et_nat _let_1 S4) R))))) (forall ((R3 tptp.fun_Pr6001797050664311790t_bool) (S2 tptp.produc6108883039684432031et_nat) (R tptp.set_Pr9222568342844664434et_nat) (S4 tptp.produc6108883039684432031et_nat)) (let ((_let_1 (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat R3))) (=> (tptp.member2818932950976722259et_nat (tptp.aa_Pro4782578008252579993et_nat _let_1 S2) R) (=> (= S4 S2) (tptp.member2818932950976722259et_nat (tptp.aa_Pro4782578008252579993et_nat _let_1 S4) R))))) (forall ((R3 tptp.fun_Pr9164807099015279978e_term) (S2 tptp.product_prod_int_int) (R tptp.set_Pr233528076387193594nt_int) (S4 tptp.product_prod_int_int)) (let ((_let_1 (tptp.aa_fun1388719692539776744nt_int tptp.produc1560874099174258678nt_int R3))) (=> (tptp.member690604328116145115nt_int (tptp.aa_Pro3513184699142849729nt_int _let_1 S2) R) (=> (= S4 S2) (tptp.member690604328116145115nt_int (tptp.aa_Pro3513184699142849729nt_int _let_1 S4) R))))) (forall ((R3 tptp.fun_in6429348457993719614e_term) (S2 tptp.product_prod_int_int) (R tptp.set_Pr5033440245338114598nt_int) (S4 tptp.product_prod_int_int)) (let ((_let_1 (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int R3))) (=> (tptp.member500491123954006279nt_int (tptp.aa_Pro835648289009615341nt_int _let_1 S2) R) (=> (= S4 S2) (tptp.member500491123954006279nt_int (tptp.aa_Pro835648289009615341nt_int _let_1 S4) R))))) (forall ((R3 tptp.a) (S2 tptp.produc6653097349344004940it_nat) (R tptp.set_Pr7098220151150636591it_nat) (S4 tptp.produc6653097349344004940it_nat)) (let ((_let_1 (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat R3))) (=> (tptp.member4554412811331277712it_nat (tptp.aa_Pro8078911840264235907it_nat _let_1 S2) R) (=> (= S4 S2) (tptp.member4554412811331277712it_nat (tptp.aa_Pro8078911840264235907it_nat _let_1 S4) R))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (not (= M N2)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M))))) (forall ((N2 tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) N2)))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)) (not (= M N2)))) (forall ((S2 tptp.nat) (T5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat S2) T5)) (not (= S2 T5)))) (forall ((N2 tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) N2)))) (forall ((P tptp.fun_nat_bool) (N2 tptp.nat)) (=> (forall ((N5 tptp.nat)) (=> (forall ((M4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M4) N5)) (tptp.pp (tptp.aa_nat_bool P M4)))) (tptp.pp (tptp.aa_nat_bool P N5)))) (tptp.pp (tptp.aa_nat_bool P N2)))) (forall ((P tptp.fun_nat_bool) (N2 tptp.nat)) (=> (forall ((N5 tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool P N5))) (exists ((M4 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M4) N5)) (not (tptp.pp (tptp.aa_nat_bool P M4))))))) (tptp.pp (tptp.aa_nat_bool P N2)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X))))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N2))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 J)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat J) K)) (tptp.pp (tptp.aa_nat_bool _let_1 K)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= M N2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (= M N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)))) (forall ((P tptp.fun_nat_bool) (K tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P K)) (=> (forall ((Y3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P Y3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y3) B)))) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool P X3)) (forall ((Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y4) X3))))))))) (forall ((X tptp.product_prod_nat_nat) (Z3 tptp.set_Pr1261947904930325089at_nat) (X6 tptp.set_Pr1261947904930325089at_nat) (P tptp.fun_Pr7757163693017731481t_bool)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat X) Z3)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat Z3) (tptp.collec3392354462482085612at_nat (tptp.aa_fun830836278467416944t_bool (tptp.aTP_Lamm_al X6) P)))) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool P X))))) (forall ((X tptp.bool) (Z3 tptp.set_bool) (X6 tptp.set_bool) (P tptp.fun_bool_bool)) (=> (tptp.pp (tptp.member_bool X Z3)) (=> (tptp.ord_less_eq_set_bool Z3 (tptp.collect_bool (tptp.aa_fun8098540714523660868l_bool (tptp.aTP_Lamm_am X6) P))) (tptp.pp (tptp.aa_bool_bool P X))))) (forall ((X tptp.product_prod_int_int) (Z3 tptp.set_Pr958786334691620121nt_int) (X6 tptp.set_Pr958786334691620121nt_int) (P tptp.fun_Pr803113274115125473t_bool)) (=> (tptp.member5262025264175285858nt_int X Z3) (=> (tptp.ord_le2843351958646193337nt_int Z3 (tptp.collec213857154873943460nt_int (tptp.aa_fun8917503761599146496t_bool (tptp.aTP_Lamm_an X6) P))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool P X))))) (forall ((X tptp.list_nat) (Z3 tptp.set_list_nat) (X6 tptp.set_list_nat) (P tptp.fun_list_nat_bool)) (=> (tptp.member_list_nat X Z3) (=> (tptp.ord_le6045566169113846134st_nat Z3 (tptp.collect_list_nat (tptp.aa_fun6009467934925565500t_bool (tptp.aTP_Lamm_ao X6) P))) (tptp.pp (tptp.aa_list_nat_bool P X))))) (forall ((X tptp.set_nat) (Z3 tptp.set_set_nat) (X6 tptp.set_set_nat) (P tptp.fun_set_nat_bool)) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat X) Z3)) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat Z3) (tptp.collect_set_nat (tptp.aa_fun3565389549526402364t_bool (tptp.aTP_Lamm_ap X6) P)))) (tptp.pp (tptp.aa_set_nat_bool P X))))) (forall ((X tptp.nat) (Z3 tptp.set_nat) (X6 tptp.set_nat) (P tptp.fun_nat_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X) Z3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat Z3) (tptp.collect_nat (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_aq X6) P)))) (tptp.pp (tptp.aa_nat_bool P X))))) (forall ((X tptp.int) (Z3 tptp.set_int) (X6 tptp.set_int) (P tptp.fun_int_bool)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X) Z3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int Z3) (tptp.collect_int (tptp.aa_fun5146555767781538748t_bool (tptp.aTP_Lamm_ar X6) P)))) (tptp.pp (tptp.aa_int_bool P X))))) (forall ((X6 tptp.set_Pr1261947904930325089at_nat) (P tptp.fun_Pr7757163693017731481t_bool)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat (tptp.collec3392354462482085612at_nat (tptp.aa_fun830836278467416944t_bool (tptp.aTP_Lamm_al X6) P))) X6))) (forall ((X6 tptp.set_bool) (P tptp.fun_bool_bool)) (tptp.ord_less_eq_set_bool (tptp.collect_bool (tptp.aa_fun8098540714523660868l_bool (tptp.aTP_Lamm_am X6) P)) X6)) (forall ((X6 tptp.set_Pr958786334691620121nt_int) (P tptp.fun_Pr803113274115125473t_bool)) (tptp.ord_le2843351958646193337nt_int (tptp.collec213857154873943460nt_int (tptp.aa_fun8917503761599146496t_bool (tptp.aTP_Lamm_an X6) P)) X6)) (forall ((X6 tptp.set_list_nat) (P tptp.fun_list_nat_bool)) (tptp.ord_le6045566169113846134st_nat (tptp.collect_list_nat (tptp.aa_fun6009467934925565500t_bool (tptp.aTP_Lamm_ao X6) P)) X6)) (forall ((X6 tptp.set_set_nat) (P tptp.fun_set_nat_bool)) (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat (tptp.collect_set_nat (tptp.aa_fun3565389549526402364t_bool (tptp.aTP_Lamm_ap X6) P))) X6))) (forall ((X6 tptp.set_nat) (P tptp.fun_nat_bool)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.collect_nat (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_aq X6) P))) X6))) (forall ((X6 tptp.set_int) (P tptp.fun_int_bool)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.collect_int (tptp.aa_fun5146555767781538748t_bool (tptp.aTP_Lamm_ar X6) P))) X6))) (forall ((T5 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X5) Z2)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat T5) X5))))))) (forall ((T5 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X5) Z2)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num T5) X5))))))) (forall ((T5 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X5) Z2)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat T5) X5))))))) (forall ((T5 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X5) Z2)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int T5) X5))))))) (forall ((T5 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X5) Z2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X5) T5)))))) (forall ((T5 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X5) Z2)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X5) T5)))))) (forall ((T5 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X5) Z2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X5) T5)))))) (forall ((T5 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X5) Z2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X5) T5)))))) (forall ((T5 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z2) X5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat T5) X5)))))) (forall ((T5 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z2) X5)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num T5) X5)))))) (forall ((T5 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z2) X5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat T5) X5)))))) (forall ((T5 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z2) X5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int T5) X5)))))) (forall ((T5 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z2) X5)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X5) T5))))))) (forall ((T5 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z2) X5)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X5) T5))))))) (forall ((T5 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z2) X5)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X5) T5))))))) (forall ((T5 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z2) X5)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X5) T5))))))) (forall ((B2 tptp.rat) (A2 tptp.rat)) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B2) A2))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A2) B2)))) (forall ((B2 tptp.num) (A2 tptp.num)) (= (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B2) A2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A2) B2)))) (forall ((B2 tptp.nat) (A2 tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B2) A2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A2) B2)))) (forall ((B2 tptp.int) (A2 tptp.int)) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) A2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A2) B2)))) (forall ((A tptp.nat) (B tptp.nat) (P tptp.fun_nat_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool P A)) (=> (not (tptp.pp (tptp.aa_nat_bool P B))) (exists ((C2 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) C2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C2) B)) (forall ((X5 tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) X5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X5) C2))) (tptp.pp (tptp.aa_nat_bool P X5)))) (forall ((D4 tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) X3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) D4))) (tptp.pp (tptp.aa_nat_bool P X3)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat D4) C2)))))))))) (forall ((A tptp.int) (B tptp.int) (P tptp.fun_int_bool)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (=> (tptp.pp (tptp.aa_int_bool P A)) (=> (not (tptp.pp (tptp.aa_int_bool P B))) (exists ((C2 tptp.int)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) C2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C2) B)) (forall ((X5 tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) X5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X5) C2))) (tptp.pp (tptp.aa_int_bool P X5)))) (forall ((D4 tptp.int)) (=> (forall ((X3 tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) X3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) D4))) (tptp.pp (tptp.aa_int_bool P X3)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int D4) C2)))))))))) (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.bijective_nat_nat tptp.bot_bo2099793752762293965at_nat)) (forall ((S tptp.set_Pr1261947904930325089at_nat)) (=> (not (= S tptp.bot_bo2099793752762293965at_nat)) (= (tptp.dflt_N6592383573632408824at_nat S) (tptp.some_s147305329494351046at_nat S)))) (forall ((S tptp.set_bool)) (=> (not (= S tptp.bot_bot_set_bool)) (= (tptp.dflt_None_set_bool S) (tptp.some_set_bool S)))) (forall ((S tptp.set_nat)) (=> (not (= S tptp.bot_bot_set_nat)) (= (tptp.dflt_None_set_nat S) (tptp.some_set_nat S)))) (forall ((S tptp.set_int)) (=> (not (= S tptp.bot_bot_set_int)) (= (tptp.dflt_None_set_int S) (tptp.some_set_int S)))) (forall ((X tptp.fun_Pr6001797050664311790t_bool) (Xa2 tptp.fun_Pr6001797050664311790t_bool) (Xb tptp.produc3658429121746597890et_nat)) (=> (not (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.aa_fun6808777976510360636t_bool (tptp.times_assn_raw X) Xa2) Xb))) (=> (tptp.pp (tptp.aa_Pro6092667153363046813t_bool (tptp.accp_P9010229746810818675et_nat tptp.times_assn_raw_rel) (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat X) (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat Xa2) Xb)))) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (tptp.produc7507926704131184380et_nat H4 As4))) (=> (= Xb _let_1) (=> (tptp.pp (tptp.aa_Pro6092667153363046813t_bool (tptp.accp_P9010229746810818675et_nat tptp.times_assn_raw_rel) (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat X) (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat Xa2) _let_1)))) (exists ((As13 tptp.set_nat) (As23 tptp.set_nat)) (and (= As4 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat As13) As23)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat As13) As23) tptp.bot_bot_set_nat) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool X (tptp.produc7507926704131184380et_nat H4 As13))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool Xa2 (tptp.produc7507926704131184380et_nat H4 As23))))))))))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C tptp.product_prod_nat_nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat C))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le7866589430770878221at_nat A3) B3)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 A3)) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 B3)))))) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool) (C tptp.bool)) (=> (tptp.ord_less_set_bool A3 B3) (=> (tptp.pp (tptp.member_bool C A3)) (tptp.pp (tptp.member_bool C B3))))) (forall ((A3 tptp.set_set_nat) (B3 tptp.set_set_nat) (C tptp.set_nat)) (let ((_let_1 (tptp.member_set_nat C))) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_less_set_set_nat A3) B3)) (=> (tptp.pp (tptp.aa_set_set_nat_bool _let_1 A3)) (tptp.pp (tptp.aa_set_set_nat_bool _let_1 B3)))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C tptp.nat)) (let ((_let_1 (tptp.member_nat C))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat A3) B3)) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A3)) (tptp.pp (tptp.aa_set_nat_bool _let_1 B3)))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (C tptp.int)) (let ((_let_1 (tptp.member_int C))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int A3) B3)) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 A3)) (tptp.pp (tptp.aa_set_int_bool _let_1 B3)))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le7866589430770878221at_nat A3) B3)) (tptp.pp (tptp.aa_fun8663595511526100224l_bool (tptp.ord_le7158584875777748973t_bool (tptp.aTP_Lamm_a A3)) (tptp.aTP_Lamm_a B3))))) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool)) (= (tptp.ord_less_set_bool A3 B3) (tptp.ord_le2077783555311705303l_bool (tptp.aTP_Lamm_aa A3) (tptp.aTP_Lamm_aa B3)))) (forall ((A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (= (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_less_set_set_nat A3) B3)) (tptp.ord_le4523237222650602006t_bool (tptp.aTP_Lamm_ad A3) (tptp.aTP_Lamm_ad B3)))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat A3) B3)) (tptp.ord_le6841235830588351564t_bool (tptp.aTP_Lamm_ae A3) (tptp.aTP_Lamm_ae B3)))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int A3) B3)) (tptp.ord_le3716944864119727344t_bool (tptp.aTP_Lamm_af A3) (tptp.aTP_Lamm_af B3)))) (forall ((A tptp.rat) (B tptp.rat)) (or (= A B) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A))))) (forall ((A tptp.num) (B tptp.num)) (or (= A B) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B))) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A))))) (forall ((A tptp.nat) (B tptp.nat)) (or (= A B) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A))))) (forall ((A tptp.int) (B tptp.int)) (or (= A B) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B))) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A))))) (forall ((A tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) A))) (forall ((A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) A))) (forall ((A tptp.num)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) A))) (forall ((A tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) A))) (forall ((A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) A))) (forall ((A tptp.assn)) (not (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) A)))) (forall ((A tptp.rat)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) A)))) (forall ((A tptp.num)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) A)))) (forall ((A tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) A)))) (forall ((A tptp.int)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) A)))) (forall ((P tptp.fun_rat_bool) (P4 tptp.fun_rat_bool) (Q tptp.fun_rat_bool) (Q3 tptp.fun_rat_bool)) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z4) X3)) (= (tptp.pp (tptp.aa_rat_bool P X3)) (tptp.pp (tptp.aa_rat_bool P4 X3)))))) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z4) X3)) (= (tptp.pp (tptp.aa_rat_bool Q X3)) (tptp.pp (tptp.aa_rat_bool Q3 X3)))))) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z2) X5)) (= (and (tptp.pp (tptp.aa_rat_bool P X5)) (tptp.pp (tptp.aa_rat_bool Q X5))) (and (tptp.pp (tptp.aa_rat_bool P4 X5)) (tptp.pp (tptp.aa_rat_bool Q3 X5)))))))))) (forall ((P tptp.fun_num_bool) (P4 tptp.fun_num_bool) (Q tptp.fun_num_bool) (Q3 tptp.fun_num_bool)) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z4) X3)) (= (tptp.pp (tptp.aa_num_bool P X3)) (tptp.pp (tptp.aa_num_bool P4 X3)))))) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z4) X3)) (= (tptp.pp (tptp.aa_num_bool Q X3)) (tptp.pp (tptp.aa_num_bool Q3 X3)))))) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z2) X5)) (= (and (tptp.pp (tptp.aa_num_bool P X5)) (tptp.pp (tptp.aa_num_bool Q X5))) (and (tptp.pp (tptp.aa_num_bool P4 X5)) (tptp.pp (tptp.aa_num_bool Q3 X5)))))))))) (forall ((P tptp.fun_nat_bool) (P4 tptp.fun_nat_bool) (Q tptp.fun_nat_bool) (Q3 tptp.fun_nat_bool)) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z4) X3)) (= (tptp.pp (tptp.aa_nat_bool P X3)) (tptp.pp (tptp.aa_nat_bool P4 X3)))))) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z4) X3)) (= (tptp.pp (tptp.aa_nat_bool Q X3)) (tptp.pp (tptp.aa_nat_bool Q3 X3)))))) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z2) X5)) (= (and (tptp.pp (tptp.aa_nat_bool P X5)) (tptp.pp (tptp.aa_nat_bool Q X5))) (and (tptp.pp (tptp.aa_nat_bool P4 X5)) (tptp.pp (tptp.aa_nat_bool Q3 X5)))))))))) (forall ((P tptp.fun_int_bool) (P4 tptp.fun_int_bool) (Q tptp.fun_int_bool) (Q3 tptp.fun_int_bool)) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z4) X3)) (= (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P4 X3)))))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z4) X3)) (= (tptp.pp (tptp.aa_int_bool Q X3)) (tptp.pp (tptp.aa_int_bool Q3 X3)))))) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z2) X5)) (= (and (tptp.pp (tptp.aa_int_bool P X5)) (tptp.pp (tptp.aa_int_bool Q X5))) (and (tptp.pp (tptp.aa_int_bool P4 X5)) (tptp.pp (tptp.aa_int_bool Q3 X5)))))))))) (forall ((P tptp.fun_rat_bool) (P4 tptp.fun_rat_bool) (Q tptp.fun_rat_bool) (Q3 tptp.fun_rat_bool)) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z4) X3)) (= (tptp.pp (tptp.aa_rat_bool P X3)) (tptp.pp (tptp.aa_rat_bool P4 X3)))))) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z4) X3)) (= (tptp.pp (tptp.aa_rat_bool Q X3)) (tptp.pp (tptp.aa_rat_bool Q3 X3)))))) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z2) X5)) (= (or (tptp.pp (tptp.aa_rat_bool P X5)) (tptp.pp (tptp.aa_rat_bool Q X5))) (or (tptp.pp (tptp.aa_rat_bool P4 X5)) (tptp.pp (tptp.aa_rat_bool Q3 X5)))))))))) (forall ((P tptp.fun_num_bool) (P4 tptp.fun_num_bool) (Q tptp.fun_num_bool) (Q3 tptp.fun_num_bool)) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z4) X3)) (= (tptp.pp (tptp.aa_num_bool P X3)) (tptp.pp (tptp.aa_num_bool P4 X3)))))) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z4) X3)) (= (tptp.pp (tptp.aa_num_bool Q X3)) (tptp.pp (tptp.aa_num_bool Q3 X3)))))) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z2) X5)) (= (or (tptp.pp (tptp.aa_num_bool P X5)) (tptp.pp (tptp.aa_num_bool Q X5))) (or (tptp.pp (tptp.aa_num_bool P4 X5)) (tptp.pp (tptp.aa_num_bool Q3 X5)))))))))) (forall ((P tptp.fun_nat_bool) (P4 tptp.fun_nat_bool) (Q tptp.fun_nat_bool) (Q3 tptp.fun_nat_bool)) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z4) X3)) (= (tptp.pp (tptp.aa_nat_bool P X3)) (tptp.pp (tptp.aa_nat_bool P4 X3)))))) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z4) X3)) (= (tptp.pp (tptp.aa_nat_bool Q X3)) (tptp.pp (tptp.aa_nat_bool Q3 X3)))))) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z2) X5)) (= (or (tptp.pp (tptp.aa_nat_bool P X5)) (tptp.pp (tptp.aa_nat_bool Q X5))) (or (tptp.pp (tptp.aa_nat_bool P4 X5)) (tptp.pp (tptp.aa_nat_bool Q3 X5)))))))))) (forall ((P tptp.fun_int_bool) (P4 tptp.fun_int_bool) (Q tptp.fun_int_bool) (Q3 tptp.fun_int_bool)) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z4) X3)) (= (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P4 X3)))))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z4) X3)) (= (tptp.pp (tptp.aa_int_bool Q X3)) (tptp.pp (tptp.aa_int_bool Q3 X3)))))) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z2) X5)) (= (or (tptp.pp (tptp.aa_int_bool P X5)) (tptp.pp (tptp.aa_int_bool Q X5))) (or (tptp.pp (tptp.aa_int_bool P4 X5)) (tptp.pp (tptp.aa_int_bool Q3 X5)))))))))) (forall ((T5 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z2) X5)) (not (= X5 T5)))))) (forall ((T5 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z2) X5)) (not (= X5 T5)))))) (forall ((T5 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z2) X5)) (not (= X5 T5)))))) (forall ((T5 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z2) X5)) (not (= X5 T5)))))) (forall ((T5 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z2) X5)) (not (= X5 T5)))))) (forall ((T5 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z2) X5)) (not (= X5 T5)))))) (forall ((T5 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z2) X5)) (not (= X5 T5)))))) (forall ((T5 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z2) X5)) (not (= X5 T5)))))) (forall ((T5 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z2) X5)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X5) T5))))))) (forall ((T5 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z2) X5)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X5) T5))))))) (forall ((T5 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z2) X5)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X5) T5))))))) (forall ((T5 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z2) X5)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X5) T5))))))) (forall ((T5 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z2) X5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat T5) X5)))))) (forall ((T5 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z2) X5)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num T5) X5)))))) (forall ((T5 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z2) X5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat T5) X5)))))) (forall ((T5 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z2) X5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int T5) X5)))))) (forall ((P tptp.fun_rat_bool) (P4 tptp.fun_rat_bool) (Q tptp.fun_rat_bool) (Q3 tptp.fun_rat_bool)) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Z4)) (= (tptp.pp (tptp.aa_rat_bool P X3)) (tptp.pp (tptp.aa_rat_bool P4 X3)))))) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Z4)) (= (tptp.pp (tptp.aa_rat_bool Q X3)) (tptp.pp (tptp.aa_rat_bool Q3 X3)))))) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X5) Z2)) (= (and (tptp.pp (tptp.aa_rat_bool P X5)) (tptp.pp (tptp.aa_rat_bool Q X5))) (and (tptp.pp (tptp.aa_rat_bool P4 X5)) (tptp.pp (tptp.aa_rat_bool Q3 X5)))))))))) (forall ((P tptp.fun_num_bool) (P4 tptp.fun_num_bool) (Q tptp.fun_num_bool) (Q3 tptp.fun_num_bool)) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X3) Z4)) (= (tptp.pp (tptp.aa_num_bool P X3)) (tptp.pp (tptp.aa_num_bool P4 X3)))))) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X3) Z4)) (= (tptp.pp (tptp.aa_num_bool Q X3)) (tptp.pp (tptp.aa_num_bool Q3 X3)))))) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X5) Z2)) (= (and (tptp.pp (tptp.aa_num_bool P X5)) (tptp.pp (tptp.aa_num_bool Q X5))) (and (tptp.pp (tptp.aa_num_bool P4 X5)) (tptp.pp (tptp.aa_num_bool Q3 X5)))))))))) (forall ((P tptp.fun_nat_bool) (P4 tptp.fun_nat_bool) (Q tptp.fun_nat_bool) (Q3 tptp.fun_nat_bool)) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) Z4)) (= (tptp.pp (tptp.aa_nat_bool P X3)) (tptp.pp (tptp.aa_nat_bool P4 X3)))))) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) Z4)) (= (tptp.pp (tptp.aa_nat_bool Q X3)) (tptp.pp (tptp.aa_nat_bool Q3 X3)))))) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X5) Z2)) (= (and (tptp.pp (tptp.aa_nat_bool P X5)) (tptp.pp (tptp.aa_nat_bool Q X5))) (and (tptp.pp (tptp.aa_nat_bool P4 X5)) (tptp.pp (tptp.aa_nat_bool Q3 X5)))))))))) (forall ((P tptp.fun_int_bool) (P4 tptp.fun_int_bool) (Q tptp.fun_int_bool) (Q3 tptp.fun_int_bool)) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) Z4)) (= (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P4 X3)))))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) Z4)) (= (tptp.pp (tptp.aa_int_bool Q X3)) (tptp.pp (tptp.aa_int_bool Q3 X3)))))) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X5) Z2)) (= (and (tptp.pp (tptp.aa_int_bool P X5)) (tptp.pp (tptp.aa_int_bool Q X5))) (and (tptp.pp (tptp.aa_int_bool P4 X5)) (tptp.pp (tptp.aa_int_bool Q3 X5)))))))))) (forall ((P tptp.fun_rat_bool) (P4 tptp.fun_rat_bool) (Q tptp.fun_rat_bool) (Q3 tptp.fun_rat_bool)) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Z4)) (= (tptp.pp (tptp.aa_rat_bool P X3)) (tptp.pp (tptp.aa_rat_bool P4 X3)))))) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Z4)) (= (tptp.pp (tptp.aa_rat_bool Q X3)) (tptp.pp (tptp.aa_rat_bool Q3 X3)))))) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X5) Z2)) (= (or (tptp.pp (tptp.aa_rat_bool P X5)) (tptp.pp (tptp.aa_rat_bool Q X5))) (or (tptp.pp (tptp.aa_rat_bool P4 X5)) (tptp.pp (tptp.aa_rat_bool Q3 X5)))))))))) (forall ((P tptp.fun_num_bool) (P4 tptp.fun_num_bool) (Q tptp.fun_num_bool) (Q3 tptp.fun_num_bool)) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X3) Z4)) (= (tptp.pp (tptp.aa_num_bool P X3)) (tptp.pp (tptp.aa_num_bool P4 X3)))))) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X3) Z4)) (= (tptp.pp (tptp.aa_num_bool Q X3)) (tptp.pp (tptp.aa_num_bool Q3 X3)))))) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X5) Z2)) (= (or (tptp.pp (tptp.aa_num_bool P X5)) (tptp.pp (tptp.aa_num_bool Q X5))) (or (tptp.pp (tptp.aa_num_bool P4 X5)) (tptp.pp (tptp.aa_num_bool Q3 X5)))))))))) (forall ((P tptp.fun_nat_bool) (P4 tptp.fun_nat_bool) (Q tptp.fun_nat_bool) (Q3 tptp.fun_nat_bool)) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) Z4)) (= (tptp.pp (tptp.aa_nat_bool P X3)) (tptp.pp (tptp.aa_nat_bool P4 X3)))))) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) Z4)) (= (tptp.pp (tptp.aa_nat_bool Q X3)) (tptp.pp (tptp.aa_nat_bool Q3 X3)))))) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X5) Z2)) (= (or (tptp.pp (tptp.aa_nat_bool P X5)) (tptp.pp (tptp.aa_nat_bool Q X5))) (or (tptp.pp (tptp.aa_nat_bool P4 X5)) (tptp.pp (tptp.aa_nat_bool Q3 X5)))))))))) (forall ((P tptp.fun_int_bool) (P4 tptp.fun_int_bool) (Q tptp.fun_int_bool) (Q3 tptp.fun_int_bool)) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) Z4)) (= (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P4 X3)))))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) Z4)) (= (tptp.pp (tptp.aa_int_bool Q X3)) (tptp.pp (tptp.aa_int_bool Q3 X3)))))) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X5) Z2)) (= (or (tptp.pp (tptp.aa_int_bool P X5)) (tptp.pp (tptp.aa_int_bool Q X5))) (or (tptp.pp (tptp.aa_int_bool P4 X5)) (tptp.pp (tptp.aa_int_bool Q3 X5)))))))))) (forall ((T5 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X5) Z2)) (not (= X5 T5)))))) (forall ((T5 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X5) Z2)) (not (= X5 T5)))))) (forall ((T5 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X5) Z2)) (not (= X5 T5)))))) (forall ((T5 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X5) Z2)) (not (= X5 T5)))))) (forall ((T5 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X5) Z2)) (not (= X5 T5)))))) (forall ((T5 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X5) Z2)) (not (= X5 T5)))))) (forall ((T5 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X5) Z2)) (not (= X5 T5)))))) (forall ((T5 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X5) Z2)) (not (= X5 T5)))))) (forall ((T5 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X5))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Z2)) (tptp.pp (tptp.aa_rat_bool _let_1 T5))))))) (forall ((T5 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num X5))) (=> (tptp.pp (tptp.aa_num_bool _let_1 Z2)) (tptp.pp (tptp.aa_num_bool _let_1 T5))))))) (forall ((T5 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X5))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 Z2)) (tptp.pp (tptp.aa_nat_bool _let_1 T5))))))) (forall ((T5 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int X5))) (=> (tptp.pp (tptp.aa_int_bool _let_1 Z2)) (tptp.pp (tptp.aa_int_bool _let_1 T5))))))) (forall ((T5 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X5) Z2)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat T5) X5))))))) (forall ((T5 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X5) Z2)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num T5) X5))))))) (forall ((T5 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X5) Z2)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat T5) X5))))))) (forall ((T5 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X5) Z2)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int T5) X5))))))) (forall ((R tptp.set_Pr1261947904930325089at_nat)) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.bijective_nat_nat R)) (and (forall ((X4 tptp.nat) (Y5 tptp.nat) (Z5 tptp.nat)) (let ((_let_1 (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat X4))) (=> (and (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat (tptp.aa_nat7603221163087113075at_nat _let_1 Y5)) R)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat (tptp.aa_nat7603221163087113075at_nat _let_1 Z5)) R))) (= Y5 Z5)))) (forall ((X4 tptp.nat) (Y5 tptp.nat) (Z5 tptp.nat)) (=> (and (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat X4) Z5)) R)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat Y5) Z5)) R))) (= X4 Y5)))))) (forall ((R tptp.set_Pr1106803562331729365et_nat)) (= (tptp.biject5596389841143135651et_nat R) (and (forall ((X4 tptp.fun_Pr6001797050664311790t_bool) (Y5 tptp.produc3658429121746597890et_nat) (Z5 tptp.produc3658429121746597890et_nat)) (let ((_let_1 (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat X4))) (=> (and (tptp.member8615881266069945910et_nat (tptp.aa_Pro1252775905504286431et_nat _let_1 Y5) R) (tptp.member8615881266069945910et_nat (tptp.aa_Pro1252775905504286431et_nat _let_1 Z5) R)) (= Y5 Z5)))) (forall ((X4 tptp.fun_Pr6001797050664311790t_bool) (Y5 tptp.fun_Pr6001797050664311790t_bool) (Z5 tptp.produc3658429121746597890et_nat)) (=> (and (tptp.member8615881266069945910et_nat (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat X4) Z5) R) (tptp.member8615881266069945910et_nat (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat Y5) Z5) R)) (= X4 Y5)))))) (forall ((R tptp.set_Pr9222568342844664434et_nat)) (= (tptp.biject2138954951139011392et_nat R) (and (forall ((X4 tptp.fun_Pr6001797050664311790t_bool) (Y5 tptp.produc6108883039684432031et_nat) (Z5 tptp.produc6108883039684432031et_nat)) (let ((_let_1 (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat X4))) (=> (and (tptp.member2818932950976722259et_nat (tptp.aa_Pro4782578008252579993et_nat _let_1 Y5) R) (tptp.member2818932950976722259et_nat (tptp.aa_Pro4782578008252579993et_nat _let_1 Z5) R)) (= Y5 Z5)))) (forall ((X4 tptp.fun_Pr6001797050664311790t_bool) (Y5 tptp.fun_Pr6001797050664311790t_bool) (Z5 tptp.produc6108883039684432031et_nat)) (=> (and (tptp.member2818932950976722259et_nat (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat X4) Z5) R) (tptp.member2818932950976722259et_nat (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat Y5) Z5) R)) (= X4 Y5)))))) (forall ((R tptp.set_Pr233528076387193594nt_int)) (= (tptp.biject4655992564398653440nt_int R) (and (forall ((X4 tptp.fun_Pr9164807099015279978e_term) (Y5 tptp.product_prod_int_int) (Z5 tptp.product_prod_int_int)) (let ((_let_1 (tptp.aa_fun1388719692539776744nt_int tptp.produc1560874099174258678nt_int X4))) (=> (and (tptp.member690604328116145115nt_int (tptp.aa_Pro3513184699142849729nt_int _let_1 Y5) R) (tptp.member690604328116145115nt_int (tptp.aa_Pro3513184699142849729nt_int _let_1 Z5) R)) (= Y5 Z5)))) (forall ((X4 tptp.fun_Pr9164807099015279978e_term) (Y5 tptp.fun_Pr9164807099015279978e_term) (Z5 tptp.product_prod_int_int)) (=> (and (tptp.member690604328116145115nt_int (tptp.aa_Pro3513184699142849729nt_int (tptp.aa_fun1388719692539776744nt_int tptp.produc1560874099174258678nt_int X4) Z5) R) (tptp.member690604328116145115nt_int (tptp.aa_Pro3513184699142849729nt_int (tptp.aa_fun1388719692539776744nt_int tptp.produc1560874099174258678nt_int Y5) Z5) R)) (= X4 Y5)))))) (forall ((R tptp.set_Pr5033440245338114598nt_int)) (= (tptp.biject4479422512835743020nt_int R) (and (forall ((X4 tptp.fun_in6429348457993719614e_term) (Y5 tptp.product_prod_int_int) (Z5 tptp.product_prod_int_int)) (let ((_let_1 (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int X4))) (=> (and (tptp.member500491123954006279nt_int (tptp.aa_Pro835648289009615341nt_int _let_1 Y5) R) (tptp.member500491123954006279nt_int (tptp.aa_Pro835648289009615341nt_int _let_1 Z5) R)) (= Y5 Z5)))) (forall ((X4 tptp.fun_in6429348457993719614e_term) (Y5 tptp.fun_in6429348457993719614e_term) (Z5 tptp.product_prod_int_int)) (=> (and (tptp.member500491123954006279nt_int (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int X4) Z5) R) (tptp.member500491123954006279nt_int (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int Y5) Z5) R)) (= X4 Y5)))))) (forall ((R tptp.set_Pr7098220151150636591it_nat)) (= (tptp.biject8592306251674886141it_nat R) (and (forall ((X4 tptp.a) (Y5 tptp.produc6653097349344004940it_nat) (Z5 tptp.produc6653097349344004940it_nat)) (let ((_let_1 (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat X4))) (=> (and (tptp.member4554412811331277712it_nat (tptp.aa_Pro8078911840264235907it_nat _let_1 Y5) R) (tptp.member4554412811331277712it_nat (tptp.aa_Pro8078911840264235907it_nat _let_1 Z5) R)) (= Y5 Z5)))) (forall ((X4 tptp.a) (Y5 tptp.a) (Z5 tptp.produc6653097349344004940it_nat)) (=> (and (tptp.member4554412811331277712it_nat (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat X4) Z5) R) (tptp.member4554412811331277712it_nat (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat Y5) Z5) R)) (= X4 Y5)))))) (forall ((X tptp.fun_Pr6001797050664311790t_bool) (Xa2 tptp.fun_Pr6001797050664311790t_bool) (Xb tptp.produc3658429121746597890et_nat) (Y tptp.bool)) (=> (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.aa_fun6808777976510360636t_bool (tptp.times_assn_raw X) Xa2) Xb)) (tptp.pp Y)) (=> (tptp.pp (tptp.aa_Pro6092667153363046813t_bool (tptp.accp_P9010229746810818675et_nat tptp.times_assn_raw_rel) (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat X) (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat Xa2) Xb)))) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (tptp.produc7507926704131184380et_nat H4 As4))) (=> (= Xb _let_1) (=> (= (tptp.pp Y) (exists ((As12 tptp.set_nat) (As22 tptp.set_nat)) (and (= As4 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat As12) As22)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat As12) As22) tptp.bot_bot_set_nat) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool X (tptp.produc7507926704131184380et_nat H4 As12))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool Xa2 (tptp.produc7507926704131184380et_nat H4 As22)))))) (not (tptp.pp (tptp.aa_Pro6092667153363046813t_bool (tptp.accp_P9010229746810818675et_nat tptp.times_assn_raw_rel) (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat X) (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat Xa2) _let_1))))))))))))) (forall ((X tptp.fun_Pr6001797050664311790t_bool) (Xa2 tptp.fun_Pr6001797050664311790t_bool) (Xb tptp.produc3658429121746597890et_nat)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.aa_fun6808777976510360636t_bool (tptp.times_assn_raw X) Xa2) Xb)) (=> (tptp.pp (tptp.aa_Pro6092667153363046813t_bool (tptp.accp_P9010229746810818675et_nat tptp.times_assn_raw_rel) (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat X) (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat Xa2) Xb)))) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (tptp.produc7507926704131184380et_nat H4 As4))) (=> (= Xb _let_1) (=> (tptp.pp (tptp.aa_Pro6092667153363046813t_bool (tptp.accp_P9010229746810818675et_nat tptp.times_assn_raw_rel) (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat X) (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat Xa2) _let_1)))) (not (exists ((As1 tptp.set_nat) (As2 tptp.set_nat)) (and (= As4 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat As1) As2)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat As1) As2) tptp.bot_bot_set_nat) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool X (tptp.produc7507926704131184380et_nat H4 As1))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool Xa2 (tptp.produc7507926704131184380et_nat H4 As2)))))))))))))) (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (tptp.the_de3668382347305825784at_nat tptp.bot_bo2099793752762293965at_nat (tptp.dflt_N6592383573632408824at_nat X)) X)) (forall ((X tptp.set_bool)) (= (tptp.the_default_set_bool tptp.bot_bot_set_bool (tptp.dflt_None_set_bool X)) X)) (forall ((X tptp.set_nat)) (= (tptp.the_default_set_nat tptp.bot_bot_set_nat (tptp.dflt_None_set_nat X)) X)) (forall ((X tptp.set_int)) (= (tptp.the_default_set_int tptp.bot_bot_set_int (tptp.dflt_None_set_int X)) X)) (forall ((R1 tptp.fun_Pr8933696392609397829t_bool) (R22 tptp.fun_Pr8933696392609397829t_bool)) (=> (tptp.ord_le5791676303284507621t_bool R1 R22) (tptp.ord_le2641096124239147918t_bool (tptp.accp_P5801069581201407417et_nat R22) (tptp.accp_P5801069581201407417et_nat R1)))) (forall ((R1 tptp.fun_Pr5837708615769641901m_bool) (R22 tptp.fun_Pr5837708615769641901m_bool)) (=> (tptp.ord_le7676714441581034317m_bool R1 R22) (tptp.ord_le998981803562422117m_bool (tptp.accp_P3113834385874906142um_num R22) (tptp.accp_P3113834385874906142um_num R1)))) (forall ((R1 tptp.fun_Pr248683899324676269t_bool) (R22 tptp.fun_Pr248683899324676269t_bool)) (=> (tptp.ord_le2087689725136068685t_bool R1 R22) (tptp.pp (tptp.aa_fun8663595511526100224l_bool (tptp.ord_le2468614981408567801t_bool (tptp.accp_P4275260045618599050at_nat R22)) (tptp.accp_P4275260045618599050at_nat R1))))) (forall ((R1 tptp.fun_Pr3099820731930151597t_bool) (R22 tptp.fun_Pr3099820731930151597t_bool)) (=> (tptp.ord_le4938826557741544013t_bool R1 R22) (tptp.ord_le4737936599360737601t_bool (tptp.accp_P1096762738010456898nt_int R22) (tptp.accp_P1096762738010456898nt_int R1)))) (forall ((R1 tptp.fun_Pr6803231168968006865t_bool) (R22 tptp.fun_Pr6803231168968006865t_bool)) (=> (tptp.ord_le1448686115963450481t_bool R1 R22) (tptp.ord_le3080736285959965524t_bool (tptp.accp_P9010229746810818675et_nat R22) (tptp.accp_P9010229746810818675et_nat R1)))) (forall ((D3 tptp.fun_Pr6001797050664311790t_bool) (R tptp.fun_Pr8933696392609397829t_bool) (X tptp.produc3658429121746597890et_nat) (P tptp.fun_Pr6001797050664311790t_bool)) (=> (tptp.ord_le2641096124239147918t_bool D3 (tptp.accp_P5801069581201407417et_nat R)) (=> (forall ((X3 tptp.produc3658429121746597890et_nat) (Z2 tptp.produc3658429121746597890et_nat)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool D3 X3)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.aa_Pro8080318727460218286t_bool R Z2) X3)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool D3 Z2))))) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool D3 X)) (=> (forall ((X3 tptp.produc3658429121746597890et_nat)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool D3 X3)) (=> (forall ((Z4 tptp.produc3658429121746597890et_nat)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.aa_Pro8080318727460218286t_bool R Z4) X3)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool P Z4)))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool P X3))))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool P X))))))) (forall ((D3 tptp.fun_Pr6287530515171585797m_bool) (R tptp.fun_Pr5837708615769641901m_bool) (X tptp.product_prod_num_num) (P tptp.fun_Pr6287530515171585797m_bool)) (=> (tptp.ord_le998981803562422117m_bool D3 (tptp.accp_P3113834385874906142um_num R)) (=> (forall ((X3 tptp.product_prod_num_num) (Z2 tptp.product_prod_num_num)) (=> (tptp.pp (tptp.aa_Pro762926636801165566m_bool D3 X3)) (=> (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.aa_Pro2164613399825298270m_bool R Z2) X3)) (tptp.pp (tptp.aa_Pro762926636801165566m_bool D3 Z2))))) (=> (tptp.pp (tptp.aa_Pro762926636801165566m_bool D3 X)) (=> (forall ((X3 tptp.product_prod_num_num)) (=> (tptp.pp (tptp.aa_Pro762926636801165566m_bool D3 X3)) (=> (forall ((Z4 tptp.product_prod_num_num)) (=> (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.aa_Pro2164613399825298270m_bool R Z4) X3)) (tptp.pp (tptp.aa_Pro762926636801165566m_bool P Z4)))) (tptp.pp (tptp.aa_Pro762926636801165566m_bool P X3))))) (tptp.pp (tptp.aa_Pro762926636801165566m_bool P X))))))) (forall ((D3 tptp.fun_Pr7757163693017731481t_bool) (R tptp.fun_Pr248683899324676269t_bool) (X tptp.product_prod_nat_nat) (P tptp.fun_Pr7757163693017731481t_bool)) (=> (tptp.pp (tptp.aa_fun8663595511526100224l_bool (tptp.ord_le2468614981408567801t_bool D3) (tptp.accp_P4275260045618599050at_nat R))) (=> (forall ((X3 tptp.product_prod_nat_nat) (Z2 tptp.product_prod_nat_nat)) (=> (tptp.pp (tptp.aa_Pro2232559814647311250t_bool D3 X3)) (=> (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool R Z2) X3)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool D3 Z2))))) (=> (tptp.pp (tptp.aa_Pro2232559814647311250t_bool D3 X)) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (tptp.pp (tptp.aa_Pro2232559814647311250t_bool D3 X3)) (=> (forall ((Z4 tptp.product_prod_nat_nat)) (=> (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool R Z4) X3)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool P Z4)))) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool P X3))))) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool P X))))))) (forall ((D3 tptp.fun_Pr803113274115125473t_bool) (R tptp.fun_Pr3099820731930151597t_bool) (X tptp.product_prod_int_int) (P tptp.fun_Pr803113274115125473t_bool)) (=> (tptp.ord_le4737936599360737601t_bool D3 (tptp.accp_P1096762738010456898nt_int R)) (=> (forall ((X3 tptp.product_prod_int_int) (Z2 tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool D3 X3)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool R Z2) X3)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool D3 Z2))))) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool D3 X)) (=> (forall ((X3 tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool D3 X3)) (=> (forall ((Z4 tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool R Z4) X3)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool P Z4)))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool P X3))))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool P X))))))) (forall ((D3 tptp.fun_Pr229822445725053876t_bool) (R tptp.fun_Pr6803231168968006865t_bool) (X tptp.produc1542783094787327164et_nat) (P tptp.fun_Pr229822445725053876t_bool)) (=> (tptp.ord_le3080736285959965524t_bool D3 (tptp.accp_P9010229746810818675et_nat R)) (=> (forall ((X3 tptp.produc1542783094787327164et_nat) (Z2 tptp.produc1542783094787327164et_nat)) (=> (tptp.pp (tptp.aa_Pro6092667153363046813t_bool D3 X3)) (=> (tptp.pp (tptp.aa_Pro6092667153363046813t_bool (tptp.aa_Pro5272727900732555578t_bool R Z2) X3)) (tptp.pp (tptp.aa_Pro6092667153363046813t_bool D3 Z2))))) (=> (tptp.pp (tptp.aa_Pro6092667153363046813t_bool D3 X)) (=> (forall ((X3 tptp.produc1542783094787327164et_nat)) (=> (tptp.pp (tptp.aa_Pro6092667153363046813t_bool D3 X3)) (=> (forall ((Z4 tptp.produc1542783094787327164et_nat)) (=> (tptp.pp (tptp.aa_Pro6092667153363046813t_bool (tptp.aa_Pro5272727900732555578t_bool R Z4) X3)) (tptp.pp (tptp.aa_Pro6092667153363046813t_bool P Z4)))) (tptp.pp (tptp.aa_Pro6092667153363046813t_bool P X3))))) (tptp.pp (tptp.aa_Pro6092667153363046813t_bool P X))))))) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.orderi2172309028950807442at_nat tptp.aTP_Lamm_cv tptp.aTP_Lamm_cw) tptp.bot_bo2099793752762293965at_nat)) (tptp.orderi3064931774899922600t_bool tptp.aTP_Lamm_cx tptp.aTP_Lamm_cy tptp.bot_bot_set_bool) (tptp.pp (tptp.aa_set_nat_bool (tptp.ordering_top_set_nat tptp.aTP_Lamm_cz tptp.aTP_Lamm_da) tptp.bot_bot_set_nat)) (tptp.ordering_top_assn tptp.aTP_Lamm_db tptp.aTP_Lamm_dc tptp.bot_bot_assn) (tptp.pp (tptp.aa_set_int_bool (tptp.ordering_top_set_int tptp.aTP_Lamm_dd tptp.aTP_Lamm_de) tptp.bot_bot_set_int)) (tptp.pp (tptp.aa_nat_bool _let_70 tptp.bot_bot_nat)) (forall ((B tptp.bool) (H tptp.heap_e7401611519738050253t_unit)) (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn (tptp.aa_bool_assn tptp.pure_assn B)) (tptp.produc7507926704131184380et_nat H tptp.bot_bot_set_nat))) (tptp.pp B))) (forall ((P tptp.assn) (C tptp.heap_Time_Heap_a) (Q tptp.fun_a_assn) (H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (tptp.hoare_hoare_triple_a P C Q) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn P) (tptp.produc7507926704131184380et_nat H As))) (exists ((H5 tptp.heap_e7401611519738050253t_unit) (R2 tptp.a) (T2 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.heap_Time_effect_a C H H5 R2) T2)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn (tptp.aa_a_assn Q R2)) (tptp.produc7507926704131184380et_nat H5 (tptp.hoare_new_addrs H As H5))))))))) (tptp.lattic5672175589177086241at_nat tptp.sup_su718114333110466843at_nat tptp.aTP_Lamm_cp tptp.aTP_Lamm_cq) (tptp.lattic5174734335190411425at_nat tptp.sup_su3035147773818789531at_nat tptp.aTP_Lamm_cr tptp.aTP_Lamm_cs) (tptp.lattic6976360593897529633at_nat tptp.sup_su5525570899277871387at_nat tptp.aTP_Lamm_ct tptp.aTP_Lamm_cu) (tptp.lattic3109210760196336428et_nat tptp.sup_sup_set_nat tptp.aTP_Lamm_cz tptp.aTP_Lamm_da) (tptp.lattic5623431474481994958t_assn tptp.sup_sup_assn tptp.aTP_Lamm_db tptp.aTP_Lamm_dc) (tptp.lattic8154731777541915528et_int tptp.sup_sup_set_int tptp.aTP_Lamm_dd tptp.aTP_Lamm_de) (tptp.lattic5374021519246970238et_rat tptp.sup_sup_rat tptp.aTP_Lamm_dh tptp.aTP_Lamm_di) (tptp.lattic6009151579333465974et_nat tptp.sup_sup_nat tptp.aTP_Lamm_df tptp.aTP_Lamm_dg) (tptp.lattic6006661108824415698et_int tptp.sup_sup_int tptp.aTP_Lamm_dj tptp.aTP_Lamm_dk) (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat) (Q tptp.assn) (R tptp.assn)) (let ((_let_1 (tptp.produc7507926704131184380et_nat H As))) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range _let_1)) (=> (forall ((H5 tptp.heap_e7401611519738050253t_unit) (As6 tptp.set_nat)) (=> (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat As) As6) tptp.bot_bot_set_nat) (=> (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.relH As H) H5)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range (tptp.produc7507926704131184380et_nat H5 As))) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn Q) (tptp.produc7507926704131184380et_nat H5 As6))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn R) (tptp.produc7507926704131184380et_nat H5 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat As) As6))))))))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.wand_assn Q) R)) _let_1)))))) (forall ((P tptp.bool) (Q tptp.bool)) (= (= (tptp.aa_bool_assn tptp.pure_assn P) (tptp.aa_bool_assn tptp.pure_assn Q)) (= (tptp.pp P) (tptp.pp Q)))) (forall ((A tptp.bool) (B tptp.bool)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.aa_bool_assn tptp.pure_assn A)) (tptp.aa_bool_assn tptp.pure_assn B)) (tptp.aa_bool_assn tptp.pure_assn (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fconj A) B)))) (forall ((A tptp.bool) (B tptp.bool)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn (tptp.aa_bool_assn tptp.pure_assn A)) (tptp.aa_bool_assn tptp.pure_assn B)) (tptp.aa_bool_assn tptp.pure_assn (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fdisj A) B)))) (forall ((P tptp.bool)) (= (= (tptp.aa_bool_assn tptp.pure_assn P) tptp.bot_bot_assn) (not (tptp.pp P)))) (= (tptp.aa_bool_assn tptp.pure_assn tptp.fFalse) tptp.bot_bot_assn) (forall ((A tptp.bool) (B tptp.bool)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn (tptp.aa_bool_assn tptp.pure_assn A)) (tptp.aa_bool_assn tptp.pure_assn B)) (tptp.aa_bool_assn tptp.pure_assn (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fconj A) B)))) (forall ((H tptp.heap_e7401611519738050253t_unit)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range (tptp.produc7507926704131184380et_nat H tptp.bot_bot_set_nat)))) (forall ((P tptp.assn) (B tptp.bool) (H tptp.produc3658429121746597890et_nat)) (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn P) (tptp.aa_bool_assn tptp.pure_assn B))) H)) (and (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn P) H)) (tptp.pp B)))) (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat) (As3 tptp.set_nat)) (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range (tptp.produc7507926704131184380et_nat H (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat As) As3)))) (and (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range (tptp.produc7507926704131184380et_nat H As))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range (tptp.produc7507926704131184380et_nat H As3)))))) (forall ((Less_eq tptp.fun_nat_fun_nat_bool) (Less tptp.fun_nat_fun_nat_bool) (Top tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.ordering_top_nat Less_eq Less) Top)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool Less_eq Top) A)) (= A Top)))) (forall ((Less_eq tptp.fun_nat_fun_nat_bool) (Less tptp.fun_nat_fun_nat_bool) (Top tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.ordering_top_nat Less_eq Less) Top)) (= (not (= A Top)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool Less A) Top))))) (forall ((Less_eq tptp.fun_nat_fun_nat_bool) (Less tptp.fun_nat_fun_nat_bool) (Top tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.ordering_top_nat Less_eq Less) Top)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool Less_eq Top) A)) (= A Top)))) (forall ((Less_eq tptp.fun_nat_fun_nat_bool) (Less tptp.fun_nat_fun_nat_bool) (Top tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.ordering_top_nat Less_eq Less) Top)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool Less Top) A))))) (forall ((Less_eq tptp.fun_nat_fun_nat_bool) (Less tptp.fun_nat_fun_nat_bool) (Top tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.ordering_top_nat Less_eq Less) Top)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool Less_eq A) Top)))) (forall ((P tptp.assn) (H tptp.produc3658429121746597890et_nat)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn P) H)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range H)))) (forall ((As tptp.set_nat) (H tptp.heap_e7401611519738050253t_unit) (H3 tptp.heap_e7401611519738050253t_unit)) (=> (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.relH As H) H3)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range (tptp.produc7507926704131184380et_nat H3 As))))) (forall ((As tptp.set_nat) (H tptp.heap_e7401611519738050253t_unit) (H3 tptp.heap_e7401611519738050253t_unit)) (=> (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.relH As H) H3)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range (tptp.produc7507926704131184380et_nat H As))))) (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range (tptp.produc7507926704131184380et_nat H As))) (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.relH As H) H)))) (forall ((As tptp.set_nat) (As3 tptp.set_nat) (H tptp.heap_e7401611519738050253t_unit)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat As) As3)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range (tptp.produc7507926704131184380et_nat H As3))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range (tptp.produc7507926704131184380et_nat H As)))))) (forall ((C tptp.heap_T5738788834812785303t_unit) (H tptp.heap_e7401611519738050253t_unit) (R3 tptp.product_unit) (H3 tptp.heap_e7401611519738050253t_unit) (N2 tptp.nat)) (=> (= (tptp.aa_hea684056619475940329it_nat (tptp.heap_T875086893843062177t_unit C) H) (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat (tptp.produc7133225469290080770it_nat R3 (tptp.produc584006145561248582it_nat H3 N2)))) (tptp.pp (tptp.aa_nat_bool (tptp.heap_T6553295506729943825t_unit C H H3 R3) N2)))) (forall ((C tptp.heap_Time_Heap_a) (H tptp.heap_e7401611519738050253t_unit) (R3 tptp.a) (H3 tptp.heap_e7401611519738050253t_unit) (N2 tptp.nat)) (=> (= (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a C) H) (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat R3) (tptp.produc584006145561248582it_nat H3 N2)))) (tptp.pp (tptp.aa_nat_bool (tptp.heap_Time_effect_a C H H3 R3) N2)))) (forall ((C tptp.heap_T5738788834812785303t_unit) (H tptp.heap_e7401611519738050253t_unit) (H3 tptp.heap_e7401611519738050253t_unit) (R3 tptp.product_unit) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.heap_T6553295506729943825t_unit C H H3 R3) N2)) (= (tptp.aa_hea684056619475940329it_nat (tptp.heap_T875086893843062177t_unit C) H) (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat (tptp.produc7133225469290080770it_nat R3 (tptp.produc584006145561248582it_nat H3 N2)))))) (forall ((C tptp.heap_Time_Heap_a) (H tptp.heap_e7401611519738050253t_unit) (H3 tptp.heap_e7401611519738050253t_unit) (R3 tptp.a) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.heap_Time_effect_a C H H3 R3) N2)) (= (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a C) H) (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat R3) (tptp.produc584006145561248582it_nat H3 N2)))))) (forall ((X tptp.produc3658429121746597890et_nat)) (=> (not (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range X))) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (=> (= X (tptp.produc7507926704131184380et_nat H4 As4)) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) As4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) (tptp.lim_Product_unit H4)))))))))) (forall ((X tptp.produc3658429121746597890et_nat)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range X)) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (=> (= X (tptp.produc7507926704131184380et_nat H4 As4)) (not (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X5) As4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X5) (tptp.lim_Product_unit H4))))))))))) (forall ((X tptp.produc3658429121746597890et_nat) (Y tptp.bool)) (=> (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range X)) (tptp.pp Y)) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (=> (= X (tptp.produc7507926704131184380et_nat H4 As4)) (= (tptp.pp Y) (not (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) As4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X4) (tptp.lim_Product_unit H4)))))))))))) (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range (tptp.produc7507926704131184380et_nat H As))) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) As)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X4) (tptp.lim_Product_unit H))))))) (forall ((F tptp.heap_Time_Heap_a) (G tptp.heap_Time_Heap_a)) (=> (forall ((H4 tptp.heap_e7401611519738050253t_unit)) (= (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a F) H4) (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a G) H4))) (= F G))) (tptp.lattic3109210760196336428et_nat tptp.inf_inf_set_nat tptp.ord_less_eq_set_nat tptp.ord_less_set_nat) (tptp.lattic5111740090977526247t_unit tptp.inf_inf_Product_unit tptp.ord_le3221252021190050221t_unit tptp.ord_le361264281704409273t_unit) (tptp.lattic6529551498584149819at_nat tptp.inf_in2572325071724192079at_nat tptp.ord_le3146513528884898305at_nat tptp.ord_le7866589430770878221at_nat) (tptp.lattic5623431474481994958t_assn tptp.inf_inf_assn tptp.ord_less_eq_assn tptp.ord_less_assn) (tptp.lattic8154731777541915528et_int tptp.inf_inf_set_int tptp.ord_less_eq_set_int tptp.ord_less_set_int) (tptp.lattic5374021519246970238et_rat tptp.inf_inf_rat tptp.ord_less_eq_rat tptp.ord_less_rat) (tptp.lattic6009151579333465974et_nat tptp.inf_inf_nat tptp.ord_less_eq_nat tptp.ord_less_nat) (tptp.lattic6006661108824415698et_int tptp.inf_inf_int tptp.ord_less_eq_int tptp.ord_less_int) (forall ((Uu tptp.produc3260487557148687353it_nat) (X tptp.produc3260487557148687353it_nat)) (= (tptp.the_de542837501814275618it_nat Uu (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat X)) X)) (forall ((Uu tptp.num) (X tptp.num)) (= (tptp.aa_option_num_num (tptp.the_default_num Uu) (tptp.aa_num_option_num tptp.some_num X)) X)) (forall ((Uu tptp.produc8664842809031399944it_nat) (X tptp.produc8664842809031399944it_nat)) (= (tptp.the_de2487931475039285041it_nat Uu (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat X)) X)) (forall ((X tptp.fun_Pr6001797050664311790t_bool) (Xa2 tptp.fun_Pr6001797050664311790t_bool) (Xb tptp.produc3658429121746597890et_nat)) (=> (not (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.aa_fun6808777976510360636t_bool (tptp.wand_raw X) Xa2) Xb))) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (tptp.produc7507926704131184380et_nat H4 As4))) (=> (= Xb _let_1) (and (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range _let_1)) (forall ((H5 tptp.heap_e7401611519738050253t_unit) (As6 tptp.set_nat)) (=> (and (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat As4) As6) tptp.bot_bot_set_nat) (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.relH As4 H4) H5)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range (tptp.produc7507926704131184380et_nat H5 As4))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool X (tptp.produc7507926704131184380et_nat H5 As6)))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool Xa2 (tptp.produc7507926704131184380et_nat H5 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat As4) As6))))))))))))) (forall ((X tptp.fun_Pr6001797050664311790t_bool) (Xa2 tptp.fun_Pr6001797050664311790t_bool) (Xb tptp.produc3658429121746597890et_nat)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.aa_fun6808777976510360636t_bool (tptp.wand_raw X) Xa2) Xb)) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (tptp.produc7507926704131184380et_nat H4 As4))) (=> (= Xb _let_1) (not (and (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range _let_1)) (forall ((H8 tptp.heap_e7401611519738050253t_unit) (As7 tptp.set_nat)) (=> (and (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat As4) As7) tptp.bot_bot_set_nat) (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.relH As4 H4) H8)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range (tptp.produc7507926704131184380et_nat H8 As4))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool X (tptp.produc7507926704131184380et_nat H8 As7)))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool Xa2 (tptp.produc7507926704131184380et_nat H8 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat As4) As7)))))))))))))) (forall ((X tptp.fun_Pr6001797050664311790t_bool) (Xa2 tptp.fun_Pr6001797050664311790t_bool) (Xb tptp.produc3658429121746597890et_nat) (Y tptp.bool)) (=> (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.aa_fun6808777976510360636t_bool (tptp.wand_raw X) Xa2) Xb)) (tptp.pp Y)) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (tptp.produc7507926704131184380et_nat H4 As4))) (=> (= Xb _let_1) (= (tptp.pp Y) (not (and (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range _let_1)) (forall ((H7 tptp.heap_e7401611519738050253t_unit) (As8 tptp.set_nat)) (=> (and (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat As4) As8) tptp.bot_bot_set_nat) (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.relH As4 H4) H7)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range (tptp.produc7507926704131184380et_nat H7 As4))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool X (tptp.produc7507926704131184380et_nat H7 As8)))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool Xa2 (tptp.produc7507926704131184380et_nat H7 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat As4) As8))))))))))))))) (forall ((P tptp.fun_Pr6001797050664311790t_bool) (Q tptp.fun_Pr6001797050664311790t_bool) (H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (tptp.produc7507926704131184380et_nat H As))) (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.aa_fun6808777976510360636t_bool (tptp.wand_raw P) Q) _let_1)) (and (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range _let_1)) (forall ((H7 tptp.heap_e7401611519738050253t_unit) (As8 tptp.set_nat)) (=> (and (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat As) As8) tptp.bot_bot_set_nat) (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.relH As H) H7)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range (tptp.produc7507926704131184380et_nat H7 As))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool P (tptp.produc7507926704131184380et_nat H7 As8)))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool Q (tptp.produc7507926704131184380et_nat H7 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat As) As8)))))))))) (forall ((X tptp.nat) (Y tptp.nat) (F tptp.fun_nat_nat)) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat X) Y)) (tptp.measure_nat F))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat F X)) (tptp.aa_nat_nat F Y))))) (forall ((X tptp.fun_Pr6001797050664311790t_bool) (Xa2 tptp.fun_Pr6001797050664311790t_bool) (Xb tptp.produc3658429121746597890et_nat)) (=> (not (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.aa_fun6808777976510360636t_bool (tptp.wand_raw X) Xa2) Xb))) (=> (tptp.pp (tptp.aa_Pro6092667153363046813t_bool (tptp.accp_P9010229746810818675et_nat tptp.wand_raw_rel) (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat X) (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat Xa2) Xb)))) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (tptp.produc7507926704131184380et_nat H4 As4))) (=> (= Xb _let_1) (=> (tptp.pp (tptp.aa_Pro6092667153363046813t_bool (tptp.accp_P9010229746810818675et_nat tptp.wand_raw_rel) (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat X) (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat Xa2) _let_1)))) (and (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range _let_1)) (forall ((H5 tptp.heap_e7401611519738050253t_unit) (As6 tptp.set_nat)) (=> (and (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat As4) As6) tptp.bot_bot_set_nat) (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.relH As4 H4) H5)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range (tptp.produc7507926704131184380et_nat H5 As4))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool X (tptp.produc7507926704131184380et_nat H5 As6)))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool Xa2 (tptp.produc7507926704131184380et_nat H5 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat As4) As6))))))))))))))) (forall ((X tptp.fun_Pr6001797050664311790t_bool) (Xa2 tptp.fun_Pr6001797050664311790t_bool) (Xb tptp.produc3658429121746597890et_nat)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.aa_fun6808777976510360636t_bool (tptp.wand_raw X) Xa2) Xb)) (=> (tptp.pp (tptp.aa_Pro6092667153363046813t_bool (tptp.accp_P9010229746810818675et_nat tptp.wand_raw_rel) (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat X) (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat Xa2) Xb)))) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (tptp.produc7507926704131184380et_nat H4 As4))) (=> (= Xb _let_1) (=> (tptp.pp (tptp.aa_Pro6092667153363046813t_bool (tptp.accp_P9010229746810818675et_nat tptp.wand_raw_rel) (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat X) (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat Xa2) _let_1)))) (not (and (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range _let_1)) (forall ((H8 tptp.heap_e7401611519738050253t_unit) (As7 tptp.set_nat)) (=> (and (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat As4) As7) tptp.bot_bot_set_nat) (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.relH As4 H4) H8)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range (tptp.produc7507926704131184380et_nat H8 As4))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool X (tptp.produc7507926704131184380et_nat H8 As7)))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool Xa2 (tptp.produc7507926704131184380et_nat H8 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat As4) As7)))))))))))))))) (forall ((X tptp.fun_Pr6001797050664311790t_bool) (Xa2 tptp.fun_Pr6001797050664311790t_bool) (Xb tptp.produc3658429121746597890et_nat) (Y tptp.bool)) (=> (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.aa_fun6808777976510360636t_bool (tptp.wand_raw X) Xa2) Xb)) (tptp.pp Y)) (=> (tptp.pp (tptp.aa_Pro6092667153363046813t_bool (tptp.accp_P9010229746810818675et_nat tptp.wand_raw_rel) (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat X) (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat Xa2) Xb)))) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (tptp.produc7507926704131184380et_nat H4 As4))) (=> (= Xb _let_1) (=> (= (tptp.pp Y) (and (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range _let_1)) (forall ((H7 tptp.heap_e7401611519738050253t_unit) (As8 tptp.set_nat)) (=> (and (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat As4) As8) tptp.bot_bot_set_nat) (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.relH As4 H4) H7)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range (tptp.produc7507926704131184380et_nat H7 As4))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool X (tptp.produc7507926704131184380et_nat H7 As8)))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool Xa2 (tptp.produc7507926704131184380et_nat H7 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat As4) As8)))))))) (not (tptp.pp (tptp.aa_Pro6092667153363046813t_bool (tptp.accp_P9010229746810818675et_nat tptp.wand_raw_rel) (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat X) (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat Xa2) _let_1))))))))))))) (forall ((X tptp.produc3658429121746597890et_nat)) (=> (not (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range X))) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.accp_P5801069581201407417et_nat tptp.in_range_rel) X)) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (tptp.produc7507926704131184380et_nat H4 As4))) (=> (= X _let_1) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.accp_P5801069581201407417et_nat tptp.in_range_rel) _let_1)) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) As4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) (tptp.lim_Product_unit H4))))))))))))) (forall ((X tptp.produc3658429121746597890et_nat)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range X)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.accp_P5801069581201407417et_nat tptp.in_range_rel) X)) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (tptp.produc7507926704131184380et_nat H4 As4))) (=> (= X _let_1) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.accp_P5801069581201407417et_nat tptp.in_range_rel) _let_1)) (not (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X5) As4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X5) (tptp.lim_Product_unit H4)))))))))))))) (forall ((X tptp.produc3658429121746597890et_nat) (Y tptp.bool)) (=> (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range X)) (tptp.pp Y)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.accp_P5801069581201407417et_nat tptp.in_range_rel) X)) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (tptp.produc7507926704131184380et_nat H4 As4))) (=> (= X _let_1) (=> (= (tptp.pp Y) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) As4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X4) (tptp.lim_Product_unit H4)))))) (not (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.accp_P5801069581201407417et_nat tptp.in_range_rel) _let_1))))))))))) (forall ((P tptp.assn) (Q tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.wand_assn P) Q) (tptp.abs_assn (tptp.aa_fun6808777976510360636t_bool (tptp.wand_raw (tptp.rep_assn P)) (tptp.rep_assn Q))))) (forall ((X tptp.option2158460348403737357at_nat) (Y tptp.option2158460348403737357at_nat)) (= (tptp.sup_su1419176701018045153at_nat X Y) (tptp.case_o7467001542679133189at_nat Y (tptp.aa_opt2198001859980869274at_nat (tptp.aTP_Lamm_dm X) Y) X))) (forall ((X tptp.option2498585697089621389at_nat) (Y tptp.option2498585697089621389at_nat)) (= (tptp.sup_su5873096292857799009at_nat X Y) (tptp.case_o8757249484648823045at_nat Y (tptp.aa_opt1741456117285354266at_nat (tptp.aTP_Lamm_do X) Y) X))) (forall ((X tptp.option1583680563626158861at_nat) (Y tptp.option1583680563626158861at_nat)) (= (tptp.sup_su2273273666271716065at_nat X Y) (tptp.case_o9080059180780454917at_nat Y (tptp.aa_opt1027706798495913626at_nat (tptp.aTP_Lamm_dq X) Y) X))) (forall ((X tptp.option_set_nat) (Y tptp.option_set_nat)) (= (tptp.sup_su3598758113090618626et_nat X Y) (tptp.case_o4054078431260844265et_nat Y (tptp.aa_opt5648106117674462701et_nat (tptp.aTP_Lamm_ds X) Y) X))) (forall ((X tptp.option_nat) (Y tptp.option_nat)) (= (tptp.sup_sup_option_nat X Y) (tptp.case_o7429725398727453821at_nat Y (tptp.aa_opt1558076126722380235on_nat (tptp.aTP_Lamm_du X) Y) X))) (forall ((S tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.dflt_N6592383573632408824at_nat S))) (let ((_let_2 (= S tptp.bot_bo2099793752762293965at_nat))) (and (=> _let_2 (= _let_1 tptp.none_s625347054029921090at_nat)) (=> (not _let_2) (= _let_1 (tptp.some_s147305329494351046at_nat S))))))) (forall ((S tptp.set_bool)) (let ((_let_1 (tptp.dflt_None_set_bool S))) (let ((_let_2 (= S tptp.bot_bot_set_bool))) (and (=> _let_2 (= _let_1 tptp.none_set_bool)) (=> (not _let_2) (= _let_1 (tptp.some_set_bool S))))))) (forall ((S tptp.set_nat)) (let ((_let_1 (tptp.dflt_None_set_nat S))) (let ((_let_2 (= S tptp.bot_bot_set_nat))) (and (=> _let_2 (= _let_1 tptp.none_set_nat)) (=> (not _let_2) (= _let_1 (tptp.some_set_nat S))))))) (forall ((S tptp.set_int)) (let ((_let_1 (tptp.dflt_None_set_int S))) (let ((_let_2 (= S tptp.bot_bot_set_int))) (and (=> _let_2 (= _let_1 tptp.none_set_int)) (=> (not _let_2) (= _let_1 (tptp.some_set_int S))))))) (forall ((P tptp.assn) (Q tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn P) Q) (tptp.abs_assn (tptp.aa_fun6808777976510360636t_bool (tptp.times_assn_raw (tptp.rep_assn P)) (tptp.rep_assn Q))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.is_emp1662574758705540307at_nat A3)) (= A3 tptp.bot_bo2099793752762293965at_nat))) (forall ((A3 tptp.set_bool)) (= (tptp.is_empty_bool A3) (= A3 tptp.bot_bot_set_bool))) (forall ((A3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool tptp.is_empty_nat A3)) (= A3 tptp.bot_bot_set_nat))) (forall ((A3 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool tptp.is_empty_int A3)) (= A3 tptp.bot_bot_set_int))) (forall ((P tptp.assn) (C tptp.heap_Time_Heap_a) (Q tptp.fun_a_assn) (H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (tptp.hoare_hoare_triple_a P C Q) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn P) (tptp.produc7507926704131184380et_nat H As))) (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.heap_Time_success_a C) H))))) (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (P tptp.fun_Pr7757163693017731481t_bool)) (let ((_let_1 (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat B3))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 A3)) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.collec3392354462482085612at_nat (tptp.aa_fun830836278467416944t_bool (tptp.aTP_Lamm_al A3) P)))) (forall ((X4 tptp.product_prod_nat_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat X4) B3)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool P X4)))))))) (forall ((B3 tptp.set_bool) (A3 tptp.set_bool) (P tptp.fun_bool_bool)) (=> (tptp.ord_less_eq_set_bool B3 A3) (= (tptp.ord_less_eq_set_bool B3 (tptp.collect_bool (tptp.aa_fun8098540714523660868l_bool (tptp.aTP_Lamm_am A3) P))) (forall ((X4 tptp.bool)) (=> (tptp.pp (tptp.member_bool X4 B3)) (tptp.pp (tptp.aa_bool_bool P X4))))))) (forall ((B3 tptp.set_Pr958786334691620121nt_int) (A3 tptp.set_Pr958786334691620121nt_int) (P tptp.fun_Pr803113274115125473t_bool)) (=> (tptp.ord_le2843351958646193337nt_int B3 A3) (= (tptp.ord_le2843351958646193337nt_int B3 (tptp.collec213857154873943460nt_int (tptp.aa_fun8917503761599146496t_bool (tptp.aTP_Lamm_an A3) P))) (forall ((X4 tptp.product_prod_int_int)) (=> (tptp.member5262025264175285858nt_int X4 B3) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool P X4))))))) (forall ((B3 tptp.set_list_nat) (A3 tptp.set_list_nat) (P tptp.fun_list_nat_bool)) (=> (tptp.ord_le6045566169113846134st_nat B3 A3) (= (tptp.ord_le6045566169113846134st_nat B3 (tptp.collect_list_nat (tptp.aa_fun6009467934925565500t_bool (tptp.aTP_Lamm_ao A3) P))) (forall ((X4 tptp.list_nat)) (=> (tptp.member_list_nat X4 B3) (tptp.pp (tptp.aa_list_nat_bool P X4))))))) (forall ((B3 tptp.set_set_nat) (A3 tptp.set_set_nat) (P tptp.fun_set_nat_bool)) (let ((_let_1 (tptp.ord_le6893508408891458716et_nat B3))) (=> (tptp.pp (tptp.aa_set_set_nat_bool _let_1 A3)) (= (tptp.pp (tptp.aa_set_set_nat_bool _let_1 (tptp.collect_set_nat (tptp.aa_fun3565389549526402364t_bool (tptp.aTP_Lamm_ap A3) P)))) (forall ((X4 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat X4) B3)) (tptp.pp (tptp.aa_set_nat_bool P X4)))))))) (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (P tptp.fun_nat_bool)) (let ((_let_1 (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B3))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A3)) (= (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.collect_nat (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_aq A3) P)))) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) B3)) (tptp.pp (tptp.aa_nat_bool P X4)))))))) (forall ((B3 tptp.set_int) (A3 tptp.set_int) (P tptp.fun_int_bool)) (let ((_let_1 (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 A3)) (= (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.collect_int (tptp.aa_fun5146555767781538748t_bool (tptp.aTP_Lamm_ar A3) P)))) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) B3)) (tptp.pp (tptp.aa_int_bool P X4)))))))) (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (Q tptp.fun_Pr7757163693017731481t_bool) (P tptp.fun_Pr7757163693017731481t_bool)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat B3) A3)) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat X3) B3)) (=> (tptp.pp (tptp.aa_Pro2232559814647311250t_bool Q X3)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool P X3))))) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat (tptp.collec3392354462482085612at_nat (tptp.aa_fun830836278467416944t_bool (tptp.aTP_Lamm_al B3) Q))) (tptp.collec3392354462482085612at_nat (tptp.aa_fun830836278467416944t_bool (tptp.aTP_Lamm_al A3) P))))))) (forall ((B3 tptp.set_bool) (A3 tptp.set_bool) (Q tptp.fun_bool_bool) (P tptp.fun_bool_bool)) (=> (tptp.ord_less_eq_set_bool B3 A3) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 B3)) (=> (tptp.pp (tptp.aa_bool_bool Q X3)) (tptp.pp (tptp.aa_bool_bool P X3))))) (tptp.ord_less_eq_set_bool (tptp.collect_bool (tptp.aa_fun8098540714523660868l_bool (tptp.aTP_Lamm_am B3) Q)) (tptp.collect_bool (tptp.aa_fun8098540714523660868l_bool (tptp.aTP_Lamm_am A3) P)))))) (forall ((B3 tptp.set_Pr958786334691620121nt_int) (A3 tptp.set_Pr958786334691620121nt_int) (Q tptp.fun_Pr803113274115125473t_bool) (P tptp.fun_Pr803113274115125473t_bool)) (=> (tptp.ord_le2843351958646193337nt_int B3 A3) (=> (forall ((X3 tptp.product_prod_int_int)) (=> (tptp.member5262025264175285858nt_int X3 B3) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool Q X3)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool P X3))))) (tptp.ord_le2843351958646193337nt_int (tptp.collec213857154873943460nt_int (tptp.aa_fun8917503761599146496t_bool (tptp.aTP_Lamm_an B3) Q)) (tptp.collec213857154873943460nt_int (tptp.aa_fun8917503761599146496t_bool (tptp.aTP_Lamm_an A3) P)))))) (forall ((B3 tptp.set_list_nat) (A3 tptp.set_list_nat) (Q tptp.fun_list_nat_bool) (P tptp.fun_list_nat_bool)) (=> (tptp.ord_le6045566169113846134st_nat B3 A3) (=> (forall ((X3 tptp.list_nat)) (=> (tptp.member_list_nat X3 B3) (=> (tptp.pp (tptp.aa_list_nat_bool Q X3)) (tptp.pp (tptp.aa_list_nat_bool P X3))))) (tptp.ord_le6045566169113846134st_nat (tptp.collect_list_nat (tptp.aa_fun6009467934925565500t_bool (tptp.aTP_Lamm_ao B3) Q)) (tptp.collect_list_nat (tptp.aa_fun6009467934925565500t_bool (tptp.aTP_Lamm_ao A3) P)))))) (forall ((B3 tptp.set_set_nat) (A3 tptp.set_set_nat) (Q tptp.fun_set_nat_bool) (P tptp.fun_set_nat_bool)) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat B3) A3)) (=> (forall ((X3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat X3) B3)) (=> (tptp.pp (tptp.aa_set_nat_bool Q X3)) (tptp.pp (tptp.aa_set_nat_bool P X3))))) (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat (tptp.collect_set_nat (tptp.aa_fun3565389549526402364t_bool (tptp.aTP_Lamm_ap B3) Q))) (tptp.collect_set_nat (tptp.aa_fun3565389549526402364t_bool (tptp.aTP_Lamm_ap A3) P))))))) (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (Q tptp.fun_nat_bool) (P tptp.fun_nat_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B3) A3)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) B3)) (=> (tptp.pp (tptp.aa_nat_bool Q X3)) (tptp.pp (tptp.aa_nat_bool P X3))))) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.collect_nat (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_aq B3) Q))) (tptp.collect_nat (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_aq A3) P))))))) (forall ((B3 tptp.set_int) (A3 tptp.set_int) (Q tptp.fun_int_bool) (P tptp.fun_int_bool)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) A3)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) B3)) (=> (tptp.pp (tptp.aa_int_bool Q X3)) (tptp.pp (tptp.aa_int_bool P X3))))) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.collect_int (tptp.aa_fun5146555767781538748t_bool (tptp.aTP_Lamm_ar B3) Q))) (tptp.collect_int (tptp.aa_fun5146555767781538748t_bool (tptp.aTP_Lamm_ar A3) P))))))) (forall ((A3 tptp.set_Pr958786334691620121nt_int) (P tptp.fun_Pr803113274115125473t_bool) (Q tptp.fun_Pr803113274115125473t_bool)) (= (tptp.ord_le2843351958646193337nt_int A3 (tptp.collec213857154873943460nt_int (tptp.aa_fun8917503761599146496t_bool (tptp.aTP_Lamm_bp P) Q))) (and (tptp.ord_le2843351958646193337nt_int A3 (tptp.collec213857154873943460nt_int P)) (tptp.ord_le2843351958646193337nt_int A3 (tptp.collec213857154873943460nt_int Q))))) (forall ((A3 tptp.set_list_nat) (P tptp.fun_list_nat_bool) (Q tptp.fun_list_nat_bool)) (= (tptp.ord_le6045566169113846134st_nat A3 (tptp.collect_list_nat (tptp.aa_fun6009467934925565500t_bool (tptp.aTP_Lamm_bq P) Q))) (and (tptp.ord_le6045566169113846134st_nat A3 (tptp.collect_list_nat P)) (tptp.ord_le6045566169113846134st_nat A3 (tptp.collect_list_nat Q))))) (forall ((A3 tptp.set_set_nat) (P tptp.fun_set_nat_bool) (Q tptp.fun_set_nat_bool)) (let ((_let_1 (tptp.ord_le6893508408891458716et_nat A3))) (= (tptp.pp (tptp.aa_set_set_nat_bool _let_1 (tptp.collect_set_nat (tptp.aa_fun3565389549526402364t_bool (tptp.aTP_Lamm_br P) Q)))) (and (tptp.pp (tptp.aa_set_set_nat_bool _let_1 (tptp.collect_set_nat P))) (tptp.pp (tptp.aa_set_set_nat_bool _let_1 (tptp.collect_set_nat Q))))))) (forall ((A3 tptp.set_nat) (P tptp.fun_nat_bool) (Q tptp.fun_nat_bool)) (let ((_let_1 (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3))) (= (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.collect_nat (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_bt P) Q)))) (and (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.collect_nat P))) (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.collect_nat Q))))))) (forall ((A3 tptp.set_int) (P tptp.fun_int_bool) (Q tptp.fun_int_bool)) (let ((_let_1 (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3))) (= (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.collect_int (tptp.aa_fun5146555767781538748t_bool (tptp.aTP_Lamm_bs P) Q)))) (and (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.collect_int P))) (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.collect_int Q))))))) (forall ((X tptp.option3562590408128118217it_nat)) (= (not (= X tptp.none_P2651198173097904984it_nat)) (exists ((Y5 tptp.produc3260487557148687353it_nat)) (= X (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat Y5))))) (forall ((X tptp.option_num)) (= (not (= X tptp.none_num)) (exists ((Y5 tptp.num)) (= X (tptp.aa_num_option_num tptp.some_num Y5))))) (forall ((X tptp.option8956607266484857688it_nat)) (= (not (= X tptp.none_P9117596204409417319it_nat)) (exists ((Y5 tptp.produc8664842809031399944it_nat)) (= X (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat Y5))))) (forall ((X tptp.option3562590408128118217it_nat)) (= (forall ((Y5 tptp.produc3260487557148687353it_nat)) (not (= X (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat Y5)))) (= X tptp.none_P2651198173097904984it_nat))) (forall ((X tptp.option_num)) (= (forall ((Y5 tptp.num)) (not (= X (tptp.aa_num_option_num tptp.some_num Y5)))) (= X tptp.none_num))) (forall ((X tptp.option8956607266484857688it_nat)) (= (forall ((Y5 tptp.produc8664842809031399944it_nat)) (not (= X (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat Y5)))) (= X tptp.none_P9117596204409417319it_nat))) (forall ((X tptp.assn)) (= (tptp.abs_assn (tptp.rep_assn X)) X)) (forall ((X tptp.option_num)) (tptp.pp (tptp.aa_option_num_bool (tptp.aa_opt4409681509335781342m_bool tptp.ord_le6622620407824499402on_num tptp.none_num) X))) (forall ((X tptp.option_num)) (not (tptp.pp (tptp.aa_option_num_bool (tptp.aa_opt4409681509335781342m_bool tptp.ord_less_option_num X) tptp.none_num)))) (forall ((X tptp.num)) (not (tptp.pp (tptp.aa_option_num_bool (tptp.aa_opt4409681509335781342m_bool tptp.ord_le6622620407824499402on_num (tptp.aa_num_option_num tptp.some_num X)) tptp.none_num)))) (forall ((X tptp.num)) (tptp.pp (tptp.aa_option_num_bool (tptp.aa_opt4409681509335781342m_bool tptp.ord_less_option_num tptp.none_num) (tptp.aa_num_option_num tptp.some_num X)))) (= (tptp.dflt_N6592383573632408824at_nat tptp.bot_bo2099793752762293965at_nat) tptp.none_s625347054029921090at_nat) (= (tptp.dflt_None_set_bool tptp.bot_bot_set_bool) tptp.none_set_bool) (= (tptp.dflt_None_set_nat tptp.bot_bot_set_nat) tptp.none_set_nat) (= (tptp.dflt_None_set_int tptp.bot_bot_set_int) tptp.none_set_int) (forall ((F1 tptp.int) (F22 tptp.fun_num_int)) (= (tptp.aa_option_num_int (tptp.case_option_int_num F1 F22) tptp.none_num) F1)) (forall ((F1 tptp.option_num) (F22 tptp.fun_num_option_num)) (= (tptp.aa_opt5369159329878751634on_num (tptp.case_o6005452278849405969um_num F1 F22) tptp.none_num) F1)) (forall ((F1 tptp.num) (F22 tptp.fun_num_num)) (= (tptp.aa_option_num_num (tptp.case_option_num_num F1 F22) tptp.none_num) F1)) (= tptp.bot_bot_option_num tptp.none_num) (forall ((H tptp.fun_int_int) (F1 tptp.int) (F22 tptp.fun_num_int) (Option tptp.option_num)) (= (tptp.aa_int_int H (tptp.aa_option_num_int (tptp.case_option_int_num F1 F22) Option)) (tptp.aa_option_num_int (tptp.case_option_int_num (tptp.aa_int_int H F1) (tptp.aa_fun329774391934724804um_int (tptp.aTP_Lamm_dv H) F22)) Option))) (forall ((H tptp.fun_int_option_num) (F1 tptp.int) (F22 tptp.fun_num_int) (Option tptp.option_num)) (= (tptp.aa_int_option_num H (tptp.aa_option_num_int (tptp.case_option_int_num F1 F22) Option)) (tptp.aa_opt5369159329878751634on_num (tptp.case_o6005452278849405969um_num (tptp.aa_int_option_num H F1) (tptp.aa_fun3858197967482829954on_num (tptp.aTP_Lamm_dw H) F22)) Option))) (forall ((H tptp.fun_int_num) (F1 tptp.int) (F22 tptp.fun_num_int) (Option tptp.option_num)) (= (tptp.aa_int_num H (tptp.aa_option_num_int (tptp.case_option_int_num F1 F22) Option)) (tptp.aa_option_num_num (tptp.case_option_num_num (tptp.aa_int_num H F1) (tptp.aa_fun5215869348392759218um_num (tptp.aTP_Lamm_dx H) F22)) Option))) (forall ((H tptp.fun_option_num_int) (F1 tptp.option_num) (F22 tptp.fun_num_option_num) (Option tptp.option_num)) (= (tptp.aa_option_num_int H (tptp.aa_opt5369159329878751634on_num (tptp.case_o6005452278849405969um_num F1 F22) Option)) (tptp.aa_option_num_int (tptp.case_option_int_num (tptp.aa_option_num_int H F1) (tptp.aa_fun2256179333612926594um_int (tptp.aTP_Lamm_dy H) F22)) Option))) (forall ((H tptp.fun_op8989173174992673105on_num) (F1 tptp.option_num) (F22 tptp.fun_num_option_num) (Option tptp.option_num)) (= (tptp.aa_opt5369159329878751634on_num H (tptp.aa_opt5369159329878751634on_num (tptp.case_o6005452278849405969um_num F1 F22) Option)) (tptp.aa_opt5369159329878751634on_num (tptp.case_o6005452278849405969um_num (tptp.aa_opt5369159329878751634on_num H F1) (tptp.aa_fun3636977833914307392on_num (tptp.aTP_Lamm_dz H) F22)) Option))) (forall ((H tptp.fun_option_num_num) (F1 tptp.option_num) (F22 tptp.fun_num_option_num) (Option tptp.option_num)) (= (tptp.aa_option_num_num H (tptp.aa_opt5369159329878751634on_num (tptp.case_o6005452278849405969um_num F1 F22) Option)) (tptp.aa_option_num_num (tptp.case_option_num_num (tptp.aa_option_num_num H F1) (tptp.aa_fun7142274290070961008um_num (tptp.aTP_Lamm_ea H) F22)) Option))) (forall ((H tptp.fun_num_int) (F1 tptp.num) (F22 tptp.fun_num_num) (Option tptp.option_num)) (= (tptp.aa_num_int H (tptp.aa_option_num_num (tptp.case_option_num_num F1 F22) Option)) (tptp.aa_option_num_int (tptp.case_option_int_num (tptp.aa_num_int H F1) (tptp.aa_fun3162900327506486194um_int (tptp.aTP_Lamm_eb H) F22)) Option))) (forall ((H tptp.fun_num_option_num) (F1 tptp.num) (F22 tptp.fun_num_num) (Option tptp.option_num)) (= (tptp.aa_num_option_num H (tptp.aa_option_num_num (tptp.case_option_num_num F1 F22) Option)) (tptp.aa_opt5369159329878751634on_num (tptp.case_o6005452278849405969um_num (tptp.aa_num_option_num H F1) (tptp.aa_fun612943910911948912on_num (tptp.aTP_Lamm_ec H) F22)) Option))) (forall ((H tptp.fun_num_num) (F1 tptp.num) (F22 tptp.fun_num_num) (Option tptp.option_num)) (= (tptp.aa_num_num H (tptp.aa_option_num_num (tptp.case_option_num_num F1 F22) Option)) (tptp.aa_option_num_num (tptp.case_option_num_num (tptp.aa_num_num H F1) (tptp.aa_fun8048995283964520608um_num (tptp.aTP_Lamm_ed H) F22)) Option))) (forall ((X2 tptp.produc3260487557148687353it_nat)) (not (= tptp.none_P2651198173097904984it_nat (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat X2)))) (forall ((X2 tptp.num)) (not (= tptp.none_num (tptp.aa_num_option_num tptp.some_num X2)))) (forall ((X2 tptp.produc8664842809031399944it_nat)) (not (= tptp.none_P9117596204409417319it_nat (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat X2)))) (forall ((Option tptp.option3562590408128118217it_nat) (X2 tptp.produc3260487557148687353it_nat)) (=> (= Option (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat X2)) (not (= Option tptp.none_P2651198173097904984it_nat)))) (forall ((Option tptp.option_num) (X2 tptp.num)) (=> (= Option (tptp.aa_num_option_num tptp.some_num X2)) (not (= Option tptp.none_num)))) (forall ((Option tptp.option8956607266484857688it_nat) (X2 tptp.produc8664842809031399944it_nat)) (=> (= Option (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat X2)) (not (= Option tptp.none_P9117596204409417319it_nat)))) (forall ((Y tptp.option3562590408128118217it_nat)) (=> (not (= Y tptp.none_P2651198173097904984it_nat)) (not (forall ((X22 tptp.produc3260487557148687353it_nat)) (not (= Y (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat X22))))))) (forall ((Y tptp.option_num)) (=> (not (= Y tptp.none_num)) (not (forall ((X22 tptp.num)) (not (= Y (tptp.aa_num_option_num tptp.some_num X22))))))) (forall ((Y tptp.option8956607266484857688it_nat)) (=> (not (= Y tptp.none_P9117596204409417319it_nat)) (not (forall ((X22 tptp.produc8664842809031399944it_nat)) (not (= Y (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat X22))))))) (forall ((P tptp.fun_op2491542651970850919t_bool)) (= (exists ((X_12 tptp.option3562590408128118217it_nat)) (tptp.pp (tptp.aa_opt753342655352099408t_bool P X_12))) (or (tptp.pp (tptp.aa_opt753342655352099408t_bool P tptp.none_P2651198173097904984it_nat)) (exists ((X4 tptp.produc3260487557148687353it_nat)) (tptp.pp (tptp.aa_opt753342655352099408t_bool P (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat X4))))))) (forall ((P tptp.fun_option_num_bool)) (= (exists ((X_12 tptp.option_num)) (tptp.pp (tptp.aa_option_num_bool P X_12))) (or (tptp.pp (tptp.aa_option_num_bool P tptp.none_num)) (exists ((X4 tptp.num)) (tptp.pp (tptp.aa_option_num_bool P (tptp.aa_num_option_num tptp.some_num X4))))))) (forall ((P tptp.fun_op5902475268499868568t_bool)) (= (exists ((X_12 tptp.option8956607266484857688it_nat)) (tptp.pp (tptp.aa_opt8953672862898910593t_bool P X_12))) (or (tptp.pp (tptp.aa_opt8953672862898910593t_bool P tptp.none_P9117596204409417319it_nat)) (exists ((X4 tptp.produc8664842809031399944it_nat)) (tptp.pp (tptp.aa_opt8953672862898910593t_bool P (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat X4))))))) (forall ((P tptp.fun_op2491542651970850919t_bool)) (= (forall ((X_12 tptp.option3562590408128118217it_nat)) (tptp.pp (tptp.aa_opt753342655352099408t_bool P X_12))) (and (tptp.pp (tptp.aa_opt753342655352099408t_bool P tptp.none_P2651198173097904984it_nat)) (forall ((X4 tptp.produc3260487557148687353it_nat)) (tptp.pp (tptp.aa_opt753342655352099408t_bool P (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat X4))))))) (forall ((P tptp.fun_option_num_bool)) (= (forall ((X_12 tptp.option_num)) (tptp.pp (tptp.aa_option_num_bool P X_12))) (and (tptp.pp (tptp.aa_option_num_bool P tptp.none_num)) (forall ((X4 tptp.num)) (tptp.pp (tptp.aa_option_num_bool P (tptp.aa_num_option_num tptp.some_num X4))))))) (forall ((P tptp.fun_op5902475268499868568t_bool)) (= (forall ((X_12 tptp.option8956607266484857688it_nat)) (tptp.pp (tptp.aa_opt8953672862898910593t_bool P X_12))) (and (tptp.pp (tptp.aa_opt8953672862898910593t_bool P tptp.none_P9117596204409417319it_nat)) (forall ((X4 tptp.produc8664842809031399944it_nat)) (tptp.pp (tptp.aa_opt8953672862898910593t_bool P (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat X4))))))) (forall ((X tptp.option3562590408128118217it_nat) (P tptp.fun_op8638339026801468471t_bool) (Y tptp.option3562590408128118217it_nat)) (let ((_let_1 (tptp.pp (tptp.aa_opt753342655352099408t_bool (tptp.aa_opt475322814783192096t_bool P X) Y)))) (=> (=> (= X tptp.none_P2651198173097904984it_nat) _let_1) (=> (=> (= Y tptp.none_P2651198173097904984it_nat) _let_1) (=> (forall ((A4 tptp.produc3260487557148687353it_nat) (B4 tptp.produc3260487557148687353it_nat)) (=> (= X (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat A4)) (=> (= Y (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat B4)) (tptp.pp (tptp.aa_opt753342655352099408t_bool (tptp.aa_opt475322814783192096t_bool P X) Y))))) _let_1))))) (forall ((X tptp.option3562590408128118217it_nat) (P tptp.fun_op2372187285662272598m_bool) (Y tptp.option_num)) (let ((_let_1 (tptp.pp (tptp.aa_option_num_bool (tptp.aa_opt1220987332178915263m_bool P X) Y)))) (=> (=> (= X tptp.none_P2651198173097904984it_nat) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A4 tptp.produc3260487557148687353it_nat) (B4 tptp.num)) (=> (= X (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat A4)) (=> (= Y (tptp.aa_num_option_num tptp.some_num B4)) (tptp.pp (tptp.aa_option_num_bool (tptp.aa_opt1220987332178915263m_bool P X) Y))))) _let_1))))) (forall ((X tptp.option3562590408128118217it_nat) (P tptp.fun_op8947389286484753896t_bool) (Y tptp.option8956607266484857688it_nat)) (let ((_let_1 (tptp.pp (tptp.aa_opt8953672862898910593t_bool (tptp.aa_opt867424377461946961t_bool P X) Y)))) (=> (=> (= X tptp.none_P2651198173097904984it_nat) _let_1) (=> (=> (= Y tptp.none_P9117596204409417319it_nat) _let_1) (=> (forall ((A4 tptp.produc3260487557148687353it_nat) (B4 tptp.produc8664842809031399944it_nat)) (=> (= X (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat A4)) (=> (= Y (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat B4)) (tptp.pp (tptp.aa_opt8953672862898910593t_bool (tptp.aa_opt867424377461946961t_bool P X) Y))))) _let_1))))) (forall ((X tptp.option_num) (P tptp.fun_op5997231755256552278t_bool) (Y tptp.option3562590408128118217it_nat)) (let ((_let_1 (tptp.pp (tptp.aa_opt753342655352099408t_bool (tptp.aa_opt2367031720031861567t_bool P X) Y)))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_P2651198173097904984it_nat) _let_1) (=> (forall ((A4 tptp.num) (B4 tptp.produc3260487557148687353it_nat)) (=> (= X (tptp.aa_num_option_num tptp.some_num A4)) (=> (= Y (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat B4)) (tptp.pp (tptp.aa_opt753342655352099408t_bool (tptp.aa_opt2367031720031861567t_bool P X) Y))))) _let_1))))) (forall ((X tptp.option_num) (P tptp.fun_op1962577433978643573m_bool) (Y tptp.option_num)) (let ((_let_1 (tptp.pp (tptp.aa_option_num_bool (tptp.aa_opt4409681509335781342m_bool P X) Y)))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A4 tptp.num) (B4 tptp.num)) (=> (= X (tptp.aa_num_option_num tptp.some_num A4)) (=> (= Y (tptp.aa_num_option_num tptp.some_num B4)) (tptp.pp (tptp.aa_option_num_bool (tptp.aa_opt4409681509335781342m_bool P X) Y))))) _let_1))))) (forall ((X tptp.option_num) (P tptp.fun_op2573228148205091335t_bool) (Y tptp.option8956607266484857688it_nat)) (let ((_let_1 (tptp.pp (tptp.aa_opt8953672862898910593t_bool (tptp.aa_opt4995739887549611632t_bool P X) Y)))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_P9117596204409417319it_nat) _let_1) (=> (forall ((A4 tptp.num) (B4 tptp.produc8664842809031399944it_nat)) (=> (= X (tptp.aa_num_option_num tptp.some_num A4)) (=> (= Y (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat B4)) (tptp.pp (tptp.aa_opt8953672862898910593t_bool (tptp.aa_opt4995739887549611632t_bool P X) Y))))) _let_1))))) (forall ((X tptp.option8956607266484857688it_nat) (P tptp.fun_op6813401651963088104t_bool) (Y tptp.option3562590408128118217it_nat)) (let ((_let_1 (tptp.pp (tptp.aa_opt753342655352099408t_bool (tptp.aa_opt3071855975851707601t_bool P X) Y)))) (=> (=> (= X tptp.none_P9117596204409417319it_nat) _let_1) (=> (=> (= Y tptp.none_P2651198173097904984it_nat) _let_1) (=> (forall ((A4 tptp.produc8664842809031399944it_nat) (B4 tptp.produc3260487557148687353it_nat)) (=> (= X (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat A4)) (=> (= Y (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat B4)) (tptp.pp (tptp.aa_opt753342655352099408t_bool (tptp.aa_opt3071855975851707601t_bool P X) Y))))) _let_1))))) (forall ((X tptp.option8956607266484857688it_nat) (P tptp.fun_op4621176226433041415m_bool) (Y tptp.option_num)) (let ((_let_1 (tptp.pp (tptp.aa_option_num_bool (tptp.aa_opt4637735243575545712m_bool P X) Y)))) (=> (=> (= X tptp.none_P9117596204409417319it_nat) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A4 tptp.produc8664842809031399944it_nat) (B4 tptp.num)) (=> (= X (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat A4)) (=> (= Y (tptp.aa_num_option_num tptp.some_num B4)) (tptp.pp (tptp.aa_option_num_bool (tptp.aa_opt4637735243575545712m_bool P X) Y))))) _let_1))))) (forall ((X tptp.option8956607266484857688it_nat) (P tptp.fun_op714873039799603609t_bool) (Y tptp.option8956607266484857688it_nat)) (let ((_let_1 (tptp.pp (tptp.aa_opt8953672862898910593t_bool (tptp.aa_opt7241141644331021826t_bool P X) Y)))) (=> (=> (= X tptp.none_P9117596204409417319it_nat) _let_1) (=> (=> (= Y tptp.none_P9117596204409417319it_nat) _let_1) (=> (forall ((A4 tptp.produc8664842809031399944it_nat) (B4 tptp.produc8664842809031399944it_nat)) (=> (= X (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat A4)) (=> (= Y (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat B4)) (tptp.pp (tptp.aa_opt8953672862898910593t_bool (tptp.aa_opt7241141644331021826t_bool P X) Y))))) _let_1))))) (forall ((X tptp.option_num)) (tptp.pp (tptp.aa_option_num_bool (tptp.aa_opt4409681509335781342m_bool tptp.ord_le6622620407824499402on_num tptp.none_num) X))) (forall ((X tptp.option_num)) (=> (tptp.pp (tptp.aa_option_num_bool (tptp.aa_opt4409681509335781342m_bool tptp.ord_le6622620407824499402on_num X) tptp.none_num)) (= X tptp.none_num))) (forall ((P tptp.fun_Pr6001797050664311790t_bool) (Pr tptp.assn)) (=> (forall ((H4 tptp.produc3658429121746597890et_nat)) (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool P H4)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn Pr) H4)))) (= (tptp.abs_assn P) Pr))) (forall ((P tptp.fun_Pr6001797050664311790t_bool) (Pr tptp.assn)) (=> (forall ((H4 tptp.produc3658429121746597890et_nat)) (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool P H4)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn Pr) H4)))) (= Pr (tptp.abs_assn P)))) (forall ((F1 tptp.int) (F22 tptp.fun_num_int) (X2 tptp.num)) (= (tptp.aa_option_num_int (tptp.case_option_int_num F1 F22) (tptp.aa_num_option_num tptp.some_num X2)) (tptp.aa_num_int F22 X2))) (forall ((F1 tptp.option_num) (F22 tptp.fun_num_option_num) (X2 tptp.num)) (= (tptp.aa_opt5369159329878751634on_num (tptp.case_o6005452278849405969um_num F1 F22) (tptp.aa_num_option_num tptp.some_num X2)) (tptp.aa_num_option_num F22 X2))) (forall ((F1 tptp.num) (F22 tptp.fun_num_num) (X2 tptp.num)) (= (tptp.aa_option_num_num (tptp.case_option_num_num F1 F22) (tptp.aa_num_option_num tptp.some_num X2)) (tptp.aa_num_num F22 X2))) (forall ((X tptp.num)) (= (tptp.aa_option_num_num (tptp.the_default_num X) tptp.none_num) X)) (forall ((X tptp.option_set_nat) (Y tptp.option_set_nat)) (= (tptp.inf_in7812914138253463912et_nat X Y) (tptp.case_o4054078431260844265et_nat tptp.none_set_nat (tptp.aTP_Lamm_ef Y) X))) (forall ((X tptp.option_assn) (Y tptp.option_assn)) (= (tptp.inf_inf_option_assn X Y) (tptp.case_o4484465799723439917n_assn tptp.none_assn (tptp.aTP_Lamm_eh Y) X))) (forall ((X tptp.option_nat) (Y tptp.option_nat)) (= (tptp.inf_inf_option_nat X Y) (tptp.case_o7429725398727453821at_nat tptp.none_nat (tptp.aTP_Lamm_ej Y) X))) (forall ((X tptp.option_Product_unit) (Y tptp.option_Product_unit)) (= (tptp.inf_in5800606384722953409t_unit X Y) (tptp.case_o2985186191577459077t_unit tptp.none_Product_unit (tptp.aTP_Lamm_el Y) X))) (forall ((X tptp.option8963830502488799655at_nat) (Y tptp.option8963830502488799655at_nat)) (= (tptp.inf_in777885744494410645at_nat X Y) (tptp.case_o311359030874850053at_nat tptp.none_s625347054029921090at_nat (tptp.aTP_Lamm_en Y) X))) (= tptp.bot_bot_assn (tptp.abs_assn tptp.aTP_Lamm_eo)) (forall ((X tptp.option_num)) (=> (tptp.pp (tptp.aa_option_num_bool (tptp.aa_opt4409681509335781342m_bool tptp.ord_less_option_num tptp.none_num) X)) (exists ((Z2 tptp.num)) (= X (tptp.aa_num_option_num tptp.some_num Z2))))) (forall ((X tptp.num)) (tptp.pp (tptp.aa_option_num_bool (tptp.aa_opt4409681509335781342m_bool tptp.ord_less_option_num tptp.none_num) (tptp.aa_num_option_num tptp.some_num X)))) (forall ((P tptp.assn) (Q tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn P) Q) (tptp.abs_assn (tptp.aa_ass8975924923219239432t_bool (tptp.aTP_Lamm_ep P) Q)))) (forall ((P tptp.assn) (Q tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn P) Q) (tptp.abs_assn (tptp.aa_ass8975924923219239432t_bool (tptp.aTP_Lamm_eq P) Q)))) (forall ((F tptp.heap_T5738788834812785303t_unit) (H tptp.heap_e7401611519738050253t_unit)) (=> (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.heap_T584514906347983379t_unit F) H)) (not (forall ((R2 tptp.product_unit) (H5 tptp.produc6653097349344004940it_nat)) (not (= (tptp.aa_hea684056619475940329it_nat (tptp.heap_T875086893843062177t_unit F) H) (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat (tptp.produc7133225469290080770it_nat R2 H5)))))))) (forall ((F tptp.heap_Time_Heap_a) (H tptp.heap_e7401611519738050253t_unit)) (=> (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.heap_Time_success_a F) H)) (not (forall ((R2 tptp.a) (H5 tptp.produc6653097349344004940it_nat)) (not (= (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a F) H) (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat R2) H5)))))))) (forall ((P tptp.fun_Pr7757163693017731481t_bool)) (= (tptp.rel_of_nat_nat tptp.aTP_Lamm_er P) tptp.bot_bo2099793752762293965at_nat)) (forall ((X5 tptp.nat)) (= (tptp.aa_nat_option_nat (tptp.set_to_map_nat_nat tptp.bot_bo2099793752762293965at_nat) X5) tptp.none_nat)) (= (tptp.map_to_set_nat_nat tptp.aTP_Lamm_er) tptp.bot_bo2099793752762293965at_nat) (forall ((P tptp.bool) (Q tptp.fun_num_bool) (X tptp.option_num) (R tptp.fun_int_bool) (F tptp.int) (G tptp.fun_num_int)) (=> (tptp.pp (tptp.aa_option_num_bool (tptp.case_option_bool_num P Q) X)) (=> (=> (tptp.pp P) (tptp.pp (tptp.aa_int_bool R F))) (=> (forall ((Q4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool Q Q4)) (tptp.pp (tptp.aa_int_bool R (tptp.aa_num_int G Q4))))) (tptp.pp (tptp.aa_int_bool R (tptp.aa_option_num_int (tptp.case_option_int_num F G) X))))))) (forall ((P tptp.bool) (Q tptp.fun_num_bool) (X tptp.option_num) (R tptp.fun_option_num_bool) (F tptp.option_num) (G tptp.fun_num_option_num)) (=> (tptp.pp (tptp.aa_option_num_bool (tptp.case_option_bool_num P Q) X)) (=> (=> (tptp.pp P) (tptp.pp (tptp.aa_option_num_bool R F))) (=> (forall ((Q4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool Q Q4)) (tptp.pp (tptp.aa_option_num_bool R (tptp.aa_num_option_num G Q4))))) (tptp.pp (tptp.aa_option_num_bool R (tptp.aa_opt5369159329878751634on_num (tptp.case_o6005452278849405969um_num F G) X))))))) (forall ((P tptp.bool) (Q tptp.fun_num_bool) (X tptp.option_num) (R tptp.fun_num_bool) (F tptp.num) (G tptp.fun_num_num)) (=> (tptp.pp (tptp.aa_option_num_bool (tptp.case_option_bool_num P Q) X)) (=> (=> (tptp.pp P) (tptp.pp (tptp.aa_num_bool R F))) (=> (forall ((Q4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool Q Q4)) (tptp.pp (tptp.aa_num_bool R (tptp.aa_num_num G Q4))))) (tptp.pp (tptp.aa_num_bool R (tptp.aa_option_num_num (tptp.case_option_num_num F G) X))))))) (forall ((B tptp.bool)) (= (tptp.aa_bool_assn tptp.pure_assn B) (tptp.abs_assn (tptp.pure_a825153325127701367it_nat B)))) (forall ((S tptp.set_Pr1261947904930325089at_nat)) (= (= tptp.aTP_Lamm_er (tptp.set_to_map_nat_nat S)) (= S tptp.bot_bo2099793752762293965at_nat))) (forall ((V tptp.option6601582610923217263et_nat)) (= (forall ((X4 tptp.fun_Pr6001797050664311790t_bool) (Y5 tptp.produc3658429121746597890et_nat)) (not (= V (tptp.some_P7593219549526818170et_nat (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat X4) Y5))))) (= V tptp.none_P8058360031770559998et_nat))) (forall ((V tptp.option7217372446798200844et_nat)) (= (forall ((X4 tptp.fun_Pr6001797050664311790t_bool) (Y5 tptp.produc6108883039684432031et_nat)) (not (= V (tptp.some_P7242348867715254423et_nat (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat X4) Y5))))) (= V tptp.none_P4874398953505285403et_nat))) (forall ((V tptp.option8369045977646850964nt_int)) (= (forall ((X4 tptp.fun_Pr9164807099015279978e_term) (Y5 tptp.product_prod_int_int)) (not (= V (tptp.some_P7592033027131854111nt_int (tptp.aa_Pro3513184699142849729nt_int (tptp.aa_fun1388719692539776744nt_int tptp.produc1560874099174258678nt_int X4) Y5))))) (= V tptp.none_P1802268335500556195nt_int))) (forall ((V tptp.option3896775892727155392nt_int)) (= (forall ((X4 tptp.fun_in6429348457993719614e_term) (Y5 tptp.product_prod_int_int)) (not (= V (tptp.some_P2931795919503530571nt_int (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int X4) Y5))))) (= V tptp.none_P6115989227272578255nt_int))) (forall ((V tptp.option3562590408128118217it_nat)) (= (forall ((X4 tptp.a) (Y5 tptp.produc6653097349344004940it_nat)) (not (= V (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat X4) Y5))))) (= V tptp.none_P2651198173097904984it_nat))) (forall ((V tptp.option8956607266484857688it_nat)) (= (forall ((X4 tptp.product_unit) (Y5 tptp.produc6653097349344004940it_nat)) (not (= V (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat (tptp.produc7133225469290080770it_nat X4 Y5))))) (= V tptp.none_P9117596204409417319it_nat))) (forall ((F tptp.heap_Time_Heap_a) (H tptp.heap_e7401611519738050253t_unit) (G tptp.fun_a_6093291656547882009Heap_a)) (=> (= (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a F) H) tptp.none_P2651198173097904984it_nat) (= (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a (tptp.heap_Time_bind_a_a F G)) H) tptp.none_P2651198173097904984it_nat))) (forall ((Option tptp.option_num)) (= (not (= Option tptp.none_num)) (tptp.pp (tptp.aa_option_num_bool (tptp.case_option_bool_num tptp.fFalse tptp.aTP_Lamm_es) Option)))) (forall ((Option tptp.option_num)) (= (= Option tptp.none_num) (tptp.pp (tptp.aa_option_num_bool (tptp.case_option_bool_num tptp.fTrue tptp.aTP_Lamm_et) Option)))) (forall ((F tptp.heap_Time_Heap_a) (H tptp.heap_e7401611519738050253t_unit)) (= (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.heap_Time_success_a F) H)) (not (= (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a F) H) tptp.none_P2651198173097904984it_nat)))) (forall ((F tptp.heap_Time_Heap_a) (H tptp.heap_e7401611519738050253t_unit)) (=> (not (= (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a F) H) tptp.none_P2651198173097904984it_nat)) (tptp.pp (tptp.aa_hea1793595068369496646t_bool (tptp.heap_Time_success_a F) H)))) (forall ((P tptp.bool) (Q tptp.fun_Pr2906233850362575543t_bool) (X tptp.option3562590408128118217it_nat)) (=> (tptp.pp (tptp.aa_opt753342655352099408t_bool (tptp.case_o4708843222389689029it_nat P Q) X)) (=> (=> (= X tptp.none_P2651198173097904984it_nat) (not (tptp.pp P))) (not (forall ((Y3 tptp.produc3260487557148687353it_nat)) (=> (= X (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat Y3)) (not (tptp.pp (tptp.aa_Pro8278066377857552544t_bool Q Y3))))))))) (forall ((P tptp.bool) (Q tptp.fun_num_bool) (X tptp.option_num)) (=> (tptp.pp (tptp.aa_option_num_bool (tptp.case_option_bool_num P Q) X)) (=> (=> (= X tptp.none_num) (not (tptp.pp P))) (not (forall ((Y3 tptp.num)) (=> (= X (tptp.aa_num_option_num tptp.some_num Y3)) (not (tptp.pp (tptp.aa_num_bool Q Y3))))))))) (forall ((P tptp.bool) (Q tptp.fun_Pr7669129556548838760t_bool) (X tptp.option8956607266484857688it_nat)) (=> (tptp.pp (tptp.aa_opt8953672862898910593t_bool (tptp.case_o1497613849220869332it_nat P Q) X)) (=> (=> (= X tptp.none_P9117596204409417319it_nat) (not (tptp.pp P))) (not (forall ((Y3 tptp.produc8664842809031399944it_nat)) (=> (= X (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat Y3)) (not (tptp.pp (tptp.aa_Pro8715207439678120785t_bool Q Y3))))))))) (forall ((M tptp.fun_nat_option_nat)) (= (= (tptp.map_to_set_nat_nat M) tptp.bot_bo2099793752762293965at_nat) (forall ((X4 tptp.nat)) (= (tptp.aa_nat_option_nat M X4) tptp.none_nat)))) (forall ((M tptp.fun_nat_option_nat)) (= (= tptp.bot_bo2099793752762293965at_nat (tptp.map_to_set_nat_nat M)) (forall ((X4 tptp.nat)) (= (tptp.aa_nat_option_nat M X4) tptp.none_nat)))) (forall ((X tptp.option_set_int) (Y tptp.option_set_int)) (= (tptp.ord_le353528952715127954et_int X Y) (tptp.case_o8226980026459171502et_int tptp.fTrue (tptp.aTP_Lamm_eu Y) X))) (forall ((X tptp.option_rat) (Y tptp.option_rat)) (= (tptp.ord_le2406147912482264968on_rat X Y) (tptp.case_option_bool_rat tptp.fTrue (tptp.aTP_Lamm_ev Y) X))) (forall ((X tptp.option_num) (Y tptp.option_num)) (= (tptp.pp (tptp.aa_option_num_bool (tptp.aa_opt4409681509335781342m_bool tptp.ord_le6622620407824499402on_num X) Y)) (tptp.pp (tptp.aa_option_num_bool (tptp.case_option_bool_num tptp.fTrue (tptp.aTP_Lamm_ew Y)) X)))) (forall ((X tptp.option_nat) (Y tptp.option_nat)) (= (tptp.ord_le5914376470875661696on_nat X Y) (tptp.case_option_bool_nat tptp.fTrue (tptp.aTP_Lamm_ex Y) X))) (forall ((X tptp.option_int) (Y tptp.option_int)) (= (tptp.ord_le1736525451366464988on_int X Y) (tptp.case_option_bool_int tptp.fTrue (tptp.aTP_Lamm_ey Y) X))) (forall ((X tptp.option_assn) (Y tptp.option_assn)) (= (tptp.ord_less_option_assn X Y) (tptp.case_o1042097560232087540l_assn tptp.fFalse (tptp.aTP_Lamm_ez X) Y))) (forall ((X tptp.option_rat) (Y tptp.option_rat)) (= (tptp.ord_less_option_rat X Y) (tptp.case_option_bool_rat tptp.fFalse (tptp.aTP_Lamm_fa X) Y))) (forall ((X tptp.option_num) (Y tptp.option_num)) (= (tptp.pp (tptp.aa_option_num_bool (tptp.aa_opt4409681509335781342m_bool tptp.ord_less_option_num X) Y)) (tptp.pp (tptp.aa_option_num_bool (tptp.case_option_bool_num tptp.fFalse (tptp.aTP_Lamm_fc X)) Y)))) (forall ((X tptp.option_nat) (Y tptp.option_nat)) (= (tptp.ord_less_option_nat X Y) (tptp.case_option_bool_nat tptp.fFalse (tptp.aTP_Lamm_fd X) Y))) (forall ((X tptp.option_int) (Y tptp.option_int)) (= (tptp.ord_less_option_int X Y) (tptp.case_option_bool_int tptp.fFalse (tptp.aTP_Lamm_fe X) Y))) (forall ((F tptp.heap_T5738788834812785303t_unit) (H tptp.heap_e7401611519738050253t_unit)) (=> (forall ((X3 tptp.product_unit) (H5 tptp.produc6653097349344004940it_nat)) (not (= (tptp.aa_hea684056619475940329it_nat (tptp.heap_T875086893843062177t_unit F) H) (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat (tptp.produc7133225469290080770it_nat X3 H5))))) (= (tptp.aa_hea684056619475940329it_nat (tptp.heap_T875086893843062177t_unit F) H) tptp.none_P9117596204409417319it_nat))) (forall ((F tptp.heap_Time_Heap_a) (H tptp.heap_e7401611519738050253t_unit)) (=> (forall ((X3 tptp.a) (H5 tptp.produc6653097349344004940it_nat)) (not (= (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a F) H) (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat X3) H5))))) (= (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a F) H) tptp.none_P2651198173097904984it_nat))) (forall ((X tptp.produc4453839368661128058it_nat)) (=> (forall ((N5 tptp.nat) (R2 tptp.a) (H4 tptp.heap_e7401611519738050253t_unit) (N4 tptp.nat)) (not (= X (tptp.produc4111269673004989362it_nat N5 (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat R2) (tptp.produc584006145561248582it_nat H4 N4))))))) (not (forall ((N5 tptp.nat)) (not (= X (tptp.produc4111269673004989362it_nat N5 tptp.none_P2651198173097904984it_nat))))))) (forall ((X tptp.produc3911288613690379145it_nat)) (=> (forall ((N5 tptp.nat) (R2 tptp.product_unit) (H4 tptp.heap_e7401611519738050253t_unit) (N4 tptp.nat)) (not (= X (tptp.produc638857205735767105it_nat N5 (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat (tptp.produc7133225469290080770it_nat R2 (tptp.produc584006145561248582it_nat H4 N4))))))) (not (forall ((N5 tptp.nat)) (not (= X (tptp.produc638857205735767105it_nat N5 tptp.none_P9117596204409417319it_nat))))))) (forall ((S tptp.set_Pr1261947904930325089at_nat)) (= (forall ((X4 tptp.nat)) (= (tptp.aa_nat_option_nat (tptp.set_to_map_nat_nat S) X4) tptp.none_nat)) (= S tptp.bot_bo2099793752762293965at_nat))) (forall ((X tptp.bool) (Xa2 tptp.produc3658429121746597890et_nat)) (=> (not (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.pure_a825153325127701367it_nat X) Xa2))) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (=> (= Xa2 (tptp.produc7507926704131184380et_nat H4 As4)) (and (= As4 tptp.bot_bot_set_nat) (tptp.pp X))))))) (forall ((X tptp.bool) (Xa2 tptp.produc3658429121746597890et_nat)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.pure_a825153325127701367it_nat X) Xa2)) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (=> (= Xa2 (tptp.produc7507926704131184380et_nat H4 As4)) (not (and (= As4 tptp.bot_bot_set_nat) (tptp.pp X)))))))) (forall ((X tptp.bool) (Xa2 tptp.produc3658429121746597890et_nat) (Y tptp.bool)) (=> (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.pure_a825153325127701367it_nat X) Xa2)) (tptp.pp Y)) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (=> (= Xa2 (tptp.produc7507926704131184380et_nat H4 As4)) (= (tptp.pp Y) (not (and (= As4 tptp.bot_bot_set_nat) (tptp.pp X))))))))) (forall ((B tptp.bool) (H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.pure_a825153325127701367it_nat B) (tptp.produc7507926704131184380et_nat H As))) (and (= As tptp.bot_bot_set_nat) (tptp.pp B)))) (forall ((X tptp.bool) (Xa2 tptp.produc3658429121746597890et_nat) (Y tptp.bool)) (=> (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.pure_a825153325127701367it_nat X) Xa2)) (tptp.pp Y)) (=> (tptp.accp_P709504461982814079et_nat tptp.pure_a6022498039421069578it_nat (tptp.produc7559599926491750594et_nat X Xa2)) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (tptp.produc7507926704131184380et_nat H4 As4))) (=> (= Xa2 _let_1) (=> (= (tptp.pp Y) (and (= As4 tptp.bot_bot_set_nat) (tptp.pp X))) (not (tptp.accp_P709504461982814079et_nat tptp.pure_a6022498039421069578it_nat (tptp.produc7559599926491750594et_nat X _let_1))))))))))) (forall ((X tptp.bool) (Xa2 tptp.produc3658429121746597890et_nat)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.pure_a825153325127701367it_nat X) Xa2)) (=> (tptp.accp_P709504461982814079et_nat tptp.pure_a6022498039421069578it_nat (tptp.produc7559599926491750594et_nat X Xa2)) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (tptp.produc7507926704131184380et_nat H4 As4))) (=> (= Xa2 _let_1) (=> (tptp.accp_P709504461982814079et_nat tptp.pure_a6022498039421069578it_nat (tptp.produc7559599926491750594et_nat X _let_1)) (not (and (= As4 tptp.bot_bot_set_nat) (tptp.pp X))))))))))) (forall ((X tptp.bool) (Xa2 tptp.produc3658429121746597890et_nat)) (=> (not (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.pure_a825153325127701367it_nat X) Xa2))) (=> (tptp.accp_P709504461982814079et_nat tptp.pure_a6022498039421069578it_nat (tptp.produc7559599926491750594et_nat X Xa2)) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (tptp.produc7507926704131184380et_nat H4 As4))) (=> (= Xa2 _let_1) (=> (tptp.accp_P709504461982814079et_nat tptp.pure_a6022498039421069578it_nat (tptp.produc7559599926491750594et_nat X _let_1)) (and (= As4 tptp.bot_bot_set_nat) (tptp.pp X)))))))))) (forall ((F tptp.heap_T5738788834812785303t_unit) (H tptp.heap_e7401611519738050253t_unit) (X tptp.product_unit) (H3 tptp.heap_e7401611519738050253t_unit) (N2 tptp.nat) (G tptp.fun_Pr5215307506330550056Heap_a)) (=> (= (tptp.aa_hea684056619475940329it_nat (tptp.heap_T875086893843062177t_unit F) H) (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat (tptp.produc7133225469290080770it_nat X (tptp.produc584006145561248582it_nat H3 N2)))) (= (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a (tptp.heap_T757603679106148408unit_a F G)) H) (tptp.heap_T7616092557645711335rame_a N2 (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a (tptp.aa_Pro7886978635576167513Heap_a G X)) H3))))) (forall ((F tptp.heap_Time_Heap_a) (H tptp.heap_e7401611519738050253t_unit) (X tptp.a) (H3 tptp.heap_e7401611519738050253t_unit) (N2 tptp.nat) (G tptp.fun_a_6093291656547882009Heap_a)) (=> (= (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a F) H) (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat X) (tptp.produc584006145561248582it_nat H3 N2)))) (= (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a (tptp.heap_Time_bind_a_a F G)) H) (tptp.heap_T7616092557645711335rame_a N2 (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a (tptp.aa_a_H8829438773920479562Heap_a G X)) H3))))) (forall ((F tptp.heap_T5738788834812785303t_unit) (H tptp.heap_e7401611519738050253t_unit) (X tptp.product_unit) (H3 tptp.heap_e7401611519738050253t_unit) (N2 tptp.nat) (G tptp.fun_Pr292408699144966967t_unit) (Y tptp.product_unit) (H9 tptp.heap_e7401611519738050253t_unit) (N6 tptp.nat)) (=> (= (tptp.aa_hea684056619475940329it_nat (tptp.heap_T875086893843062177t_unit F) H) (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat (tptp.produc7133225469290080770it_nat X (tptp.produc584006145561248582it_nat H3 N2)))) (=> (= (tptp.aa_hea684056619475940329it_nat (tptp.heap_T875086893843062177t_unit (tptp.aa_Pro1108561329362217960t_unit G X)) H3) (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat (tptp.produc7133225469290080770it_nat Y (tptp.produc584006145561248582it_nat H9 N6)))) (= (tptp.aa_hea684056619475940329it_nat (tptp.heap_T875086893843062177t_unit (tptp.heap_T2633723481742716231t_unit F G)) H) (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat (tptp.produc7133225469290080770it_nat Y (tptp.produc584006145561248582it_nat H9 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) N6)))))))) (forall ((F tptp.heap_T5738788834812785303t_unit) (H tptp.heap_e7401611519738050253t_unit) (X tptp.product_unit) (H3 tptp.heap_e7401611519738050253t_unit) (N2 tptp.nat) (G tptp.fun_Pr5215307506330550056Heap_a) (Y tptp.a) (H9 tptp.heap_e7401611519738050253t_unit) (N6 tptp.nat)) (let ((_let_1 (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat Y))) (=> (= (tptp.aa_hea684056619475940329it_nat (tptp.heap_T875086893843062177t_unit F) H) (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat (tptp.produc7133225469290080770it_nat X (tptp.produc584006145561248582it_nat H3 N2)))) (=> (= (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a (tptp.aa_Pro7886978635576167513Heap_a G X)) H3) (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat (tptp.aa_Pro8078911840264235907it_nat _let_1 (tptp.produc584006145561248582it_nat H9 N6)))) (= (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a (tptp.heap_T757603679106148408unit_a F G)) H) (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat (tptp.aa_Pro8078911840264235907it_nat _let_1 (tptp.produc584006145561248582it_nat H9 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) N6))))))))) (forall ((F tptp.heap_Time_Heap_a) (H tptp.heap_e7401611519738050253t_unit) (X tptp.a) (H3 tptp.heap_e7401611519738050253t_unit) (N2 tptp.nat) (G tptp.fun_a_2990225006182978344t_unit) (Y tptp.product_unit) (H9 tptp.heap_e7401611519738050253t_unit) (N6 tptp.nat)) (=> (= (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a F) H) (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat X) (tptp.produc584006145561248582it_nat H3 N2)))) (=> (= (tptp.aa_hea684056619475940329it_nat (tptp.heap_T875086893843062177t_unit (tptp.aa_a_H4862568901524997081t_unit G X)) H3) (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat (tptp.produc7133225469290080770it_nat Y (tptp.produc584006145561248582it_nat H9 N6)))) (= (tptp.aa_hea684056619475940329it_nat (tptp.heap_T875086893843062177t_unit (tptp.heap_T8685611227969916822t_unit F G)) H) (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat (tptp.produc7133225469290080770it_nat Y (tptp.produc584006145561248582it_nat H9 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) N6)))))))) (forall ((F tptp.heap_Time_Heap_a) (H tptp.heap_e7401611519738050253t_unit) (X tptp.a) (H3 tptp.heap_e7401611519738050253t_unit) (N2 tptp.nat) (G tptp.fun_a_6093291656547882009Heap_a) (Y tptp.a) (H9 tptp.heap_e7401611519738050253t_unit) (N6 tptp.nat)) (let ((_let_1 (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat Y))) (=> (= (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a F) H) (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat X) (tptp.produc584006145561248582it_nat H3 N2)))) (=> (= (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a (tptp.aa_a_H8829438773920479562Heap_a G X)) H3) (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat (tptp.aa_Pro8078911840264235907it_nat _let_1 (tptp.produc584006145561248582it_nat H9 N6)))) (= (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a (tptp.heap_Time_bind_a_a F G)) H) (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat (tptp.aa_Pro8078911840264235907it_nat _let_1 (tptp.produc584006145561248582it_nat H9 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) N6))))))))) (forall ((S tptp.set_Pr1261947904930325089at_nat) (K tptp.nat)) (= (tptp.aa_nat_option_nat (tptp.set_to_map_nat_nat S) K) (tptp.eps_Opt_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_as S) K)))) (forall ((S tptp.set_Pr1106803562331729365et_nat) (K tptp.fun_Pr6001797050664311790t_bool)) (= (tptp.aa_fun3443883199727375236et_nat (tptp.set_to2413977260772829625et_nat S) K) (tptp.aa_fun3443883199727375236et_nat tptp.eps_Op2013419657081471078et_nat (tptp.aa_fun6808777976510360636t_bool (tptp.aTP_Lamm_at S) K)))) (forall ((S tptp.set_Pr9222568342844664434et_nat) (K tptp.fun_Pr6001797050664311790t_bool)) (= (tptp.aa_fun5342968722616283297et_nat (tptp.set_to5446503370794493270et_nat S) K) (tptp.eps_Op7150027340430904579et_nat (tptp.aa_fun1003322038264691679t_bool (tptp.aTP_Lamm_au S) K)))) (forall ((S tptp.set_Pr233528076387193594nt_int) (K tptp.fun_Pr9164807099015279978e_term)) (= (tptp.aa_fun2000036126570120791nt_int (tptp.set_to3174691005185795862nt_int S) K) (tptp.eps_Op2446201859369042517nt_int (tptp.aa_fun5300525129335604105t_bool (tptp.aTP_Lamm_av S) K)))) (forall ((S tptp.set_Pr5033440245338114598nt_int) (K tptp.fun_in6429348457993719614e_term)) (= (tptp.aa_fun4554338130361792899nt_int (tptp.set_to3419737211476968514nt_int S) K) (tptp.eps_Op2446201859369042517nt_int (tptp.aa_fun4446166836006121821t_bool (tptp.aTP_Lamm_aw S) K)))) (forall ((S tptp.set_Pr7098220151150636591it_nat) (K tptp.a)) (= (tptp.aa_a_o5231022909227610846it_nat (tptp.set_to2008915276733485075it_nat S) K) (tptp.eps_Op8301357815426737072it_nat (tptp.aa_a_f736957945511644770t_bool (tptp.aTP_Lamm_ax S) K)))) (forall ((P tptp.fun_he6201055237484778573t_bool) (H tptp.heap_e7401611519738050253t_unit) (F tptp.fun_he4944555133437423336it_nat)) (=> (tptp.pp (tptp.aa_hea1793595068369496646t_bool P H)) (= (tptp.aa_hea684056619475940329it_nat (tptp.heap_T875086893843062177t_unit (tptp.heap_T8440541562793052209t_unit P F)) H) (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat (tptp.aa_hea256619718444519449it_nat F H))))) (forall ((P tptp.fun_he6201055237484778573t_bool) (H tptp.heap_e7401611519738050253t_unit) (F tptp.fun_he8889679731534893401it_nat)) (=> (tptp.pp (tptp.aa_hea1793595068369496646t_bool P H)) (= (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a (tptp.heap_Time_guard_a P F)) H) (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat (tptp.aa_hea5645563107516622602it_nat F H))))) (forall ((F tptp.fun_nat_nat) (X tptp.nat) (Y tptp.nat) (R tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat X) Y)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat F X)) (tptp.aa_nat_nat F Y))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 R)) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.mlex_prod_nat F R))))))) (forall ((F tptp.fun_Pr3073222722562426257t_bool) (A tptp.fun_Pr6001797050664311790t_bool) (B tptp.produc3658429121746597890et_nat)) (=> (tptp.pp (tptp.aa_Pro7454463142485379962t_bool F (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat A) B))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.aa_fun6808777976510360636t_bool (tptp.produc2846001210079453936t_bool F) A) B)))) (forall ((F tptp.fun_Pr229822445725053876t_bool) (A tptp.fun_Pr6001797050664311790t_bool) (B tptp.produc6108883039684432031et_nat)) (=> (tptp.pp (tptp.aa_Pro6092667153363046813t_bool F (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat A) B))) (tptp.pp (tptp.aa_Pro7454463142485379962t_bool (tptp.aa_fun1003322038264691679t_bool (tptp.produc3943886704551727507t_bool F) A) B)))) (forall ((F tptp.fun_Pr6019674992625747500t_bool) (A tptp.fun_Pr9164807099015279978e_term) (B tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro5031108791230793749t_bool F (tptp.aa_Pro3513184699142849729nt_int (tptp.aa_fun1388719692539776744nt_int tptp.produc1560874099174258678nt_int A) B))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun5300525129335604105t_bool (tptp.produc7693670431277826643t_bool F) A) B)))) (forall ((F tptp.fun_Pr5504123824928244736t_bool) (A tptp.fun_in6429348457993719614e_term) (B tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro7591400126937138665t_bool F (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int A) B))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun4446166836006121821t_bool (tptp.produc6897183239252912167t_bool F) A) B)))) (forall ((F tptp.fun_Pr2906233850362575543t_bool) (A tptp.a) (B tptp.produc6653097349344004940it_nat)) (=> (tptp.pp (tptp.aa_Pro8278066377857552544t_bool F (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat A) B))) (tptp.pp (tptp.aa_Pro3182513528956304653t_bool (tptp.aa_a_f736957945511644770t_bool (tptp.produc3493786077380676886t_bool F) A) B)))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2))))) (forall ((X tptp.produc3260487557148687353it_nat)) (= (tptp.eps_Op1741419982095519837it_nat (tptp.fequal7405809337025681252it_nat X)) (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat X))) (forall ((X tptp.num)) (= (tptp.eps_Opt_num (tptp.aa_num_fun_num_bool tptp.fequal_num X)) (tptp.aa_num_option_num tptp.some_num X))) (forall ((X tptp.produc8664842809031399944it_nat)) (= (tptp.eps_Op3393321821070424684it_nat (tptp.fequal1407654770548522611it_nat X)) (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat X))) (forall ((X tptp.produc3260487557148687353it_nat)) (= (tptp.eps_Op1741419982095519837it_nat (tptp.aTP_Lamm_ff X)) (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat X))) (forall ((X tptp.num)) (= (tptp.eps_Opt_num (tptp.aa_num_fun_num_bool tptp.aTP_Lamm_fg X)) (tptp.aa_num_option_num tptp.some_num X))) (forall ((X tptp.produc8664842809031399944it_nat)) (= (tptp.eps_Op3393321821070424684it_nat (tptp.aTP_Lamm_fh X)) (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat X))) (= (tptp.eps_Opt_num tptp.aTP_Lamm_et) tptp.none_num) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) J)) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) K)))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) J)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K) L)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L)))))) (forall ((I2 tptp.nat) (J tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) J)) I2)))) (forall ((J tptp.nat) (I2 tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) I2)) I2)))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) J)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) K))))) (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 J)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) M)))))) (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 J)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) J)))))) (forall ((K tptp.nat) (L tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K) L)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) L) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2))))) (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K)) N2)) (not (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2))))))) (forall ((N2 tptp.nat) (M tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) M)))) (forall ((N2 tptp.nat) (M tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2)))) (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K)) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K)) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)))) (forall ((K tptp.nat) (L tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) L)) (exists ((N5 tptp.nat)) (= L (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) N5))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) J)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) L)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L)))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) J)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) K))))) (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 J)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) M)))))) (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 J)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) J)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (exists ((K3 tptp.nat)) (= N2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K3))))) (forall ((F tptp.fun_Pr3073222722562426257t_bool) (A tptp.fun_Pr6001797050664311790t_bool) (B tptp.produc3658429121746597890et_nat)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.aa_fun6808777976510360636t_bool (tptp.produc2846001210079453936t_bool F) A) B)) (tptp.pp (tptp.aa_Pro7454463142485379962t_bool F (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat A) B))))) (forall ((F tptp.fun_Pr229822445725053876t_bool) (A tptp.fun_Pr6001797050664311790t_bool) (B tptp.produc6108883039684432031et_nat)) (=> (tptp.pp (tptp.aa_Pro7454463142485379962t_bool (tptp.aa_fun1003322038264691679t_bool (tptp.produc3943886704551727507t_bool F) A) B)) (tptp.pp (tptp.aa_Pro6092667153363046813t_bool F (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat A) B))))) (forall ((F tptp.fun_Pr6019674992625747500t_bool) (A tptp.fun_Pr9164807099015279978e_term) (B tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun5300525129335604105t_bool (tptp.produc7693670431277826643t_bool F) A) B)) (tptp.pp (tptp.aa_Pro5031108791230793749t_bool F (tptp.aa_Pro3513184699142849729nt_int (tptp.aa_fun1388719692539776744nt_int tptp.produc1560874099174258678nt_int A) B))))) (forall ((F tptp.fun_Pr5504123824928244736t_bool) (A tptp.fun_in6429348457993719614e_term) (B tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun4446166836006121821t_bool (tptp.produc6897183239252912167t_bool F) A) B)) (tptp.pp (tptp.aa_Pro7591400126937138665t_bool F (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int A) B))))) (forall ((F tptp.fun_Pr2906233850362575543t_bool) (A tptp.a) (B tptp.produc6653097349344004940it_nat)) (=> (tptp.pp (tptp.aa_Pro3182513528956304653t_bool (tptp.aa_a_f736957945511644770t_bool (tptp.produc3493786077380676886t_bool F) A) B)) (tptp.pp (tptp.aa_Pro8278066377857552544t_bool F (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat A) B))))) (forall ((F tptp.fun_Pr3073222722562426257t_bool) (A tptp.fun_Pr6001797050664311790t_bool) (B tptp.produc3658429121746597890et_nat)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.aa_fun6808777976510360636t_bool (tptp.produc2846001210079453936t_bool F) A) B)) (tptp.pp (tptp.aa_Pro7454463142485379962t_bool F (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat A) B))))) (forall ((F tptp.fun_Pr229822445725053876t_bool) (A tptp.fun_Pr6001797050664311790t_bool) (B tptp.produc6108883039684432031et_nat)) (=> (tptp.pp (tptp.aa_Pro7454463142485379962t_bool (tptp.aa_fun1003322038264691679t_bool (tptp.produc3943886704551727507t_bool F) A) B)) (tptp.pp (tptp.aa_Pro6092667153363046813t_bool F (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat A) B))))) (forall ((F tptp.fun_Pr6019674992625747500t_bool) (A tptp.fun_Pr9164807099015279978e_term) (B tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun5300525129335604105t_bool (tptp.produc7693670431277826643t_bool F) A) B)) (tptp.pp (tptp.aa_Pro5031108791230793749t_bool F (tptp.aa_Pro3513184699142849729nt_int (tptp.aa_fun1388719692539776744nt_int tptp.produc1560874099174258678nt_int A) B))))) (forall ((F tptp.fun_Pr5504123824928244736t_bool) (A tptp.fun_in6429348457993719614e_term) (B tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun4446166836006121821t_bool (tptp.produc6897183239252912167t_bool F) A) B)) (tptp.pp (tptp.aa_Pro7591400126937138665t_bool F (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int A) B))))) (forall ((F tptp.fun_Pr2906233850362575543t_bool) (A tptp.a) (B tptp.produc6653097349344004940it_nat)) (=> (tptp.pp (tptp.aa_Pro3182513528956304653t_bool (tptp.aa_a_f736957945511644770t_bool (tptp.produc3493786077380676886t_bool F) A) B)) (tptp.pp (tptp.aa_Pro8278066377857552544t_bool F (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat A) B))))) (forall ((N2 tptp.nat) (R3 tptp.a) (H tptp.heap_e7401611519738050253t_unit) (N6 tptp.nat)) (let ((_let_1 (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat R3))) (= (tptp.heap_T7616092557645711335rame_a N2 (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat (tptp.aa_Pro8078911840264235907it_nat _let_1 (tptp.produc584006145561248582it_nat H N6)))) (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat (tptp.aa_Pro8078911840264235907it_nat _let_1 (tptp.produc584006145561248582it_nat H (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) N6))))))) (forall ((N2 tptp.nat) (R3 tptp.product_unit) (H tptp.heap_e7401611519738050253t_unit) (N6 tptp.nat)) (= (tptp.heap_T3616969660504097270t_unit N2 (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat (tptp.produc7133225469290080770it_nat R3 (tptp.produc584006145561248582it_nat H N6)))) (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat (tptp.produc7133225469290080770it_nat R3 (tptp.produc584006145561248582it_nat H (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) N6)))))) (forall ((X tptp.nat) (Xa2 tptp.option3562590408128118217it_nat) (Y tptp.option3562590408128118217it_nat)) (=> (= (tptp.heap_T7616092557645711335rame_a X Xa2) Y) (=> (forall ((R2 tptp.a) (H4 tptp.heap_e7401611519738050253t_unit) (N4 tptp.nat)) (let ((_let_1 (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat R2))) (=> (= Xa2 (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat (tptp.aa_Pro8078911840264235907it_nat _let_1 (tptp.produc584006145561248582it_nat H4 N4)))) (not (= Y (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat (tptp.aa_Pro8078911840264235907it_nat _let_1 (tptp.produc584006145561248582it_nat H4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) N4))))))))) (not (=> (= Xa2 tptp.none_P2651198173097904984it_nat) (not (= Y tptp.none_P2651198173097904984it_nat))))))) (forall ((X tptp.nat) (Xa2 tptp.option8956607266484857688it_nat) (Y tptp.option8956607266484857688it_nat)) (=> (= (tptp.heap_T3616969660504097270t_unit X Xa2) Y) (=> (forall ((R2 tptp.product_unit) (H4 tptp.heap_e7401611519738050253t_unit) (N4 tptp.nat)) (=> (= Xa2 (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat (tptp.produc7133225469290080770it_nat R2 (tptp.produc584006145561248582it_nat H4 N4)))) (not (= Y (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat (tptp.produc7133225469290080770it_nat R2 (tptp.produc584006145561248582it_nat H4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) N4)))))))) (not (=> (= Xa2 tptp.none_P9117596204409417319it_nat) (not (= Y tptp.none_P9117596204409417319it_nat))))))) (forall ((F tptp.fun_nat_nat) (M tptp.nat) (K tptp.nat)) (=> (forall ((M5 tptp.nat) (N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M5) N5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat F M5)) (tptp.aa_nat_nat F N5))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat F M)) K)) (tptp.aa_nat_nat F (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K)))))) (forall ((P tptp.fun_Pr2906233850362575543t_bool) (X tptp.produc3260487557148687353it_nat)) (=> (forall ((X7 tptp.produc3260487557148687353it_nat)) (=> (tptp.pp (tptp.aa_Pro8278066377857552544t_bool P X)) (=> (tptp.pp (tptp.aa_Pro8278066377857552544t_bool P X7)) (= X7 X)))) (= (= (tptp.eps_Op1741419982095519837it_nat P) (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat X)) (tptp.pp (tptp.aa_Pro8278066377857552544t_bool P X))))) (forall ((P tptp.fun_num_bool) (X tptp.num)) (=> (forall ((X7 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool P X)) (=> (tptp.pp (tptp.aa_num_bool P X7)) (= X7 X)))) (= (= (tptp.eps_Opt_num P) (tptp.aa_num_option_num tptp.some_num X)) (tptp.pp (tptp.aa_num_bool P X))))) (forall ((P tptp.fun_Pr7669129556548838760t_bool) (X tptp.produc8664842809031399944it_nat)) (=> (forall ((X7 tptp.produc8664842809031399944it_nat)) (=> (tptp.pp (tptp.aa_Pro8715207439678120785t_bool P X)) (=> (tptp.pp (tptp.aa_Pro8715207439678120785t_bool P X7)) (= X7 X)))) (= (= (tptp.eps_Op3393321821070424684it_nat P) (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat X)) (tptp.pp (tptp.aa_Pro8715207439678120785t_bool P X))))) (forall ((P tptp.fun_Pr2906233850362575543t_bool) (X tptp.produc3260487557148687353it_nat)) (=> (= (tptp.eps_Op1741419982095519837it_nat P) (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat X)) (tptp.pp (tptp.aa_Pro8278066377857552544t_bool P X)))) (forall ((P tptp.fun_num_bool) (X tptp.num)) (=> (= (tptp.eps_Opt_num P) (tptp.aa_num_option_num tptp.some_num X)) (tptp.pp (tptp.aa_num_bool P X)))) (forall ((P tptp.fun_Pr7669129556548838760t_bool) (X tptp.produc8664842809031399944it_nat)) (=> (= (tptp.eps_Op3393321821070424684it_nat P) (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat X)) (tptp.pp (tptp.aa_Pro8715207439678120785t_bool P X)))) (forall ((P tptp.fun_he6201055237484778573t_bool) (H tptp.heap_e7401611519738050253t_unit) (F tptp.fun_he8889679731534893401it_nat)) (=> (not (tptp.pp (tptp.aa_hea1793595068369496646t_bool P H))) (= (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a (tptp.heap_Time_guard_a P F)) H) tptp.none_P2651198173097904984it_nat))) (forall ((F tptp.fun_nat_nat) (X tptp.nat) (Y tptp.nat) (R tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat F X)) (tptp.aa_nat_nat F Y))) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat X) Y)) (tptp.mlex_prod_nat F R))))) (forall ((X tptp.nat) (Y tptp.nat) (F tptp.fun_nat_nat) (R tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat X) Y)))) (let ((_let_2 (tptp.aa_nat_nat F Y))) (let ((_let_3 (tptp.aa_nat_nat F X))) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.mlex_prod_nat F R))) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) _let_2)) (and (= _let_3 _let_2) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 R))))))))) (forall ((X tptp.nat) (Xa2 tptp.option3562590408128118217it_nat) (Y tptp.option3562590408128118217it_nat)) (=> (= (tptp.heap_T7616092557645711335rame_a X Xa2) Y) (=> (tptp.accp_P6263092265436569219it_nat tptp.heap_T8132184524487034138_rel_a (tptp.produc4111269673004989362it_nat X Xa2)) (=> (forall ((R2 tptp.a) (H4 tptp.heap_e7401611519738050253t_unit) (N4 tptp.nat)) (let ((_let_1 (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat R2))) (let ((_let_2 (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat (tptp.aa_Pro8078911840264235907it_nat _let_1 (tptp.produc584006145561248582it_nat H4 N4))))) (=> (= Xa2 _let_2) (=> (= Y (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat (tptp.aa_Pro8078911840264235907it_nat _let_1 (tptp.produc584006145561248582it_nat H4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) N4))))) (not (tptp.accp_P6263092265436569219it_nat tptp.heap_T8132184524487034138_rel_a (tptp.produc4111269673004989362it_nat X _let_2)))))))) (not (=> (= Xa2 tptp.none_P2651198173097904984it_nat) (=> (= Y tptp.none_P2651198173097904984it_nat) (not (tptp.accp_P6263092265436569219it_nat tptp.heap_T8132184524487034138_rel_a (tptp.produc4111269673004989362it_nat X tptp.none_P2651198173097904984it_nat)))))))))) (forall ((X tptp.nat) (Xa2 tptp.option8956607266484857688it_nat) (Y tptp.option8956607266484857688it_nat)) (=> (= (tptp.heap_T3616969660504097270t_unit X Xa2) Y) (=> (tptp.accp_P414730952086964626it_nat tptp.heap_T996182799752388649t_unit (tptp.produc638857205735767105it_nat X Xa2)) (=> (forall ((R2 tptp.product_unit) (H4 tptp.heap_e7401611519738050253t_unit) (N4 tptp.nat)) (let ((_let_1 (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat (tptp.produc7133225469290080770it_nat R2 (tptp.produc584006145561248582it_nat H4 N4))))) (=> (= Xa2 _let_1) (=> (= Y (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat (tptp.produc7133225469290080770it_nat R2 (tptp.produc584006145561248582it_nat H4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) N4))))) (not (tptp.accp_P414730952086964626it_nat tptp.heap_T996182799752388649t_unit (tptp.produc638857205735767105it_nat X _let_1))))))) (not (=> (= Xa2 tptp.none_P9117596204409417319it_nat) (=> (= Y tptp.none_P9117596204409417319it_nat) (not (tptp.accp_P414730952086964626it_nat tptp.heap_T996182799752388649t_unit (tptp.produc638857205735767105it_nat X tptp.none_P9117596204409417319it_nat)))))))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat C))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int C))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B))))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) C))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) C))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) C))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat C))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int C))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B))))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) C))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) C))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) C))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)))) (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat I2) J)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat K) L))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat I2) K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat J) L))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) J)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K) L))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L))))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I2) J)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) L))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I2) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) L))))) (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat I2) J)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat K) L))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat I2) K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat J) L))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) J)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) L))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L))))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int I2) J)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) L))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I2) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) L))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) D2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) D2)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C) D2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) D2)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) D2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) D2)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) D2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) D2)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) D2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) D2)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) D2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) D2)))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B))) (let ((_let_2 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A))) (= (and (not (= A B)) (not (= C D2))) (not (= (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger _let_2 C)) (tptp.aa_Cod1783974652533396728nteger _let_1 D2)) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger _let_2 D2)) (tptp.aa_Cod1783974652533396728nteger _let_1 C)))))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B))) (let ((_let_2 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A))) (= (and (not (= A B)) (not (= C D2))) (not (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat _let_2 C)) (tptp.aa_rat_rat _let_1 D2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat _let_2 D2)) (tptp.aa_rat_rat _let_1 C)))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (= (and (not (= A B)) (not (= C D2))) (not (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_2 C)) (tptp.aa_nat_nat _let_1 D2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_2 D2)) (tptp.aa_nat_nat _let_1 C)))))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int B))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (= (and (not (= A B)) (not (= C D2))) (not (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_2 C)) (tptp.aa_int_int _let_1 D2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_2 D2)) (tptp.aa_int_int _let_1 C)))))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) J)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 I2)) (tptp.aa_nat_nat _let_1 J)))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) J)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat I2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat J) K))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) J)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) L)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat I2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat J) L)))))) (forall ((M tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) M)))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat _let_1 M)))))) (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2)) K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) K)))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N2))))) (forall ((A tptp.nat) (A3 tptp.nat) (B tptp.nat) (N7 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) A3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) N7)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) N7)) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A3) N7)))))) (forall ((A tptp.nat) (A2 tptp.nat) (B tptp.nat) (N7 tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) A2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) N7)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2) N7)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) N7)) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A2) N7)) B2))))))) (forall ((A tptp.nat) (A2 tptp.nat) (B tptp.nat) (B2 tptp.nat) (N7 tptp.nat)) (=> (= A A2) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) N7)) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A2) N7)) B2)))))) (forall ((A tptp.nat) (A2 tptp.nat) (B tptp.nat) (B2 tptp.nat) (N7 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) A2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) N7)) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A2) N7)) B2)))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B)) C) (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C))))) (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn A))) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.aa_assn_assn _let_1 B)) C) (tptp.aa_assn_assn _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn B) C))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat _let_1 B)) C) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 B)) C) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int _let_1 B)) C) (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) A))) (forall ((A tptp.assn) (B tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn A) B) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn B) A))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) A))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) A))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) A))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B))) (let ((_let_2 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A))) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger _let_2 C)) (tptp.aa_Cod1783974652533396728nteger _let_2 (tptp.aa_Cod1783974652533396728nteger _let_1 C)))))) (forall ((B tptp.assn) (A tptp.assn) (C tptp.assn)) (let ((_let_1 (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn B))) (let ((_let_2 (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn A))) (= (tptp.aa_assn_assn _let_1 (tptp.aa_assn_assn _let_2 C)) (tptp.aa_assn_assn _let_2 (tptp.aa_assn_assn _let_1 C)))))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B))) (let ((_let_2 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat _let_2 C)) (tptp.aa_rat_rat _let_2 (tptp.aa_rat_rat _let_1 C)))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat _let_2 C)) (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat _let_1 C)))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int B))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int _let_2 C)) (tptp.aa_int_int _let_2 (tptp.aa_int_int _let_1 C)))))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) C))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) C))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) C))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B))))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (exists ((C4 tptp.nat)) (= B (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C4))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) C))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (not (forall ((C2 tptp.nat)) (not (= B (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C2))))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) D2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) D2)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) D2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) D2)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) D2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) D2)))))) (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat I2) J)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat K) L))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat I2) K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat J) L))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) J)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) L))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L))))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I2) J)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) L))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I2) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) L))))) (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I2 J) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat K) L))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat I2) K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat J) L))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I2 J) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) L))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L))))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I2 J) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) L))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I2) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) L))))) (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat I2) J)) (= K L)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat I2) K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat J) L))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) J)) (= K L)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L))))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I2) J)) (= K L)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I2) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) L))))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) C))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) C))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) C))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) C))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) D2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) D2)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C) D2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) D2)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) D2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) D2)))))) (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat I2) J)) (= K L)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat I2) K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat J) L))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) J)) (= K L)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L))))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int I2) J)) (= K L)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I2) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) L))))) (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I2 J) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat K) L))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat I2) K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat J) L))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I2 J) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K) L))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L))))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I2 J) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) L))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I2) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) L))))) (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat I2) J)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat K) L))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat I2) K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat J) L))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) J)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K) L))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L))))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int I2) J)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) L))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I2) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) L))))) (forall ((W2 tptp.code_integer) (Y tptp.code_integer) (X tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger X))) (let ((_let_2 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger W2))) (= (= (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger _let_2 Y)) (tptp.aa_Cod1783974652533396728nteger _let_1 Z)) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger _let_2 Z)) (tptp.aa_Cod1783974652533396728nteger _let_1 Y))) (or (= W2 X) (= Y Z)))))) (forall ((W2 tptp.rat) (Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X))) (let ((_let_2 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat W2))) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat _let_2 Y)) (tptp.aa_rat_rat _let_1 Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat _let_2 Z)) (tptp.aa_rat_rat _let_1 Y))) (or (= W2 X) (= Y Z)))))) (forall ((W2 tptp.nat) (Y tptp.nat) (X tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat X))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat W2))) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_2 Y)) (tptp.aa_nat_nat _let_1 Z)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_2 Z)) (tptp.aa_nat_nat _let_1 Y))) (or (= W2 X) (= Y Z)))))) (forall ((W2 tptp.int) (Y tptp.int) (X tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int X))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.times_times_int W2))) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_2 Y)) (tptp.aa_int_int _let_1 Z)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_2 Z)) (tptp.aa_int_int _let_1 Y))) (or (= W2 X) (= Y Z)))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) B)) C) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B)) C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C)))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A))) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger B) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B)) (tptp.aa_Cod1783974652533396728nteger _let_1 C))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat _let_1 B)) (tptp.aa_rat_rat _let_1 C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_1 B)) (tptp.aa_int_int _let_1 C))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) B)) C) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B)) C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C)))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A))) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger B) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B)) (tptp.aa_Cod1783974652533396728nteger _let_1 C))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat _let_1 B)) (tptp.aa_rat_rat _let_1 C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_1 B)) (tptp.aa_nat_nat _let_1 C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_1 B)) (tptp.aa_int_int _let_1 C))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) B)) C) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B)) C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C)))) (forall ((A tptp.code_integer) (E tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) E)) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) E)) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) B)) E)) C))) (forall ((A tptp.rat) (E tptp.rat) (B tptp.rat) (C tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) E)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) E)) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B)) E)) C))) (forall ((A tptp.nat) (E tptp.nat) (B tptp.nat) (C tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) E)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) E)) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)) E)) C))) (forall ((A tptp.int) (E tptp.int) (B tptp.int) (C tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) E)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) E)) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) E)) C))) (forall ((S2 tptp.list_char) (X5 tptp.heap_e7401611519738050253t_unit)) (= (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a (tptp.heap_Time_raise_a S2)) X5) tptp.none_P2651198173097904984it_nat)) (forall ((P tptp.fun_he6201055237484778573t_bool) (F tptp.fun_he8889679731534893401it_nat)) (= (tptp.heap_Time_guard_a P F) (tptp.heap_Time_Heap_a2 (tptp.aa_fun3370411987892275404it_nat (tptp.aTP_Lamm_fi P) F)))) (forall ((P tptp.fun_he6201055237484778573t_bool) (F tptp.fun_he4944555133437423336it_nat)) (= (tptp.heap_T8440541562793052209t_unit P F) (tptp.heap_T6183433275982383450t_unit (tptp.aa_fun2986507860694160780it_nat (tptp.aTP_Lamm_fj P) F)))) (forall ((P tptp.fun_a_bool) (X tptp.a) (H tptp.heap_e7401611519738050253t_unit)) (=> (not (tptp.pp (tptp.aa_a_bool P X))) (= (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a (tptp.aa_a_H8829438773920479562Heap_a (tptp.heap_Time_assert_a P) X)) H) tptp.none_P2651198173097904984it_nat))) (forall ((P tptp.assn) (Q tptp.assn) (B tptp.bool)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.entails P))) (= (tptp.pp (tptp.aa_assn_bool _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn Q) (tptp.aa_bool_assn tptp.pure_assn B)))) (and (forall ((H6 tptp.produc3658429121746597890et_nat)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn P) H6)) (tptp.pp B))) (tptp.pp (tptp.aa_assn_bool _let_1 Q)))))) (forall ((F tptp.heap_Time_Heap_a)) (= (tptp.heap_Time_Heap_a2 (tptp.heap_Time_execute_a F)) F)) (forall ((F tptp.heap_T5738788834812785303t_unit)) (= (tptp.heap_T6183433275982383450t_unit (tptp.heap_T875086893843062177t_unit F)) F)) (forall ((P tptp.assn) (B tptp.bool) (Q tptp.assn)) (= (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.entails (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn P) (tptp.aa_bool_assn tptp.pure_assn B))) Q)) (=> (tptp.pp B) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.entails P) Q))))) (forall ((P tptp.assn)) (= (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.entails P) tptp.bot_bot_assn)) (forall ((H6 tptp.produc3658429121746597890et_nat)) (not (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn P) H6)))))) (forall ((P tptp.assn) (Q tptp.assn) (R tptp.assn)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.entails P))) (=> (tptp.pp (tptp.aa_assn_bool _let_1 Q)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.entails Q) R)) (tptp.pp (tptp.aa_assn_bool _let_1 R)))))) (forall ((P tptp.assn)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.entails P) P))) (forall ((A3 tptp.assn) (B3 tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.entails A3) B3)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.entails B3) A3)) (= A3 B3)))) (forall ((S2 tptp.list_char)) (= (tptp.heap_T2927564422264180874t_unit S2) (tptp.heap_T6183433275982383450t_unit tptp.aTP_Lamm_fk))) (forall ((P tptp.assn) (Q tptp.assn)) (= (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.entails P) Q)) (forall ((H6 tptp.produc3658429121746597890et_nat)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn P) H6)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn Q) H6)))))) (forall ((P tptp.assn) (Q tptp.assn)) (=> (forall ((H4 tptp.produc3658429121746597890et_nat)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn P) H4)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn Q) H4)))) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.entails P) Q)))) (forall ((P tptp.assn) (Q tptp.assn) (H tptp.produc3658429121746597890et_nat)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.entails P) Q)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn P) H)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn Q) H))))) (forall ((P tptp.assn) (H tptp.produc3658429121746597890et_nat) (Q tptp.assn)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn P) H)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.entails P) Q)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn Q) H))))) (forall ((P tptp.assn) (P4 tptp.assn) (Q tptp.assn) (Q3 tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.entails P) P4)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.entails Q) Q3)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.entails (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn P) Q)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn P4) Q3)))))) (forall ((A3 tptp.assn) (C3 tptp.assn) (B3 tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.entails A3) C3)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.entails B3) C3)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.entails (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn A3) B3)) C3))))) (forall ((P tptp.assn) (Q tptp.assn) (R tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.entails (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn P) Q)) R)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.entails P) R)))) (forall ((P tptp.assn) (Q tptp.assn) (R tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.entails (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn P) Q)) R)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.entails Q) R)))) (forall ((A3 tptp.assn) (B3 tptp.assn) (C3 tptp.assn)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.entails A3))) (=> (tptp.pp (tptp.aa_assn_bool _let_1 B3)) (tptp.pp (tptp.aa_assn_bool _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn B3) C3)))))) (forall ((A3 tptp.assn) (C3 tptp.assn) (B3 tptp.assn)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.entails A3))) (=> (tptp.pp (tptp.aa_assn_bool _let_1 C3)) (tptp.pp (tptp.aa_assn_bool _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn B3) C3)))))) (forall ((A3 tptp.assn) (B3 tptp.assn)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.entails A3) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn A3) B3)))) (forall ((B3 tptp.assn) (A3 tptp.assn)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.entails B3) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn A3) B3)))) (forall ((F tptp.fun_he1921015881043195817it_nat)) (= (tptp.heap_Time_execute_a (tptp.heap_Time_Heap_a2 F)) F)) (forall ((F tptp.fun_he5234484606919320760it_nat)) (= (tptp.heap_T875086893843062177t_unit (tptp.heap_T6183433275982383450t_unit F)) F)) (forall ((P tptp.assn)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.entails tptp.bot_bot_assn) P))) (forall ((A3 tptp.assn) (B3 tptp.assn) (C3 tptp.assn)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.entails A3))) (=> (tptp.pp (tptp.aa_assn_bool _let_1 B3)) (=> (tptp.pp (tptp.aa_assn_bool _let_1 C3)) (tptp.pp (tptp.aa_assn_bool _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn B3) C3))))))) (forall ((A3 tptp.assn) (C3 tptp.assn) (B3 tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.entails A3) C3)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.entails (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A3) B3)) C3)))) (forall ((B3 tptp.assn) (C3 tptp.assn) (A3 tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.entails B3) C3)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.entails (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A3) B3)) C3)))) (forall ((Q tptp.assn) (P tptp.assn) (R tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.entails (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn Q) P)) R)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.entails P) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.wand_assn Q) R))))) (forall ((P tptp.assn) (Q tptp.assn)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.entails (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn P) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.wand_assn P) Q))) Q))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (= X Y)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X))))) (forall ((X tptp.int) (Y tptp.int)) (=> (not (= X Y)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X))))) (forall ((P tptp.fun_Pr1572506220757514509t_bool) (X tptp.product_unit) (H tptp.heap_e7401611519738050253t_unit)) (=> (tptp.pp (tptp.aa_Product_unit_bool P X)) (= (tptp.aa_hea684056619475940329it_nat (tptp.heap_T875086893843062177t_unit (tptp.aa_Pro1108561329362217960t_unit (tptp.heap_T4208721593536448476t_unit P) X)) H) (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat (tptp.produc7133225469290080770it_nat X (tptp.produc584006145561248582it_nat H tptp.one_one_nat)))))) (forall ((P tptp.fun_a_bool) (X tptp.a) (H tptp.heap_e7401611519738050253t_unit)) (=> (tptp.pp (tptp.aa_a_bool P X)) (= (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a (tptp.aa_a_H8829438773920479562Heap_a (tptp.heap_Time_assert_a P) X)) H) (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat X) (tptp.produc584006145561248582it_nat H tptp.one_one_nat)))))) (= (tptp.heap_T4436805183663264329t_unit tptp.bot_bo8105976889876132193t_unit) (tptp.heap_T6183433275982383450t_unit tptp.aTP_Lamm_fk)) (forall ((P tptp.assn) (B tptp.bool)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.entails P))) (= (tptp.pp (tptp.aa_assn_bool _let_1 (tptp.aa_bool_assn tptp.pure_assn B))) (and (forall ((H6 tptp.produc3658429121746597890et_nat)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn P) H6)) (tptp.pp B))) (tptp.pp (tptp.aa_assn_bool _let_1 tptp.one_one_assn)))))) (forall ((X tptp.fun_in6429348457993719614e_term) (Xa2 tptp.product_prod_int_int) (Y tptp.produc4503464469895592971e_term)) (=> (= (tptp.pairse6911044277884061409e_term X Xa2) Y) (=> (tptp.pp (tptp.aa_Pro7591400126937138665t_bool (tptp.accp_P2898571771989476391nt_int tptp.pairse1033078303111491230e_term) (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int X) Xa2))) (not (forall ((A4 tptp.int) (B4 tptp.int)) (let ((_let_1 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A4) B4))) (=> (= Xa2 _let_1) (=> (= Y (tptp.produc4150800135984932291e_term (tptp.aa_int7340569405841786623e_term X A4) (tptp.aa_int7340569405841786623e_term X B4))) (not (tptp.pp (tptp.aa_Pro7591400126937138665t_bool (tptp.accp_P2898571771989476391nt_int tptp.pairse1033078303111491230e_term) (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int X) _let_1)))))))))))) (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.one_assn_raw (tptp.produc7507926704131184380et_nat H As))) (= As tptp.bot_bot_set_nat))) (forall ((X tptp.produc3658429121746597890et_nat) (Y tptp.bool)) (=> (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.one_assn_raw X)) (tptp.pp Y)) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (=> (= X (tptp.produc7507926704131184380et_nat H4 As4)) (= (tptp.pp Y) (not (= As4 tptp.bot_bot_set_nat)))))))) (forall ((X tptp.produc3658429121746597890et_nat)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.one_assn_raw X)) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (=> (= X (tptp.produc7507926704131184380et_nat H4 As4)) (not (= As4 tptp.bot_bot_set_nat))))))) (forall ((X tptp.produc3658429121746597890et_nat)) (=> (not (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.one_assn_raw X))) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (=> (= X (tptp.produc7507926704131184380et_nat H4 As4)) (= As4 tptp.bot_bot_set_nat)))))) (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2))))) (forall ((F tptp.fun_Pr7750636411365408485it_nat) (X tptp.option3562590408128118217it_nat) (Y tptp.option3562590408128118217it_nat)) (= (tptp.combin5819755802923621690it_nat F X Y) (tptp.case_o6061097939050036047it_nat Y (tptp.aa_opt996909609682481350it_nat (tptp.aTP_Lamm_fm F) Y) X))) (forall ((F tptp.fun_Pr1003294667014919570it_nat) (X tptp.option8956607266484857688it_nat) (Y tptp.option8956607266484857688it_nat)) (= (tptp.combin4318129983670048329it_nat F X Y) (tptp.case_o2963978774867076333it_nat Y (tptp.aa_opt7728438819757478003it_nat (tptp.aTP_Lamm_fo F) Y) X))) (forall ((F tptp.fun_num_fun_num_num) (X tptp.option_num) (Y tptp.option_num)) (= (tptp.aa_opt5369159329878751634on_num (tptp.combine_options_num F X) Y) (tptp.aa_opt5369159329878751634on_num (tptp.case_o6005452278849405969um_num Y (tptp.aa_opt8899475237019873193on_num (tptp.aTP_Lamm_fq F) Y)) X))) (forall ((N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) tptp.zero_zero_nat)) (= N2 tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2))) (= N2 tptp.zero_zero_nat))) (forall ((A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int tptp.zero_zero_int) A) tptp.zero_zero_int)) (forall ((A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B) tptp.zero_z3403309356797280102nteger) (or (= A tptp.zero_z3403309356797280102nteger) (= B tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))) (forall ((A tptp.nat) (B tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))) (forall ((A tptp.int) (B tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B tptp.zero_zero_int)))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C))) (= (= (tptp.aa_Cod1783974652533396728nteger _let_1 A) (tptp.aa_Cod1783974652533396728nteger _let_1 B)) (or (= C tptp.zero_z3403309356797280102nteger) (= A B))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (= (= (tptp.aa_rat_rat _let_1 A) (tptp.aa_rat_rat _let_1 B)) (or (= C tptp.zero_zero_rat) (= A B))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C))) (= (= (tptp.aa_nat_nat _let_1 A) (tptp.aa_nat_nat _let_1 B)) (or (= C tptp.zero_zero_nat) (= A B))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (= (= (tptp.aa_int_int _let_1 A) (tptp.aa_int_int _let_1 B)) (or (= C tptp.zero_zero_int) (= A B))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C)) (or (= C tptp.zero_z3403309356797280102nteger) (= A B)))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (= A B)))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C)) (or (= C tptp.zero_zero_nat) (= A B)))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (= A B)))) (forall ((A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) tptp.one_one_Code_integer) A)) (forall ((A tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn A) tptp.one_one_assn) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) tptp.one_one_rat) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) tptp.one_one_nat) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) tptp.one_one_int) A)) (forall ((A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger tptp.one_one_Code_integer) A) A)) (forall ((A tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn tptp.one_one_assn) A) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat tptp.one_one_rat) A) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat tptp.one_one_nat) A) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int tptp.one_one_int) A) A)) (forall ((N2 tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) tptp.zero_zero_nat)))) (forall ((N2 tptp.nat)) (= (not (= N2 tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) A)))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) N2))) (forall ((A tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2) tptp.zero_zero_nat) (and (= M tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat)))) (forall ((M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) tptp.zero_zero_nat) M)) (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) K)) (or (= M N2) (= K tptp.zero_zero_nat)))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K))) (= (= (tptp.aa_nat_nat _let_1 M) (tptp.aa_nat_nat _let_1 N2)) (or (= M N2) (= K tptp.zero_zero_nat))))) (forall ((M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N2) tptp.zero_zero_nat) (or (= M tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N2) tptp.one_one_nat) (and (= M tptp.one_one_nat) (= N2 tptp.one_one_nat)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= tptp.one_one_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N2)) (and (= M tptp.one_one_nat) (= N2 tptp.one_one_nat)))) (forall ((F tptp.fun_Pr7750636411365408485it_nat) (A tptp.produc3260487557148687353it_nat) (B tptp.produc3260487557148687353it_nat)) (= (tptp.combin5819755802923621690it_nat F (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat A) (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat B)) (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat (tptp.aa_Pro4202338132779708464it_nat (tptp.aa_Pro2263720180353132454it_nat F A) B)))) (forall ((F tptp.fun_num_fun_num_num) (A tptp.num) (B tptp.num)) (= (tptp.aa_opt5369159329878751634on_num (tptp.combine_options_num F (tptp.aa_num_option_num tptp.some_num A)) (tptp.aa_num_option_num tptp.some_num B)) (tptp.aa_num_option_num tptp.some_num (tptp.aa_num_num (tptp.aa_num_fun_num_num F A) B)))) (forall ((F tptp.fun_Pr1003294667014919570it_nat) (A tptp.produc8664842809031399944it_nat) (B tptp.produc8664842809031399944it_nat)) (= (tptp.combin4318129983670048329it_nat F (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat A) (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat B)) (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat (tptp.aa_Pro550487673543749710it_nat (tptp.aa_Pro4096753284154920275it_nat F A) B)))) (forall ((F tptp.fun_num_fun_num_num) (X tptp.option_num)) (= (tptp.aa_opt5369159329878751634on_num (tptp.combine_options_num F X) tptp.none_num) X)) (forall ((F tptp.fun_num_fun_num_num) (Y tptp.option_num)) (= (tptp.aa_opt5369159329878751634on_num (tptp.combine_options_num F tptp.none_num) Y) Y)) (= (tptp.aa_bool_assn tptp.pure_assn tptp.fTrue) tptp.one_one_assn) (forall ((P tptp.bool)) (= (= (tptp.aa_bool_assn tptp.pure_assn P) tptp.one_one_assn) (tptp.pp P))) (not (= tptp.bot_bot_assn tptp.one_one_assn)) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) A))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 A))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) A))) (tptp.pp (tptp.aa_rat_bool _let_1 A))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) A))) (tptp.pp (tptp.aa_int_bool _let_1 A))))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) A)) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) A)) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) A)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger B) A))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) B)))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) A))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) B)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) B))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) B)))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) B)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) B)) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B)) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.zero_zero_nat)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger B) A)) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger)))) (forall ((B tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) A)) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)))) (forall ((B tptp.nat) (A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) A)) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.zero_zero_nat)))) (forall ((B tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) A)) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) A))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 A))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) A))) (tptp.pp (tptp.aa_rat_bool _let_1 A))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) A))) (tptp.pp (tptp.aa_int_bool _let_1 A))))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) A)) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) A)) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) A)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger B) A))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) B)))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) A))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) B)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) B))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) B)))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) B)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) B)) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B)) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) tptp.zero_zero_nat)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger B) A)) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger)))) (forall ((B tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) A)) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)))) (forall ((B tptp.nat) (A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) A)) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) tptp.zero_zero_nat)))) (forall ((B tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) A)) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)))) (forall ((C tptp.code_integer) (B tptp.code_integer)) (= (= C (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) B)) (or (= C tptp.zero_z3403309356797280102nteger) (= B tptp.one_one_Code_integer)))) (forall ((C tptp.rat) (B tptp.rat)) (= (= C (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) B)) (or (= C tptp.zero_zero_rat) (= B tptp.one_one_rat)))) (forall ((C tptp.int) (B tptp.int)) (= (= C (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B)) (or (= C tptp.zero_zero_int) (= B tptp.one_one_int)))) (forall ((C tptp.code_integer) (A tptp.code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) A) C) (or (= C tptp.zero_z3403309356797280102nteger) (= A tptp.one_one_Code_integer)))) (forall ((C tptp.rat) (A tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) A) C) (or (= C tptp.zero_zero_rat) (= A tptp.one_one_rat)))) (forall ((C tptp.int) (A tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) A) C) (or (= C tptp.zero_zero_int) (= A tptp.one_one_int)))) (forall ((C tptp.code_integer) (B tptp.code_integer)) (= (= C (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C)) (or (= C tptp.zero_z3403309356797280102nteger) (= B tptp.one_one_Code_integer)))) (forall ((C tptp.rat) (B tptp.rat)) (= (= C (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (= B tptp.one_one_rat)))) (forall ((C tptp.int) (B tptp.int)) (= (= C (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (= B tptp.one_one_int)))) (forall ((A tptp.code_integer) (C tptp.code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C) C) (or (= C tptp.zero_z3403309356797280102nteger) (= A tptp.one_one_Code_integer)))) (forall ((A tptp.rat) (C tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C) C) (or (= C tptp.zero_zero_rat) (= A tptp.one_one_rat)))) (forall ((A tptp.int) (C tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C) C) (or (= C tptp.zero_zero_int) (= A tptp.one_one_int)))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2))) (or (tptp.pp (tptp.aa_nat_bool _let_1 M)) (tptp.pp (tptp.aa_nat_bool _let_1 N2)))))) (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) K))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N2))) (and (tptp.pp (tptp.aa_nat_bool _let_1 M)) (tptp.pp (tptp.aa_nat_bool _let_1 N2)))))) (forall ((N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) tptp.one_one_nat)) (= N2 tptp.zero_zero_nat))) (forall ((B tptp.bool) (Q tptp.assn)) (= (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.entails (tptp.aa_bool_assn tptp.pure_assn B)) Q)) (=> (tptp.pp B) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.entails tptp.one_one_assn) Q))))) _let_74 _let_73 _let_72 _let_71 _let_74 _let_73 _let_72 _let_71 (not (tptp.pp (tptp.aa_Code_integer_bool _let_58 tptp.zero_z3403309356797280102nteger))) (not (tptp.pp (tptp.aa_rat_bool _let_57 tptp.zero_zero_rat))) (not (tptp.pp (tptp.aa_nat_bool _let_62 tptp.zero_zero_nat))) (not (tptp.pp (tptp.aa_int_bool _let_56 tptp.zero_zero_int))) _let_69 _let_68 _let_67 _let_66 (not (tptp.pp (tptp.aa_Code_integer_bool _let_54 tptp.zero_z3403309356797280102nteger))) (not (tptp.pp (tptp.aa_rat_bool _let_53 tptp.zero_zero_rat))) (not (tptp.pp (tptp.aa_nat_bool _let_65 tptp.zero_zero_nat))) (not (tptp.pp (tptp.aa_int_bool _let_55 tptp.zero_zero_int))) (= tptp.bot_bot_nat tptp.zero_zero_nat) (forall ((X tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) X)) (not (= X tptp.zero_zero_nat)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= M (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N2)) (or (= N2 tptp.one_one_nat) (= M tptp.zero_zero_nat)))) (= tptp.one_one_assn (tptp.abs_assn tptp.one_assn_raw)) (forall ((C tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger C) tptp.one_one_Code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) A))))) (forall ((C tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) tptp.one_one_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) A))))) (forall ((C tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) tptp.one_one_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) A))))) (forall ((C tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) tptp.one_one_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) A))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)) tptp.one_one_Code_integer)))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.one_one_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)) tptp.one_one_rat)))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.one_one_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B)) tptp.one_one_nat)))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.one_one_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) tptp.one_one_int)))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 X)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger Y) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger X) Y)) X))))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Y)) X))))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) Y)) X))))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 X)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger Y) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger Y) X)) X))))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) X)) X))))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) X)) X))))))) (tptp.pp (tptp.aa_Code_integer_bool _let_37 (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) tptp.one_one_Code_integer))) (tptp.pp (tptp.aa_rat_bool _let_42 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat))) (tptp.pp (tptp.aa_nat_bool _let_63 (tptp.aa_nat_nat _let_61 tptp.one_one_nat))) (tptp.pp (tptp.aa_int_bool _let_44 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int))) (forall ((X tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) X))) (forall ((A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger tptp.one_one_Code_integer) A) A)) (forall ((A tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn tptp.one_one_assn) A) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat tptp.one_one_rat) A) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat tptp.one_one_nat) A) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int tptp.one_one_int) A) A)) (forall ((A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) tptp.one_one_Code_integer) A)) (forall ((A tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn A) tptp.one_one_assn) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) tptp.one_one_rat) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) tptp.one_one_nat) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) tptp.one_one_int) A)) (forall ((N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (not (= N2 tptp.zero_zero_nat)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (not (= N2 tptp.zero_zero_nat)))) (forall ((N2 tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) tptp.zero_zero_nat)))) (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B) tptp.zero_z3403309356797280102nteger)) (and (not (= A tptp.zero_z3403309356797280102nteger)) (not (= B tptp.zero_z3403309356797280102nteger))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B) tptp.zero_zero_rat)) (and (not (= A tptp.zero_zero_rat)) (not (= B tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B) tptp.zero_zero_nat)) (and (not (= A tptp.zero_zero_nat)) (not (= B tptp.zero_zero_nat))))) (forall ((A tptp.int) (B tptp.int)) (=> (not (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B) tptp.zero_zero_int)) (and (not (= A tptp.zero_zero_int)) (not (= B tptp.zero_zero_int))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B) tptp.zero_z3403309356797280102nteger) (or (= A tptp.zero_z3403309356797280102nteger) (= B tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))) (forall ((A tptp.int) (B tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B tptp.zero_zero_int)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (not (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B) tptp.zero_z3403309356797280102nteger))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (not (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= B tptp.zero_zero_nat)) (not (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= B tptp.zero_zero_int)) (not (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B) tptp.zero_zero_int))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C))) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (= (= (tptp.aa_Cod1783974652533396728nteger _let_1 A) (tptp.aa_Cod1783974652533396728nteger _let_1 B)) (= A B))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (=> (not (= C tptp.zero_zero_rat)) (= (= (tptp.aa_rat_rat _let_1 A) (tptp.aa_rat_rat _let_1 B)) (= A B))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (= (tptp.aa_nat_nat _let_1 A) (tptp.aa_nat_nat _let_1 B)) (= A B))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (= (tptp.aa_int_int _let_1 A) (tptp.aa_int_int _let_1 B)) (= A B))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (= (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C)) (= A B)))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C)) (= A B)))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C)) (= A B)))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C)) (= A B)))) (forall ((P tptp.fun_nat_bool) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat)) (=> (forall ((N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N5)) (=> (not (tptp.pp (tptp.aa_nat_bool P N5))) (exists ((M4 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M4) N5)) (not (tptp.pp (tptp.aa_nat_bool P M4)))))))) (tptp.pp (tptp.aa_nat_bool P N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (not (= N2 tptp.zero_zero_nat)))) (forall ((N2 tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) tptp.zero_zero_nat)))) (forall ((N2 tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) tptp.zero_zero_nat)))) (forall ((N2 tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2))) (= N2 tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((A tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) tptp.zero_zero_nat)))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) tptp.one_one_nat) N2)) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat tptp.one_one_nat) N2) N2)) (forall ((N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) tptp.zero_zero_nat)) (= N2 tptp.zero_zero_nat))) (forall ((A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.zero_zero_nat)) (= A tptp.zero_zero_nat))) (forall ((A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.zero_zero_nat)) (= A tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) N2))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.zero_zero_nat) N2) N2)) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2) M) (= N2 tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)) (forall ((P tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn tptp.one_one_assn) P) P)) (forall ((C tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger C) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) B))) (and (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) B))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) tptp.one_one_Code_integer)))))) (forall ((C tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) B))) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) tptp.one_one_rat)))))) (forall ((C tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B))) (and (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) tptp.one_one_int)))))) (forall ((C tptp.code_integer) (A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) A)) C)) (and (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A)))))) (forall ((C tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) A)) C)) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.one_one_rat))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) A)))))) (forall ((C tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) A)) C)) (and (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) A)))))) (forall ((C tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger C) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C))) (and (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) B))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) tptp.one_one_Code_integer)))))) (forall ((C tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C))) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) tptp.one_one_rat)))))) (forall ((C tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C))) (and (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) tptp.one_one_int)))))) (forall ((A tptp.code_integer) (C tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) C)) (and (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A)))))) (forall ((A tptp.rat) (C tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) C)) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.one_one_rat))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) A)))))) (forall ((A tptp.int) (C tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) C)) (and (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) A)))))) (forall ((C tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger C) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) B))) (and (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger B) tptp.one_one_Code_integer)))))) (forall ((C tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) B))) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) tptp.one_one_rat)))))) (forall ((C tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B))) (and (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) tptp.one_one_int)))))) (forall ((C tptp.code_integer) (A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) A)) C)) (and (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) tptp.one_one_Code_integer))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A)))))) (forall ((C tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) A)) C)) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.one_one_rat))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) A)))))) (forall ((C tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) A)) C)) (and (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) A)))))) (forall ((C tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger C) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C))) (and (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger B) tptp.one_one_Code_integer)))))) (forall ((C tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C))) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) tptp.one_one_rat)))))) (forall ((C tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C))) (and (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) tptp.one_one_int)))))) (forall ((A tptp.code_integer) (C tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) C)) (and (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) tptp.one_one_Code_integer))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A)))))) (forall ((A tptp.rat) (C tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) C)) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.one_one_rat))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) A)))))) (forall ((A tptp.int) (C tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) C)) (and (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) A)))))) (forall ((X tptp.code_integer) (A tptp.code_integer) (Y tptp.code_integer) (U tptp.code_integer) (V tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger X) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger Y) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 U)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 V)) (=> (= (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger U) V) tptp.one_one_Code_integer) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger U) X)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger V) Y))) A))))))))) (forall ((X tptp.rat) (A tptp.rat) (Y tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 U)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 V)) (=> (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat U) V) tptp.one_one_rat) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat U) X)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat V) Y))) A))))))))) (forall ((X tptp.int) (A tptp.int) (Y tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 U)) (=> (tptp.pp (tptp.aa_int_bool _let_1 V)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int U) V) tptp.one_one_int) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int U) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int V) Y))) A))))))))) (= tptp.aTP_Lamm_fr (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger tptp.one_one_Code_integer)) (= tptp.aTP_Lamm_fs (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn tptp.one_one_assn)) (= tptp.aTP_Lamm_ft (tptp.aa_rat_fun_rat_rat tptp.times_times_rat tptp.one_one_rat)) (= tptp.aTP_Lamm_fu (tptp.aa_nat_fun_nat_nat tptp.times_times_nat tptp.one_one_nat)) (= tptp.aTP_Lamm_fv (tptp.aa_int_fun_int_int tptp.times_times_int tptp.one_one_int)) (= tptp.aTP_Lamm_fw (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger tptp.zero_z3403309356797280102nteger)) (= tptp.aTP_Lamm_fx (tptp.aa_rat_fun_rat_rat tptp.times_times_rat tptp.zero_zero_rat)) (= tptp.aTP_Lamm_fy (tptp.aa_nat_fun_nat_nat tptp.times_times_nat tptp.zero_zero_nat)) (= tptp.aTP_Lamm_fz (tptp.aa_int_fun_int_int tptp.times_times_int tptp.zero_zero_int)) (forall ((X tptp.code_integer) (A tptp.code_integer) (Y tptp.code_integer) (U tptp.code_integer) (V tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger X) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger Y) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 U)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 V)) (=> (= (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger U) V) tptp.one_one_Code_integer) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger U) X)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger V) Y))) A))))))))) (forall ((X tptp.rat) (A tptp.rat) (Y tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 U)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 V)) (=> (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat U) V) tptp.one_one_rat) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat U) X)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat V) Y))) A))))))))) (forall ((X tptp.int) (A tptp.int) (Y tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 U)) (=> (tptp.pp (tptp.aa_int_bool _let_1 V)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int U) V) tptp.one_one_int) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int U) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int V) Y))) A))))))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger B) tptp.one_one_Code_integer))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) tptp.one_one_rat)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) tptp.one_one_rat))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) tptp.one_one_nat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) tptp.one_one_nat))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) tptp.one_one_int)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) tptp.one_one_int))))) (forall ((A tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)))) (forall ((A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) tptp.one_one_rat)))) (forall ((A tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) tptp.one_one_nat)))) (forall ((A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) tptp.one_one_int)))) (forall ((M tptp.code_integer) (N2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 M)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 N2)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger M) N2))))))) (forall ((M tptp.rat) (N2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 M)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 N2)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat M) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 M)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 N2)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N2))))))) (forall ((M tptp.int) (N2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 M)) (=> (tptp.pp (tptp.aa_int_bool _let_1 N2)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int M) N2))))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger X) tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger Y) tptp.zero_z3403309356797280102nteger)) (= (= (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger X) Y) tptp.zero_z3403309356797280102nteger) (and (= X tptp.zero_z3403309356797280102nteger) (= Y tptp.zero_z3403309356797280102nteger)))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) tptp.zero_zero_rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) tptp.zero_zero_nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) tptp.zero_zero_int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) Y) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 X)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 Y)) (= (= (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger X) Y) tptp.zero_z3403309356797280102nteger) (and (= X tptp.zero_z3403309356797280102nteger) (= Y tptp.zero_z3403309356797280102nteger))))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 Y)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat))))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) Y) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) B)) tptp.zero_z3403309356797280102nteger))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B)) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) tptp.zero_zero_int))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) B))))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B))))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B))))))) (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) C))))))) (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C))))))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C))))))) (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C))))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) C)) B))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C)) B))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)) B))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) B))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 C)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) C))))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 C)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 C)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C))))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 C)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C))))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger C) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) C)) B))))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C)) B))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)) B))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) B))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger _let_1 A)) (tptp.aa_Cod1783974652533396728nteger _let_1 B))))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B))))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B))))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B))) (or (and (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 B))) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger))))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B))) (or (and (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 B))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) tptp.zero_zero_rat))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B))) (or (and (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 B))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) tptp.zero_zero_int))))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) A)) tptp.zero_z3403309356797280102nteger))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) A)) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) A)) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) A)) tptp.zero_zero_int))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)) tptp.zero_z3403309356797280102nteger))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B)) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) tptp.zero_zero_int))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)) tptp.zero_z3403309356797280102nteger))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B)) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) tptp.zero_zero_int))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B))))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B))))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B))))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (or (and (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger))) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)) tptp.zero_z3403309356797280102nteger))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) tptp.zero_zero_rat))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool _let_1 B)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (or (and (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) tptp.zero_zero_nat))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool _let_1 B)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B)) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) tptp.zero_zero_int))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool _let_1 B)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) tptp.zero_zero_int))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)) tptp.zero_z3403309356797280102nteger)) (or (and (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger))) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 B))))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)) tptp.zero_zero_rat)) (or (and (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) tptp.zero_zero_rat))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool _let_1 B))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) tptp.zero_zero_int)) (or (and (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) tptp.zero_zero_int))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool _let_1 B))))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C)))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C)))))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C)))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C)))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger _let_1 A)) (tptp.aa_Cod1783974652533396728nteger _let_1 B))))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B))))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B))))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger _let_1 A)) (tptp.aa_Cod1783974652533396728nteger _let_1 B))))))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B))))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B))))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (or (and (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 B))) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger)))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 B))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) tptp.zero_zero_rat)))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 B))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) tptp.zero_zero_int)))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)))))) (forall ((A tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) A)))) (forall ((A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) A)))) (forall ((A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) A)))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger C) D2)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) D2))))))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) D2)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) D2))))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) D2)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) D2))))))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) D2)) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) D2))))))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger C) D2)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) D2))))))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) D2)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) D2))))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) D2)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) D2))))))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) D2)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (=> (tptp.pp (tptp.aa_int_bool _let_1 C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) D2))))))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger B))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 C)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) C))))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 C)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 C)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C))))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 C)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C))))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (not (forall ((C2 tptp.nat)) (=> (= B (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C2)) (= C2 tptp.zero_zero_nat)))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) B))))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B))))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B))))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger B) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) B)) tptp.zero_z3403309356797280102nteger))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B)) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) tptp.zero_zero_int))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger X) Y)) tptp.zero_z3403309356797280102nteger)) (or (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger X) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger Y) tptp.zero_z3403309356797280102nteger))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y)) tptp.zero_zero_rat)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) tptp.zero_zero_rat))))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) Y)) tptp.zero_zero_int)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) tptp.zero_zero_int))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger _let_1 A)) (tptp.aa_Cod1783974652533396728nteger _let_1 B))))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B))))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B))))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C))) (or (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B))) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger B) A)))))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C))) (or (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C))) (or (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C)))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger B) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C)))))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C)))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C)))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C))) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger _let_1 A)) (tptp.aa_Cod1783974652533396728nteger _let_1 B))) (or (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B))) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger B) A))))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B))) (or (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A))))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B))) (or (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A))))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger _let_1 A)) (tptp.aa_Cod1783974652533396728nteger _let_1 B))))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B))))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B))))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger B) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger _let_1 A)) (tptp.aa_Cod1783974652533396728nteger _let_1 B))))))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B))))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B))))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger _let_1 A)) (tptp.aa_Cod1783974652533396728nteger _let_1 B))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B)))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger _let_1 A)) (tptp.aa_Cod1783974652533396728nteger _let_1 B))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger B) A)))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) tptp.zero_zero_int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)))))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) A))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)))))) (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 B)))))) (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 B)))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 B)))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 B)))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 B)))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 B)))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B))) (or (and (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 B))) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger B) tptp.zero_z3403309356797280102nteger))))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B))) (or (and (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 B))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) tptp.zero_zero_rat))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B))) (or (and (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 B))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) tptp.zero_zero_int))))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger B) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) A)) tptp.zero_z3403309356797280102nteger))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) A)) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) A)) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) A)) tptp.zero_zero_int))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B))))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B))))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B))))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger B) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)) tptp.zero_z3403309356797280102nteger))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B)) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) tptp.zero_zero_int))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)) tptp.zero_z3403309356797280102nteger))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B)) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) tptp.zero_zero_int))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)) tptp.zero_z3403309356797280102nteger)) (or (and (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger B) tptp.zero_z3403309356797280102nteger))) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 B))))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)) tptp.zero_zero_rat)) (or (and (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) tptp.zero_zero_rat))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool _let_1 B))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) tptp.zero_zero_int)) (or (and (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) tptp.zero_zero_int))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool _let_1 B))))))) (forall ((A tptp.code_integer)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) A)) tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.rat)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) A)) tptp.zero_zero_rat)))) (forall ((A tptp.int)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) A)) tptp.zero_zero_int)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger B) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)))))) (forall ((R3 tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger R3))) (=> (not (= R3 tptp.zero_z3403309356797280102nteger)) (=> (and (= A B) (not (= C D2))) (not (= (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) (tptp.aa_Cod1783974652533396728nteger _let_1 C)) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger B) (tptp.aa_Cod1783974652533396728nteger _let_1 D2)))))))) (forall ((R3 tptp.rat) (A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat R3))) (=> (not (= R3 tptp.zero_zero_rat)) (=> (and (= A B) (not (= C D2))) (not (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) (tptp.aa_rat_rat _let_1 C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) (tptp.aa_rat_rat _let_1 D2)))))))) (forall ((R3 tptp.nat) (A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat R3))) (=> (not (= R3 tptp.zero_zero_nat)) (=> (and (= A B) (not (= C D2))) (not (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) (tptp.aa_nat_nat _let_1 C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) (tptp.aa_nat_nat _let_1 D2)))))))) (forall ((R3 tptp.int) (A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int R3))) (=> (not (= R3 tptp.zero_zero_int)) (=> (and (= A B) (not (= C D2))) (not (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) (tptp.aa_int_int _let_1 C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) (tptp.aa_int_int _let_1 D2)))))))) (forall ((P tptp.fun_nat_bool) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P N2)) (=> (not (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat))) (exists ((K2 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K2) N2)) (forall ((I tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) K2)) (not (tptp.pp (tptp.aa_nat_bool P I))))) (tptp.pp (tptp.aa_nat_bool P K2))))))) (forall ((I2 tptp.nat) (J tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) J)) (exists ((K2 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) K2) J))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) J)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat I2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat J) K)))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) J)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 I2)) (tptp.aa_nat_nat _let_1 J))))))) (tptp.pp (tptp.aa_nat_bool _let_70 tptp.zero_zero_nat)) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger B))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 C)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) C))))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 C)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 C)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C))))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 C)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C))))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger B) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) C)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) C)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) B))))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) B)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B))))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) B)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) B)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B))))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger B) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) B)) tptp.zero_z3403309356797280102nteger))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B)) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) tptp.zero_zero_int))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) B))))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B))))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B))))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) B)) tptp.zero_z3403309356797280102nteger))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B)) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) tptp.zero_zero_int))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger C) D2)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) D2)))))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) D2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) D2)))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) D2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) D2)))))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) D2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) D2)))))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger C) D2)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) D2)))))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) D2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) D2)))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C) D2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) D2)))))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) D2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) D2)))))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B))))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger _let_1 A)) (tptp.aa_Cod1783974652533396728nteger _let_1 B))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B)))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger _let_1 A)) (tptp.aa_Cod1783974652533396728nteger _let_1 B))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B)))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger _let_1 A)) (tptp.aa_Cod1783974652533396728nteger _let_1 B))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) A)))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) tptp.zero_zero_int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C))) (and (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger B) A)))))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C))) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C))) (and (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger C) D2)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) D2))))))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) D2)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) D2))))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C) D2)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) D2))))))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) D2)) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) D2))))))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B))))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C))) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger _let_1 A)) (tptp.aa_Cod1783974652533396728nteger _let_1 B))) (and (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger B) A))))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B))) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A))))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B))) (and (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A))))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger C) D2)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) D2)))))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) D2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) D2)))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C) D2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) D2)))))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) D2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) D2)))))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger _let_1 A)) (tptp.aa_Cod1783974652533396728nteger _let_1 B))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B)))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C))) (and (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) A)))))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C))) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C))) (and (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C))) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger _let_1 A)) (tptp.aa_Cod1783974652533396728nteger _let_1 B))) (and (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) A))))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B))) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A))))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B))) (and (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A))))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger X) X)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger Y) Y))))) (forall ((X tptp.rat) (Y tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) X)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Y))))) (forall ((X tptp.int) (Y tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) Y))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger X) X)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger Y) Y))) tptp.zero_z3403309356797280102nteger)))) (forall ((X tptp.rat) (Y tptp.rat)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) X)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Y))) tptp.zero_zero_rat)))) (forall ((X tptp.int) (Y tptp.int)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) Y))) tptp.zero_zero_int)))) (forall ((H tptp.heap_e7401611519738050253t_unit)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn tptp.one_one_assn) (tptp.produc7507926704131184380et_nat H tptp.bot_bot_set_nat)))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N2))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (forall ((Z2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Z2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z2) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Z2) X)) Y))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) B)))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) tptp.one_one_nat)) B)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) tptp.one_one_int)) B)))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger X) X)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger Y) Y)))) (or (not (= X tptp.zero_z3403309356797280102nteger)) (not (= Y tptp.zero_z3403309356797280102nteger))))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) X)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Y)))) (or (not (= X tptp.zero_zero_rat)) (not (= Y tptp.zero_zero_rat))))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) Y)))) (or (not (= X tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger X) X)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger Y) Y))) tptp.zero_z3403309356797280102nteger)) (and (= X tptp.zero_z3403309356797280102nteger) (= Y tptp.zero_z3403309356797280102nteger)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) X)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Y))) tptp.zero_zero_rat)) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) Y))) tptp.zero_zero_int)) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))) (forall ((Z tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger Z))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) Z)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger _let_1 X)) (tptp.aa_Cod1783974652533396728nteger _let_1 Y))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger X) Y)))))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Z))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Z)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 X)) (tptp.aa_rat_rat _let_1 Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)))))) (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int Z))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Z)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int _let_1 X)) (tptp.aa_int_int _let_1 Y))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)))))) (forall ((Z tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) Z)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger X) Z)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger Y) Z))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger X) Y))))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Z)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Z))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y))))) (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Z)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) Z)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y))))) (forall ((X5 tptp.rat)) (exists ((Y3 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y3) X5)))) (forall ((X5 tptp.rat)) (exists ((X_1 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X5) X_1)))) (forall ((Z tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) Z)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger X) Z)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger Y) Z))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger X) Y))))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Z)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Z))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y))))) (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Z)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) Z)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger X) X)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger Y) Y)) tptp.zero_z3403309356797280102nteger) (and (= X tptp.zero_z3403309356797280102nteger) (= Y tptp.zero_z3403309356797280102nteger)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) X)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Y)) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))) (forall ((X tptp.int) (Y tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) Y)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (= (tptp.aa_nat_nat _let_1 M) (tptp.aa_nat_nat _let_1 N2)) (= M N2))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (forall ((E2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) E2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Y) E2))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)))) (forall ((Q5 tptp.code_integer) (R3 tptp.code_integer)) (= (tptp.unique5706413561485394159nteger (tptp.produc1086072967326762835nteger Q5 R3)) (= R3 tptp.zero_z3403309356797280102nteger))) (forall ((Q5 tptp.nat) (R3 tptp.nat)) (= (tptp.pp (tptp.aa_Pro2232559814647311250t_bool tptp.unique6322359934112328802ux_nat (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat Q5) R3))) (= R3 tptp.zero_zero_nat))) (forall ((Q5 tptp.int) (R3 tptp.int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool tptp.unique6319869463603278526ux_int (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q5) R3))) (= R3 tptp.zero_zero_int))) (forall ((F tptp.fun_he6342020308413958580unit_a)) (= (tptp.heap_Time_tap_a F) (tptp.heap_Time_Heap_a2 (tptp.aTP_Lamm_ga F)))) (forall ((F tptp.fun_he5123621388056232515t_unit)) (= (tptp.heap_T560649228465745139t_unit F) (tptp.heap_T6183433275982383450t_unit (tptp.aTP_Lamm_gb F)))) (forall ((F tptp.fun_he5123621388056232515t_unit) (H tptp.heap_e7401611519738050253t_unit)) (= (tptp.aa_hea684056619475940329it_nat (tptp.heap_T875086893843062177t_unit (tptp.heap_T560649228465745139t_unit F)) H) (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat (tptp.produc7133225469290080770it_nat (tptp.aa_hea4146273921685161788t_unit F H) (tptp.produc584006145561248582it_nat H tptp.one_one_nat))))) (forall ((F tptp.fun_he6342020308413958580unit_a) (H tptp.heap_e7401611519738050253t_unit)) (= (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a (tptp.heap_Time_tap_a F)) H) (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat (tptp.aa_hea5100639427662539565unit_a F H)) (tptp.produc584006145561248582it_nat H tptp.one_one_nat))))) (forall ((X tptp.produc3658429121746597890et_nat)) (=> (not (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.one_assn_raw X))) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.accp_P5801069581201407417et_nat tptp.one_assn_raw_rel) X)) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (tptp.produc7507926704131184380et_nat H4 As4))) (=> (= X _let_1) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.accp_P5801069581201407417et_nat tptp.one_assn_raw_rel) _let_1)) (= As4 tptp.bot_bot_set_nat))))))))) (forall ((X tptp.produc3658429121746597890et_nat)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.one_assn_raw X)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.accp_P5801069581201407417et_nat tptp.one_assn_raw_rel) X)) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (tptp.produc7507926704131184380et_nat H4 As4))) (=> (= X _let_1) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.accp_P5801069581201407417et_nat tptp.one_assn_raw_rel) _let_1)) (not (= As4 tptp.bot_bot_set_nat)))))))))) (forall ((X tptp.produc3658429121746597890et_nat) (Y tptp.bool)) (=> (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.one_assn_raw X)) (tptp.pp Y)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.accp_P5801069581201407417et_nat tptp.one_assn_raw_rel) X)) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (tptp.produc7507926704131184380et_nat H4 As4))) (=> (= X _let_1) (=> (= (tptp.pp Y) (= As4 tptp.bot_bot_set_nat)) (not (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.accp_P5801069581201407417et_nat tptp.one_assn_raw_rel) _let_1))))))))))) _let_69 _let_68 _let_67 _let_66 (not (tptp.pp (tptp.aa_Code_integer_bool _let_54 tptp.one_one_Code_integer))) (not (tptp.pp (tptp.aa_rat_bool _let_53 tptp.one_one_rat))) (not (tptp.pp (tptp.aa_nat_bool _let_65 tptp.one_one_nat))) (not (tptp.pp (tptp.aa_int_bool _let_55 tptp.one_one_int))) (forall ((P tptp.fun_nat_bool) (X tptp.nat) (M6 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P X)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P X3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) M6)))) (not (forall ((M5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P M5)) (not (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P X5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X5) M5))))))))))) _let_40 (tptp.pp (tptp.aa_rat_bool _let_49 tptp.zero_zero_rat)) (tptp.pp (tptp.aa_nat_bool _let_64 tptp.zero_zero_nat)) _let_60 _let_38 (not (tptp.pp (tptp.aa_rat_bool _let_42 tptp.zero_zero_rat))) (not (tptp.pp (tptp.aa_nat_bool _let_63 tptp.zero_zero_nat))) _let_59 (tptp.pp (tptp.aa_Code_integer_bool _let_58 tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_rat_bool _let_57 tptp.one_one_rat)) (tptp.pp (tptp.aa_nat_bool _let_62 tptp.one_one_nat)) (tptp.pp (tptp.aa_int_bool _let_56 tptp.one_one_int)) (forall ((B tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger B))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger B) tptp.one_one_Code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer _let_1 M)) (tptp.aa_nat_Code_integer _let_1 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M))))))) (forall ((B tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_power_rat B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) tptp.one_one_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat _let_1 M)) (tptp.aa_nat_rat _let_1 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M))))))) (forall ((B tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) tptp.one_one_nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M))))))) (forall ((B tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) tptp.one_one_int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int _let_1 M)) (tptp.aa_nat_int _let_1 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M))))))) (forall ((B tptp.nat) (A tptp.nat) (F tptp.fun_nat_fun_nat_nat) (Acc tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat F A) B) Acc))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A)))) (and (=> _let_2 (= _let_1 Acc)) (=> (not _let_2) (= _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat F (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) tptp.one_one_nat)) B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat F A) Acc)))))))) (forall ((X tptp.fun_nat_fun_nat_nat) (Xa2 tptp.nat) (Xb tptp.nat) (Xc tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Xb) Xa2)))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat X Xa2) Xb) Xc) Y) (and (=> _let_1 (= Y Xc)) (=> (not _let_1) (= Y (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat X (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Xa2) tptp.one_one_nat)) Xb) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat X Xa2) Xc)))))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger B) N2))))))) (forall ((A tptp.rat) (B tptp.rat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N2)) (tptp.aa_nat_rat (tptp.power_power_rat B) N2))))))) (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) N2))))))) (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int B) N2))))))) (forall ((B tptp.code_integer) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger B))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer _let_1 X)) (tptp.aa_nat_Code_integer _let_1 Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)))))) (forall ((B tptp.rat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.power_power_rat B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) B)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat _let_1 X)) (tptp.aa_nat_rat _let_1 Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)))))) (forall ((B tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat) B)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 X)) (tptp.aa_nat_nat _let_1 Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)))))) (forall ((B tptp.int) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) B)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int _let_1 X)) (tptp.aa_nat_int _let_1 Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) A)) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) A)) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat _let_1 B)) C)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) B))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat _let_1 B)) C) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C))))) (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C)) A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) A)) C))) (forall ((X tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) N2))) (or (tptp.pp (tptp.aa_nat_bool _let_1 X)) (= N2 tptp.zero_zero_nat))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (let ((_let_2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_rat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_3) (= _let_2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A) B)))))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (=> (not (= C tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A) B))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) A)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A) B)))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A) B)))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) B)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A) B)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B)) B) A))) (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) B) A))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)) B) A))) (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)) B) A))) (forall ((B tptp.code_natural) (A tptp.code_natural)) (=> (not (= B tptp.zero_z2226904508553997617atural)) (= (tptp.divide5121882707175180666atural (tptp.times_2397367101498566445atural A B) B) A))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B)) A) B))) (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)) A) B))) (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)) A) B))) (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (not (= A tptp.zero_z2226904508553997617atural)) (= (tptp.divide5121882707175180666atural (tptp.times_2397367101498566445atural A B) A) B))) (forall ((A tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A)) (= (= (tptp.aa_nat_Code_integer _let_1 M) (tptp.aa_nat_Code_integer _let_1 N2)) (= M N2))))) (forall ((A tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_power_rat A))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) A)) (= (= (tptp.aa_nat_rat _let_1 M) (tptp.aa_nat_rat _let_1 N2)) (= M N2))))) (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat) A)) (= (= (tptp.aa_nat_nat _let_1 M) (tptp.aa_nat_nat _let_1 N2)) (= M N2))))) (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) A)) (= (= (tptp.aa_nat_int _let_1 M) (tptp.aa_nat_int _let_1 N2)) (= M N2))))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat tptp.one_one_rat) A)) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat tptp.one_one_rat) A))) (tptp.pp (tptp.aa_rat_bool _let_1 A))))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat tptp.one_one_rat) A)) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) A)) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool _let_1 B)))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) A)) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat tptp.one_one_rat) A))) (tptp.pp (tptp.aa_rat_bool _let_1 A))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat tptp.one_one_rat) B)))) (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat tptp.one_one_rat) A)))) (forall ((B tptp.code_integer) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger B))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer _let_1 X)) (tptp.aa_nat_Code_integer _let_1 Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)))))) (forall ((B tptp.rat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.power_power_rat B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) B)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat _let_1 X)) (tptp.aa_nat_rat _let_1 Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)))))) (forall ((B tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat) B)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 X)) (tptp.aa_nat_nat _let_1 Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)))))) (forall ((B tptp.int) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) B)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int _let_1 X)) (tptp.aa_nat_int _let_1 Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2) tptp.zero_z3403309356797280102nteger) (and (= A tptp.zero_z3403309356797280102nteger) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2))))) (forall ((A tptp.rat) (N2 tptp.nat)) (= (= (tptp.aa_nat_rat (tptp.power_power_rat A) N2) tptp.zero_zero_rat) (and (= A tptp.zero_zero_rat) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2))))) (forall ((A tptp.nat) (N2 tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N2) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2))))) (forall ((A tptp.int) (N2 tptp.nat)) (= (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2) tptp.zero_zero_int) (and (= A tptp.zero_zero_int) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))))) (forall ((B tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger B))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger B) tptp.one_one_Code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer _let_1 M)) (tptp.aa_nat_Code_integer _let_1 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M))))))) (forall ((B tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_power_rat B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) tptp.one_one_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat _let_1 M)) (tptp.aa_nat_rat _let_1 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M))))))) (forall ((B tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) tptp.one_one_nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M))))))) (forall ((B tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) tptp.one_one_int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int _let_1 M)) (tptp.aa_nat_int _let_1 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M))))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger B) N2))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B)))))))) (forall ((A tptp.rat) (B tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N2)) (tptp.aa_nat_rat (tptp.power_power_rat B) N2))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)))))))) (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)))))))) (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int B) N2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)))))))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) N2))) (let ((_let_2 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger Y))) (=> (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger X) Y) (tptp.aa_Cod1783974652533396728nteger _let_2 X)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) Y) (tptp.aa_Cod1783974652533396728nteger _let_2 _let_1)))))) (forall ((X tptp.assn) (Y tptp.assn) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_assn (tptp.power_power_assn X) N2))) (let ((_let_2 (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn Y))) (=> (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn X) Y) (tptp.aa_assn_assn _let_2 X)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn _let_1) Y) (tptp.aa_assn_assn _let_2 _let_1)))))) (forall ((X tptp.rat) (Y tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.power_power_rat X) N2))) (let ((_let_2 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y))) (=> (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Y) (tptp.aa_rat_rat _let_2 X)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) Y) (tptp.aa_rat_rat _let_2 _let_1)))))) (forall ((X tptp.nat) (Y tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) N2))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Y))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat X) Y) (tptp.aa_nat_nat _let_2 X)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) Y) (tptp.aa_nat_nat _let_2 _let_1)))))) (forall ((X tptp.int) (Y tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int X) N2))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.times_times_int Y))) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) Y) (tptp.aa_int_int _let_2 X)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) Y) (tptp.aa_int_int _let_2 _let_1)))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (N2 tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)) N2) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger B) N2)))) (forall ((A tptp.assn) (B tptp.assn) (N2 tptp.nat)) (= (tptp.aa_nat_assn (tptp.power_power_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn A) B)) N2) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.aa_nat_assn (tptp.power_power_assn A) N2)) (tptp.aa_nat_assn (tptp.power_power_assn B) N2)))) (forall ((A tptp.rat) (B tptp.rat) (N2 tptp.nat)) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)) N2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N2)) (tptp.aa_nat_rat (tptp.power_power_rat B) N2)))) (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B)) N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) N2)))) (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) N2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int B) N2)))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) _let_1)))) (forall ((A tptp.assn) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_assn (tptp.power_power_assn A) N2))) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn _let_1) A) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn A) _let_1)))) (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N2))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1)))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N2))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) _let_1)))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) _let_1)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat _let_1 B)) C) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) B))))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat) (W2 tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Y)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat Z) W2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) W2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Z)))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat) (W2 tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Y)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat Z) W2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) W2)))) (forall ((A tptp.code_integer) (B tptp.code_integer) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger B) N2)))))) (forall ((A tptp.rat) (B tptp.rat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N2)) (tptp.aa_nat_rat (tptp.power_power_rat B) N2)))))) (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) N2)))))) (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int B) N2)))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2)))))) (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N2)))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N2)))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2)))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2)))))) (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N2)))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N2)))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2)))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2)))))) (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N2)))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N2)))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2)))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A) B)) tptp.zero_zero_rat)) (or (and (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) tptp.zero_zero_rat))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool _let_1 B))))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C)))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A) B))) (or (and (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 B))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) tptp.zero_zero_rat))))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Y))))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) X)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Y)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A) C)))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Y)))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) X)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Y))))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A) B)) tptp.zero_zero_rat)) (or (and (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) tptp.zero_zero_rat))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool _let_1 B))))))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C))) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A))) (not (= C tptp.zero_zero_rat))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A) B))) (or (and (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 B))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) tptp.zero_zero_rat))))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C)))))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C)))))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (N2 tptp.nat)) (=> (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger X) Y) tptp.one_one_Code_integer) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) N2)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Y) N2)) tptp.one_one_Code_integer))) (forall ((X tptp.assn) (Y tptp.assn) (N2 tptp.nat)) (=> (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn X) Y) tptp.one_one_assn) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.aa_nat_assn (tptp.power_power_assn X) N2)) (tptp.aa_nat_assn (tptp.power_power_assn Y) N2)) tptp.one_one_assn))) (forall ((X tptp.rat) (Y tptp.rat) (N2 tptp.nat)) (=> (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Y) tptp.one_one_rat) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat X) N2)) (tptp.aa_nat_rat (tptp.power_power_rat Y) N2)) tptp.one_one_rat))) (forall ((X tptp.nat) (Y tptp.nat) (N2 tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat X) Y) tptp.one_one_nat) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Y) N2)) tptp.one_one_nat))) (forall ((X tptp.int) (Y tptp.int) (N2 tptp.nat)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) Y) tptp.one_one_int) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int X) N2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Y) N2)) tptp.one_one_int))) (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W2 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Y) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat W2) Z)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Z) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat W2) Y)))))) (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C) A) (and (=> (not _let_1) (= B (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C))) (=> _let_1 (= A tptp.zero_zero_rat)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= A (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C)) (and (=> (not _let_1) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C) B)) (=> _let_1 (= A tptp.zero_zero_rat)))))) (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (=> (= B (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C) A)))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (=> (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C) B) (= A (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C))))) (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C) A) (= B (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= A (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C) B)))) (forall ((A tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger A))) (= (tptp.aa_nat_Code_integer _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer _let_1 M)) (tptp.aa_nat_Code_integer _let_1 N2))))) (forall ((A tptp.assn) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_power_assn A))) (= (tptp.aa_nat_assn _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.aa_nat_assn _let_1 M)) (tptp.aa_nat_assn _let_1 N2))))) (forall ((A tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_power_rat A))) (= (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 M)) (tptp.aa_nat_rat _let_1 N2))))) (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N2))))) (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int A))) (= (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_1 M)) (tptp.aa_nat_int _let_1 N2))))) (forall ((I2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat I2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) I2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))))) (forall ((A tptp.code_integer) (N2 tptp.nat) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger B) N2))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B))))) (forall ((A tptp.rat) (N2 tptp.nat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N2)) (tptp.aa_nat_rat (tptp.power_power_rat B) N2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))))) (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B))))) (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int B) N2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2)) tptp.one_one_Code_integer))))) (forall ((A tptp.rat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N2)) tptp.one_one_rat))))) (forall ((A tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N2)) tptp.one_one_nat))))) (forall ((A tptp.int) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2)) tptp.one_one_int))))) (forall ((Y tptp.rat) (X tptp.rat) (W2 tptp.rat) (Z tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) W2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat W2) Z)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat Y) W2)))))))) (forall ((X tptp.rat) (Y tptp.rat) (W2 tptp.rat) (Z tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) X)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) W2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat W2) Z)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat Y) W2)))))))) (forall ((X tptp.rat) (Y tptp.rat) (W2 tptp.rat) (Z tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 W2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat W2) Z)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat Y) W2))))))))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C))) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) X)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Y)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Y))))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Y)))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B) tptp.zero_zero_nat)))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B) tptp.zero_zero_int)))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) A)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) B))))))) (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B))))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B))))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2))))))) (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) (tptp.aa_nat_rat (tptp.power_power_rat A) N2))))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N2))))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2))))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) _let_1)))))) (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_1) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1)))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) _let_1)))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) _let_1)))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.divide6298287555418463151nteger A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C)) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B)) C))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 B)) C))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.divide_divide_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int _let_1 B)) C))))) (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_3 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C))) (let ((_let_4 (tptp.pp (tptp.aa_rat_bool _let_1 C)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C)) A)) (and (=> _let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) _let_3))) (=> (not _let_4) (and (=> _let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_3) B))) (=> (not _let_2) (tptp.pp (tptp.aa_rat_bool _let_1 A)))))))))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_3 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C))) (let ((_let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C))) (and (=> _let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_3) B))) (=> (not _let_4) (and (=> _let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) _let_3))) (=> (not _let_2) (tptp.pp (tptp.aa_rat_bool _let_1 tptp.zero_zero_rat)))))))))))) (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) B))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)))))) (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) B))))) (forall ((Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Z) Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Y)) Z))))) (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Z) Y)) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Y)))))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat C))) (let ((_let_2 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (=> (tptp.pp (tptp.aa_rat_bool _let_2 C)) (=> (tptp.pp (tptp.aa_rat_bool _let_2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B))))))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B)))))))) (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) A)) tptp.one_one_rat)) (or (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A))) (and (tptp.pp (tptp.aa_rat_bool _let_1 tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool _let_1 B))) (= A tptp.zero_zero_rat))))) (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) A))) (or (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (tptp.pp (tptp.aa_rat_bool _let_1 B))) (and (tptp.pp (tptp.aa_rat_bool _let_1 tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A))))))) (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) Z))) Z))))))) (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) Z)) B)) Z))))))) (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W2 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Y)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat W2) Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat W2) Y))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Z)))))) (forall ((Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Y)) Z) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Z) Y))) Y)))) (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Z) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Y)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Z) Y))) Y)))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat Y) Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Z)) Y)) Z)))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Z)) Y) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Z))) Z)))) (forall ((A tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer _let_1 M)) (tptp.aa_nat_Code_integer _let_1 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))))) (forall ((A tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_power_rat A))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat _let_1 M)) (tptp.aa_nat_rat _let_1 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))))) (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))))) (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int _let_1 M)) (tptp.aa_nat_int _let_1 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))))) (forall ((N2 tptp.nat) (N7 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.power_8256067586552552935nteger A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) N7)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer _let_1 N2)) (tptp.aa_nat_Code_integer _let_1 N7))))))) (forall ((N2 tptp.nat) (N7 tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.power_power_rat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) N7)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat _let_1 N2)) (tptp.aa_nat_rat _let_1 N7))))))) (forall ((N2 tptp.nat) (N7 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) N7)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 N2)) (tptp.aa_nat_nat _let_1 N7))))))) (forall ((N2 tptp.nat) (N7 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) N7)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int _let_1 N2)) (tptp.aa_nat_int _let_1 N7))))))) (forall ((N2 tptp.nat) (N7 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.power_8256067586552552935nteger A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N7)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer _let_1 N2)) (tptp.aa_nat_Code_integer _let_1 N7))))))) (forall ((N2 tptp.nat) (N7 tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.power_power_rat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N7)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat _let_1 N2)) (tptp.aa_nat_rat _let_1 N7))))))) (forall ((N2 tptp.nat) (N7 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N7)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 N2)) (tptp.aa_nat_nat _let_1 N7))))))) (forall ((N2 tptp.nat) (N7 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N7)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int _let_1 N2)) (tptp.aa_nat_int _let_1 N7))))))) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger tptp.zero_z3403309356797280102nteger) N2) tptp.zero_z3403309356797280102nteger))) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_nat_rat (tptp.power_power_rat tptp.zero_zero_rat) N2) tptp.zero_zero_rat))) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int tptp.zero_zero_int) N2) tptp.zero_zero_int))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat))) B)))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat))))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2))))) (forall ((X tptp.fun_nat_fun_nat_nat) (Xa2 tptp.nat) (Xb tptp.nat) (Xc tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.accp_P4694664897847628410at_nat tptp.set_fo3699595496184130361el_nat (tptp.produc2818902965508115497at_nat X (tptp.produc487386426758144856at_nat Xa2 (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat Xb) Xc)))))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Xb) Xa2)))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat X Xa2) Xb) Xc) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y Xc)) (=> (not _let_2) (= Y (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat X (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Xa2) tptp.one_one_nat)) Xb) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat X Xa2) Xc))))) (not _let_1)))))))) (forall ((F tptp.fun_nat_fun_nat_nat) (A tptp.nat) (B tptp.nat) (Acc tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat F A) B) Acc))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A)))) (=> (tptp.accp_P4694664897847628410at_nat tptp.set_fo3699595496184130361el_nat (tptp.produc2818902965508115497at_nat F (tptp.produc487386426758144856at_nat A (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat B) Acc)))) (and (=> _let_2 (= _let_1 Acc)) (=> (not _let_2) (= _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat F (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) tptp.one_one_nat)) B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat F A) Acc))))))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) _let_1)) _let_1)))))) (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1)) _let_1)))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) _let_1)) _let_1)))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) _let_1)) _let_1)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B)))))))) (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Z) Y)) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Z) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Y)))))) (forall ((Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Z) Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Y)) Z))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) B))))) (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)))))) (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) B))))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B)))))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_3 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C))) (let ((_let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C))) (and (=> _let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_3) B))) (=> (not _let_4) (and (=> _let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) _let_3))) (=> (not _let_2) (tptp.pp (tptp.aa_rat_bool _let_1 tptp.zero_zero_rat)))))))))))) (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C))) (let ((_let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C)) A)) (and (=> _let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) _let_2))) (=> (not _let_3) (and (=> _let_1 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_2) B))) (=> (not _let_1) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))))))))) (forall ((B tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) A)) tptp.one_one_rat)) (or (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))) (= A tptp.zero_zero_rat)))) (forall ((B tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) A))) (or (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)))))) (forall ((N2 tptp.nat) (N7 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.power_8256067586552552935nteger A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) N7)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer _let_1 N7)) (tptp.aa_nat_Code_integer _let_1 N2)))))))) (forall ((N2 tptp.nat) (N7 tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.power_power_rat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) N7)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat _let_1 N7)) (tptp.aa_nat_rat _let_1 N2)))))))) (forall ((N2 tptp.nat) (N7 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) N7)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 N7)) (tptp.aa_nat_nat _let_1 N2)))))))) (forall ((N2 tptp.nat) (N7 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) N7)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int _let_1 N7)) (tptp.aa_nat_int _let_1 N2)))))))) (forall ((N2 tptp.nat) (N7 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.power_8256067586552552935nteger A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N7)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer _let_1 N7)) (tptp.aa_nat_Code_integer _let_1 N2)))))))) (forall ((N2 tptp.nat) (N7 tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.power_power_rat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N7)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat _let_1 N7)) (tptp.aa_nat_rat _let_1 N2)))))))) (forall ((N2 tptp.nat) (N7 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N7)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 N7)) (tptp.aa_nat_nat _let_1 N2)))))))) (forall ((N2 tptp.nat) (N7 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N7)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int _let_1 N7)) (tptp.aa_nat_int _let_1 N2)))))))) (forall ((N2 tptp.nat) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)) (= (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger B) N2)) (= A B))))))) (forall ((N2 tptp.nat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (= (= (tptp.aa_nat_rat (tptp.power_power_rat A) N2) (tptp.aa_nat_rat (tptp.power_power_rat B) N2)) (= A B))))))) (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) N2)) (= A B))))))) (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (= (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int B) N2)) (= A B))))))) (forall ((A tptp.code_integer) (N2 tptp.nat) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger B) N2)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= A B))))))) (forall ((A tptp.rat) (N2 tptp.nat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (tptp.aa_nat_rat (tptp.power_power_rat A) N2) (tptp.aa_nat_rat (tptp.power_power_rat B) N2)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= A B))))))) (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) N2)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= A B))))))) (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int B) N2)) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= A B))))))) (forall ((A tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer _let_1 M)) (tptp.aa_nat_Code_integer _let_1 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))))) (forall ((A tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_power_rat A))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat _let_1 M)) (tptp.aa_nat_rat _let_1 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))))) (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))))) (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int _let_1 M)) (tptp.aa_nat_int _let_1 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2)))))) (forall ((A tptp.rat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_nat_rat (tptp.power_power_rat A) N2)))))) (forall ((A tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N2)))))) (forall ((A tptp.int) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2)))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2))))))) (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N2))))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N2))))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2))))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) B))) B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B))) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) B))) B) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger C) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) B))))) (forall ((B tptp.code_natural) (A tptp.code_natural) (C tptp.code_natural)) (=> (not (= B tptp.zero_z2226904508553997617atural)) (= (tptp.divide5121882707175180666atural (tptp.plus_p4538020629002901425atural A (tptp.times_2397367101498566445atural C B)) B) (tptp.plus_p4538020629002901425atural C (tptp.divide5121882707175180666atural A B))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C))) B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C))) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C))) B) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger C) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) B))))) (forall ((B tptp.code_natural) (A tptp.code_natural) (C tptp.code_natural)) (=> (not (= B tptp.zero_z2226904508553997617atural)) (= (tptp.divide5121882707175180666atural (tptp.plus_p4538020629002901425atural A (tptp.times_2397367101498566445atural B C)) B) (tptp.plus_p4538020629002901425atural C (tptp.divide5121882707175180666atural A B))))) (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) B)) A)) B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B))))) (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B)) A)) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B))))) (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) B)) A)) B) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger C) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) B))))) (forall ((B tptp.code_natural) (C tptp.code_natural) (A tptp.code_natural)) (=> (not (= B tptp.zero_z2226904508553997617atural)) (= (tptp.divide5121882707175180666atural (tptp.plus_p4538020629002901425atural (tptp.times_2397367101498566445atural C B) A) B) (tptp.plus_p4538020629002901425atural C (tptp.divide5121882707175180666atural A B))))) (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C)) A)) B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B))))) (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C)) A)) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B))))) (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C)) A)) B) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger C) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) B))))) (forall ((B tptp.code_natural) (C tptp.code_natural) (A tptp.code_natural)) (=> (not (= B tptp.zero_z2226904508553997617atural)) (= (tptp.divide5121882707175180666atural (tptp.plus_p4538020629002901425atural (tptp.times_2397367101498566445atural B C) A) B) (tptp.plus_p4538020629002901425atural C (tptp.divide5121882707175180666atural A B))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) M)) N2) M))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N2)) N2) M))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C))) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger _let_1 A)) (tptp.aa_Cod1783974652533396728nteger _let_1 B)) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) B))))) (forall ((C tptp.code_natural) (A tptp.code_natural) (B tptp.code_natural)) (=> (not (= C tptp.zero_z2226904508553997617atural)) (= (tptp.divide5121882707175180666atural (tptp.times_2397367101498566445atural C A) (tptp.times_2397367101498566445atural C B)) (tptp.divide5121882707175180666atural A B)))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B)))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) B)))) (forall ((C tptp.code_natural) (A tptp.code_natural) (B tptp.code_natural)) (=> (not (= C tptp.zero_z2226904508553997617atural)) (= (tptp.divide5121882707175180666atural (tptp.times_2397367101498566445atural A C) (tptp.times_2397367101498566445atural B C)) (tptp.divide5121882707175180666atural A B)))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B)))))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (let ((_let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_int))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)))))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C))) (let ((_let_2 (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger _let_1 A)) (tptp.aa_Cod1783974652533396728nteger _let_1 B)))) (let ((_let_3 (= C tptp.zero_z3403309356797280102nteger))) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) B)))))))) (forall ((C tptp.code_natural) (A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (tptp.divide5121882707175180666atural (tptp.times_2397367101498566445atural C A) (tptp.times_2397367101498566445atural C B)))) (let ((_let_2 (= C tptp.zero_z2226904508553997617atural))) (and (=> _let_2 (= _let_1 tptp.zero_z2226904508553997617atural)) (=> (not _let_2) (= _let_1 (tptp.divide5121882707175180666atural A B))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2) tptp.zero_zero_nat))) (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N2) K))))) (forall ((M tptp.nat) (N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2)) M))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2) tptp.zero_zero_nat) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (= N2 tptp.zero_zero_nat)))) (forall ((M tptp.nat) (I2 tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat I2) N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2)) I2)))) (forall ((N2 tptp.nat) (M tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2))) M))) (forall ((M tptp.nat) (N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2)) N2)) M))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (tptp.pp (tptp.aa_nat_bool _let_1 N2)))))) (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 N2)) (tptp.aa_nat_nat _let_1 M))))))) (forall ((Q5 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) Q5)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) Q5)) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) Q5)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2) M) (= N2 tptp.one_one_nat)))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2)) M))))) (forall ((Q5 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) Q5)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N2) Q5))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) Q5)) N2))))) (forall ((P tptp.fun_nat_bool) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (= N2 tptp.zero_zero_nat))) (= (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2))) (and (=> _let_1 (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat))) (=> (not _let_1) (forall ((I4 tptp.nat) (J3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J3) N2)) (=> (= M (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) I4)) J3)) (tptp.pp (tptp.aa_nat_bool P I4)))))))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2)) N2)))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2))))))) (forall ((A3 tptp.nat) (B3 tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A3) B3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A3) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat B3) N2)) tptp.zero_zero_nat)) tptp.one_one_nat) tptp.zero_zero_nat))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B3) N2)))))) (forall ((X tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat X)) N2))) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) X)) (= N2 tptp.zero_zero_nat)))) (forall ((X tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X)) N2))) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) X)) (= N2 tptp.zero_zero_nat)))) (forall ((X tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X)) N2))) (or (tptp.pp (tptp.aa_nat_bool _let_1 X)) (= N2 tptp.zero_zero_nat))))) (forall ((X tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger X)) N2))) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) X)) (= N2 tptp.zero_zero_nat)))) (forall ((X tptp.nat) (Y tptp.nat) (C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_nat6120813132205607877r_bool tptp.nO_MAT8694959213317031834nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X) Y)) C)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) B)) C) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C))))) (forall ((X tptp.nat) (Y tptp.nat) (C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.nO_MATCH_nat_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X) Y)) C)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B)) C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C))))) (forall ((X tptp.nat) (Y tptp.nat) (C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.nO_MATCH_nat_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X) Y)) C)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C))))) (forall ((X tptp.nat) (Y tptp.nat) (C tptp.int) (A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_nat_fun_int_bool tptp.nO_MATCH_nat_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X) Y)) C)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C))))) (forall ((X tptp.int) (Y tptp.int) (C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_int3865899974016033897r_bool tptp.nO_MAT9066612773553876470nteger (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int X) Y)) C)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) B)) C) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C))))) (forall ((X tptp.int) (Y tptp.int) (C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.nO_MATCH_int_rat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int X) Y)) C)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B)) C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C))))) (forall ((X tptp.int) (Y tptp.int) (C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.nO_MATCH_int_nat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int X) Y)) C)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C))))) (forall ((X tptp.int) (Y tptp.int) (C tptp.int) (A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.nO_MATCH_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int X) Y)) C)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C))))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.nO_MAT8252062027627875367nteger (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger X) Y)) C)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) B)) C) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C))))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.nO_MAT7795273704451493282er_rat (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger X) Y)) C)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B)) C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C))))) (forall ((X tptp.nat) (Y tptp.nat) (A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_nat6120813132205607877r_bool tptp.nO_MAT8694959213317031834nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X) Y)) A)) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger B) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B)) (tptp.aa_Cod1783974652533396728nteger _let_1 C)))))) (forall ((X tptp.nat) (Y tptp.nat) (A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.nO_MATCH_nat_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X) Y)) A)) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat _let_1 B)) (tptp.aa_rat_rat _let_1 C)))))) (forall ((X tptp.nat) (Y tptp.nat) (A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.nO_MATCH_nat_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X) Y)) A)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_1 B)) (tptp.aa_nat_nat _let_1 C)))))) (forall ((X tptp.nat) (Y tptp.nat) (A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_nat_fun_int_bool tptp.nO_MATCH_nat_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X) Y)) A)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_1 B)) (tptp.aa_int_int _let_1 C)))))) (forall ((X tptp.int) (Y tptp.int) (A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_int3865899974016033897r_bool tptp.nO_MAT9066612773553876470nteger (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int X) Y)) A)) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger B) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B)) (tptp.aa_Cod1783974652533396728nteger _let_1 C)))))) (forall ((X tptp.int) (Y tptp.int) (A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.nO_MATCH_int_rat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int X) Y)) A)) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat _let_1 B)) (tptp.aa_rat_rat _let_1 C)))))) (forall ((X tptp.int) (Y tptp.int) (A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.nO_MATCH_int_nat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int X) Y)) A)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_1 B)) (tptp.aa_nat_nat _let_1 C)))))) (forall ((X tptp.int) (Y tptp.int) (A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.nO_MATCH_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int X) Y)) A)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_1 B)) (tptp.aa_int_int _let_1 C)))))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.nO_MAT8252062027627875367nteger (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger X) Y)) A)) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger B) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B)) (tptp.aa_Cod1783974652533396728nteger _let_1 C)))))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.nO_MAT7795273704451493282er_rat (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger X) Y)) A)) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat _let_1 B)) (tptp.aa_rat_rat _let_1 C)))))) (forall ((P tptp.fun_nat_bool) (M tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2))) (or (and (= N2 tptp.zero_zero_nat) (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat))) (exists ((Q6 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 Q6)) M)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc Q6)))) (tptp.pp (tptp.aa_nat_bool P Q6)))))))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.power_8256067586552552935nteger A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (tptp.aa_nat_Code_integer _let_1 N2))))) (forall ((N2 tptp.nat) (A tptp.assn)) (let ((_let_1 (tptp.power_power_assn A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.aa_nat_assn _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (tptp.aa_nat_assn _let_1 N2))))) (forall ((N2 tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.power_power_rat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (tptp.aa_nat_rat _let_1 N2))))) (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (tptp.aa_nat_nat _let_1 N2))))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (tptp.aa_nat_int _let_1 N2))))) (forall ((M tptp.nat) (P3 tptp.code_integer)) (let ((_let_1 (tptp.power_8256067586552552935nteger P3))) (let ((_let_2 (tptp.aa_nat_Code_integer _let_1 M))) (let ((_let_3 (= M tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_Code_integer)) (=> (not _let_3) (= _let_2 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger P3) (tptp.aa_nat_Code_integer _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat)))))))))) (forall ((M tptp.nat) (P3 tptp.assn)) (let ((_let_1 (tptp.power_power_assn P3))) (let ((_let_2 (tptp.aa_nat_assn _let_1 M))) (let ((_let_3 (= M tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_assn)) (=> (not _let_3) (= _let_2 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn P3) (tptp.aa_nat_assn _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat)))))))))) (forall ((M tptp.nat) (P3 tptp.rat)) (let ((_let_1 (tptp.power_power_rat P3))) (let ((_let_2 (tptp.aa_nat_rat _let_1 M))) (let ((_let_3 (= M tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_rat)) (=> (not _let_3) (= _let_2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat P3) (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat)))))))))) (forall ((M tptp.nat) (P3 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat P3))) (let ((_let_2 (tptp.aa_nat_nat _let_1 M))) (let ((_let_3 (= M tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_nat)) (=> (not _let_3) (= _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat P3) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat)))))))))) (forall ((M tptp.nat) (P3 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int P3))) (let ((_let_2 (tptp.aa_nat_int _let_1 M))) (let ((_let_3 (= M tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_int)) (=> (not _let_3) (= _let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int P3) (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat)))))))))) (forall ((A tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N2)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)))) (=> (not (= A tptp.zero_zero_nat)) (and (=> _let_3 (= _let_2 (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)))) (=> (not _let_3) (= _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.one_one_nat) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M))))))))))) (forall ((A tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int A))) (let ((_let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_nat_int _let_1 M)) (tptp.aa_nat_int _let_1 N2)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)))) (=> (not (= A tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)))) (=> (not _let_3) (= _let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int tptp.one_one_int) (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M))))))))))) (forall ((A tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger A))) (let ((_let_2 (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_nat_Code_integer _let_1 M)) (tptp.aa_nat_Code_integer _let_1 N2)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)))) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (and (=> _let_3 (= _let_2 (tptp.aa_nat_Code_integer _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)))) (=> (not _let_3) (= _let_2 (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (tptp.aa_nat_Code_integer _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M))))))))))) (forall ((A tptp.code_natural) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.power_7079662738309270450atural A))) (let ((_let_2 (tptp.divide5121882707175180666atural (tptp.aa_nat_Code_natural _let_1 M) (tptp.aa_nat_Code_natural _let_1 N2)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)))) (=> (not (= A tptp.zero_z2226904508553997617atural)) (and (=> _let_3 (= _let_2 (tptp.aa_nat_Code_natural _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)))) (=> (not _let_3) (= _let_2 (tptp.divide5121882707175180666atural tptp.one_one_Code_natural (tptp.aa_nat_Code_natural _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M))))))))))) (forall ((W2 tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W2))) (let ((_let_2 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_4 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) C))) (let ((_let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool _let_2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C))) (and (=> _let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_4) B))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) _let_4))) (=> (not _let_3) (tptp.pp (tptp.aa_rat_bool _let_2 tptp.zero_zero_rat))))))))))))) (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (tptp.aa_nat_nat tptp.suc Nat) (tptp.aa_nat_nat tptp.suc Nat2)) (= Nat Nat2))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (= (tptp.aa_nat_nat tptp.suc X2) (tptp.aa_nat_nat tptp.suc Y2)) (= X2 Y2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)) (= M N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2)) (= M N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2)) (= M N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_Code_natural_bool (tptp.aa_Cod6910080592713026658l_bool tptp.ord_le1926595141338095240atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural M)) (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)) (tptp.aa_num_rat tptp.numeral_numeral_rat N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat M)) (tptp.aa_num_nat tptp.numeral_numeral_nat N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_num_int tptp.numeral_numeral_int N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_num_nat tptp.numeral_numeral_nat M)) (tptp.aa_num_nat tptp.numeral_numeral_nat N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_num_int tptp.numeral_numeral_int N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)) (tptp.aa_num_rat tptp.numeral_numeral_rat N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_Code_natural_bool (tptp.aa_Cod6910080592713026658l_bool tptp.ord_le5570908160329646204atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural M)) (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N2)))) (forall ((V tptp.num) (W2 tptp.num) (Z tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat V)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat W2)) Z)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W2))) Z))) (forall ((V tptp.num) (W2 tptp.num) (Z tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int V)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int W2)) Z)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W2))) Z))) (forall ((V tptp.num) (W2 tptp.num) (Z tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger V)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger W2)) Z)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W2))) Z))) (forall ((V tptp.num) (W2 tptp.num) (Z tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W2)) Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W2))) Z))) (forall ((V tptp.num) (W2 tptp.num) (Z tptp.code_natural)) (= (tptp.times_2397367101498566445atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural V) (tptp.times_2397367101498566445atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural W2) Z)) (tptp.times_2397367101498566445atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W2)) Z))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat M)) (tptp.aa_num_nat tptp.numeral_numeral_nat N2)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_num_int tptp.numeral_numeral_int N2)) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)) (tptp.aa_num_rat tptp.numeral_numeral_rat N2)) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.times_2397367101498566445atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural M) (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural N2)) (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2)))) (forall ((A tptp.code_integer) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.power_8256067586552552935nteger A))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (tptp.aa_nat_Code_integer _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N2))) (tptp.aa_nat_Code_integer _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)))))) (forall ((A tptp.assn) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.power_power_assn A))) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.aa_nat_assn _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (tptp.aa_nat_assn _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N2))) (tptp.aa_nat_assn _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)))))) (forall ((A tptp.rat) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.power_power_rat A))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (tptp.aa_nat_rat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N2))) (tptp.aa_nat_rat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)))))) (forall ((A tptp.nat) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N2))) (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)))))) (forall ((A tptp.int) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int A))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (tptp.aa_nat_int _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N2))) (tptp.aa_nat_int _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)))))) (forall ((A tptp.code_integer) (M tptp.num) (N2 tptp.num) (B tptp.code_integer)) (let ((_let_1 (tptp.power_8256067586552552935nteger A))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N2))) B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)))) B)))) (forall ((A tptp.assn) (M tptp.num) (N2 tptp.num) (B tptp.assn)) (let ((_let_1 (tptp.power_power_assn A))) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.aa_nat_assn _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.aa_nat_assn _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N2))) B)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.aa_nat_assn _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)))) B)))) (forall ((A tptp.rat) (M tptp.num) (N2 tptp.num) (B tptp.rat)) (let ((_let_1 (tptp.power_power_rat A))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N2))) B)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)))) B)))) (forall ((A tptp.nat) (M tptp.num) (N2 tptp.num) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N2))) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)))) B)))) (forall ((A tptp.int) (M tptp.num) (N2 tptp.num) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int A))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N2))) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)))) B)))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat tptp.suc N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc M)) (tptp.aa_nat_nat tptp.suc N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc M)) (tptp.aa_nat_nat tptp.suc N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_nat_nat tptp.suc M))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat _let_1 N2))))) (forall ((M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) M) tptp.zero_zero_nat)) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)) (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat tptp.suc M)) N2)) (tptp.aa_nat_nat tptp.suc K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) K))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat tptp.suc M)) (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2))) (forall ((I2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) N2)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat _let_1 I2)) I2)))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat I2))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 J)) K) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) K))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N2) M))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger A) B))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) A)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger A) B))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) A)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger A) B))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger B) A)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger A) B))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger B) A)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)))) (forall ((B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) B)) A))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) B)) A))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)) A))) (forall ((B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) B)) B) A))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) B)) B) A))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)) B) A))) (forall ((V tptp.num) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat V)))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_1 B)) (tptp.aa_nat_nat _let_1 C))))) (forall ((V tptp.num) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int V)))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_1 B)) (tptp.aa_int_int _let_1 C))))) (forall ((V tptp.num) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger V)))) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger B) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B)) (tptp.aa_Cod1783974652533396728nteger _let_1 C))))) (forall ((V tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V)))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat _let_1 B)) (tptp.aa_rat_rat _let_1 C))))) (forall ((V tptp.num) (B tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural V))) (= (tptp.times_2397367101498566445atural _let_1 (tptp.plus_p4538020629002901425atural B C)) (tptp.plus_p4538020629002901425atural (tptp.times_2397367101498566445atural _let_1 B) (tptp.times_2397367101498566445atural _let_1 C))))) (forall ((A tptp.nat) (B tptp.nat) (V tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat V))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) _let_1))))) (forall ((A tptp.int) (B tptp.int) (V tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int V))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) _let_1))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (V tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger V))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) B)) _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) _let_1)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) _let_1))))) (forall ((A tptp.rat) (B tptp.rat) (V tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat V))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B)) _let_1) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) _let_1))))) (forall ((A tptp.code_natural) (B tptp.code_natural) (V tptp.num)) (let ((_let_1 (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural V))) (= (tptp.times_2397367101498566445atural (tptp.plus_p4538020629002901425atural A B) _let_1) (tptp.plus_p4538020629002901425atural (tptp.times_2397367101498566445atural A _let_1) (tptp.times_2397367101498566445atural B _let_1))))) (forall ((V tptp.num) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int V)))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 B)) (tptp.aa_int_int _let_1 C))))) (forall ((V tptp.num) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger V)))) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger B) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B)) (tptp.aa_Cod1783974652533396728nteger _let_1 C))))) (forall ((V tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V)))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat B) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 B)) (tptp.aa_rat_rat _let_1 C))))) (forall ((A tptp.int) (B tptp.int) (V tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int V))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)) _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) _let_1))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (V tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger V))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger A) B)) _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) _let_1)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) _let_1))))) (forall ((A tptp.rat) (B tptp.rat) (V tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat V))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) B)) _let_1) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) _let_1))))) (forall ((B tptp.nat) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) A)) B) tptp.zero_zero_nat)) (forall ((B tptp.int) (A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) A)) B) tptp.zero_zero_int)) (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) A)) B) tptp.zero_z3403309356797280102nteger)) (forall ((B tptp.code_natural) (A tptp.code_natural)) (= (tptp.modulo8411746178871703098atural (tptp.times_2397367101498566445atural B A) B) tptp.zero_z2226904508553997617atural)) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B)) B) tptp.zero_zero_nat)) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) B) tptp.zero_zero_int)) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)) B) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (tptp.modulo8411746178871703098atural (tptp.times_2397367101498566445atural A B) B) tptp.zero_z2226904508553997617atural)) (forall ((M tptp.nat)) (= (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M) tptp.zero_zero_int) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M) tptp.zero_z3403309356797280102nteger) (= M tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2)) (= tptp.zero_zero_nat N2))) (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)) (= tptp.zero_zero_nat N2))) (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2)) (= tptp.zero_zero_nat N2))) (forall ((N2 tptp.nat)) (= (= tptp.zero_z3403309356797280102nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2)) (= tptp.zero_zero_nat N2))) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat tptp.zero_zero_nat) tptp.zero_zero_rat) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat tptp.zero_zero_nat) tptp.zero_zero_nat) (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger tptp.zero_zero_nat) tptp.zero_z3403309356797280102nteger) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) B))) B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B))) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) B))) B) (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) B))) (forall ((A tptp.code_natural) (C tptp.code_natural) (B tptp.code_natural)) (= (tptp.modulo8411746178871703098atural (tptp.plus_p4538020629002901425atural A (tptp.times_2397367101498566445atural C B)) B) (tptp.modulo8411746178871703098atural A B))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C))) B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C))) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C))) B) (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) B))) (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (= (tptp.modulo8411746178871703098atural (tptp.plus_p4538020629002901425atural A (tptp.times_2397367101498566445atural B C)) B) (tptp.modulo8411746178871703098atural A B))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) B)) A)) B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B))) (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B)) A)) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B))) (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) B)) A)) B) (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) B))) (forall ((C tptp.code_natural) (B tptp.code_natural) (A tptp.code_natural)) (= (tptp.modulo8411746178871703098atural (tptp.plus_p4538020629002901425atural (tptp.times_2397367101498566445atural C B) A) B) (tptp.modulo8411746178871703098atural A B))) (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C)) A)) B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B))) (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C)) A)) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B))) (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C)) A)) B) (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) B))) (forall ((B tptp.code_natural) (C tptp.code_natural) (A tptp.code_natural)) (= (tptp.modulo8411746178871703098atural (tptp.plus_p4538020629002901425atural (tptp.times_2397367101498566445atural B C) A) B) (tptp.modulo8411746178871703098atural A B))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat tptp.suc N2)))) (forall ((N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (= N2 tptp.zero_zero_nat))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2)))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N2) _let_1) (and (= M _let_1) (= N2 _let_1))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N2)) (and (= M _let_1) (= N2 _let_1))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2) tptp.zero_zero_nat))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2) tptp.zero_zero_nat) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (forall ((N2 tptp.nat)) (= (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2) tptp.one_one_rat) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2) tptp.one_one_int) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2) tptp.one_one_nat) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2) tptp.one_one_Code_integer) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= tptp.one_one_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2)) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= tptp.one_one_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= tptp.one_one_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2)) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= tptp.one_one_Code_integer (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2)) (= N2 tptp.one_one_nat))) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat tptp.one_one_nat) tptp.one_one_rat) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat tptp.one_one_nat) tptp.one_one_nat) (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger tptp.one_one_nat) tptp.one_one_Code_integer) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) (tptp.aa_nat_nat _let_1 N2))))) (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) J)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat I2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) K)) J)))) (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) J)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) K)) I2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) I2)) K)))) (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) J)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 J)) K))))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat tptp.suc N2)) tptp.one_one_nat) N2)) (forall ((B tptp.rat) (W2 tptp.num) (A tptp.rat)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W2))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) _let_1)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1)))))) (forall ((A tptp.rat) (B tptp.rat) (W2 tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W2))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) _let_1))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1)) B))))) (forall ((B tptp.rat) (W2 tptp.num) (A tptp.rat)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W2))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) _let_1) A) (and (=> (not _let_2) (= B (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1))) (=> _let_2 (= A tptp.zero_zero_rat))))))) (forall ((A tptp.rat) (B tptp.rat) (W2 tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W2))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= A (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) _let_1)) (and (=> (not _let_2) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_rat))))))) (forall ((B tptp.rat) (W2 tptp.num) (A tptp.rat)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W2))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) _let_1)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1)))))) (forall ((A tptp.rat) (B tptp.rat) (W2 tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W2))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) _let_1))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1)) B))))) (forall ((M tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M)) tptp.zero_z3403309356797280102nteger)) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat)) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat)) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int)) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat tptp.suc M)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat tptp.one_one_rat) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)))) (forall ((M tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat tptp.suc M)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)))) (forall ((M tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat tptp.suc M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)))) (forall ((M tptp.nat)) (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat tptp.suc M)) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M)))) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N2))) (and (tptp.pp (tptp.aa_nat_bool _let_1 M)) (tptp.pp (tptp.aa_nat_bool _let_1 N2)))))) (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) J)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat I2) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) K))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) K)) (tptp.aa_nat_nat tptp.suc J))))) (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) J)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) K))) I2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat tptp.suc J)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) I2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) M)) (= (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat))))))) (forall ((N2 tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((N2 tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2))) (tptp.pp (tptp.aa_nat_bool _let_1 N2))))) (forall ((N2 tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat)) N2))) (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat B)) W2)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) W2)) X)))) (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int B)) W2)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) W2)) X)))) (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat B)) W2)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) W2)) X)))) (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger B)) W2)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) W2)) X)))) (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat X)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat B)) W2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) W2))))) (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int B)) W2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) W2))))) (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat B)) W2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) W2))))) (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger X)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger B)) W2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) W2))))) (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger X)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger B)) W2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) W2))))) (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat X)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat B)) W2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) W2))))) (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat B)) W2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) W2))))) (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int B)) W2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) W2))))) (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger B)) W2)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) W2)) X)))) (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat B)) W2)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) W2)) X)))) (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat B)) W2)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) W2)) X)))) (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int B)) W2)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) W2)) X)))) (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat X)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat I2)) N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I2)) N2))))) (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_Code_natural_bool (tptp.aa_Cod6910080592713026658l_bool tptp.ord_le5570908160329646204atural (tptp.aa_nat_Code_natural tptp.semiri3763490453095760265atural X)) (tptp.aa_nat_Code_natural (tptp.power_7079662738309270450atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural I2)) N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I2)) N2))))) (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int I2)) N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I2)) N2))))) (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I2)) N2))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X)) _let_1)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) _let_1))))) (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger X)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger I2)) N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I2)) N2))))) (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat I2)) N2)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I2)) N2)) X)))) (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_Code_natural_bool (tptp.aa_Cod6910080592713026658l_bool tptp.ord_le5570908160329646204atural (tptp.aa_nat_Code_natural (tptp.power_7079662738309270450atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural I2)) N2)) (tptp.aa_nat_Code_natural tptp.semiri3763490453095760265atural X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I2)) N2)) X)))) (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int I2)) N2)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I2)) N2)) X)))) (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I2)) N2)))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X))) (tptp.pp (tptp.aa_nat_bool _let_1 X))))) (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger I2)) N2)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I2)) N2)) X)))) (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_Code_natural_bool (tptp.aa_Cod6910080592713026658l_bool tptp.ord_le1926595141338095240atural (tptp.aa_nat_Code_natural tptp.semiri3763490453095760265atural X)) (tptp.aa_nat_Code_natural (tptp.power_7079662738309270450atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural I2)) N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I2)) N2))))) (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger X)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger I2)) N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I2)) N2))))) (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat X)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat I2)) N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I2)) N2))))) (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I2)) N2))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X)) _let_1)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) _let_1))))) (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int I2)) N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I2)) N2))))) (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_Code_natural_bool (tptp.aa_Cod6910080592713026658l_bool tptp.ord_le1926595141338095240atural (tptp.aa_nat_Code_natural (tptp.power_7079662738309270450atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural I2)) N2)) (tptp.aa_nat_Code_natural tptp.semiri3763490453095760265atural X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I2)) N2)) X)))) (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger I2)) N2)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I2)) N2)) X)))) (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat I2)) N2)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I2)) N2)) X)))) (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I2)) N2)))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X))) (tptp.pp (tptp.aa_nat_bool _let_1 X))))) (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int I2)) N2)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat I2)) N2)) X)))) (forall ((P tptp.fun_nat_bool) (N2 tptp.nat) (P3 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) P3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) P3)) (=> (forall ((N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N5) P3)) (=> (tptp.pp (tptp.aa_nat_bool P N5)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc N5)) P3)))))) (tptp.pp (tptp.aa_nat_bool P M))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N2))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (and (=> _let_2 (= _let_1 M)) (=> (not _let_2) (= _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) (tptp.aa_nat_nat tptp.suc N2))) N2))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) N2)))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)) (= (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_nat _let_1 N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) (tptp.aa_nat_nat tptp.suc M)))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat tptp.suc M)) N2) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2))))) (forall ((P tptp.fun_nat_bool) (K tptp.nat) (I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P K)) (=> (forall ((N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc N5))) (tptp.pp (tptp.aa_nat_bool P N5)))) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat K) I2)))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat I2))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 J)) K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 K)) J)))) (forall ((N2 tptp.nat)) (not (= N2 (tptp.aa_nat_nat tptp.suc N2)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (= (tptp.aa_nat_nat tptp.suc X) (tptp.aa_nat_nat tptp.suc Y)) (= X Y))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) N2)))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (= (tptp.aa_nat_nat tptp.suc N2) M) (= N2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 tptp.one_one_nat)) N2)))) (forall ((N2 tptp.nat)) (not (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat tptp.suc N2)) tptp.zero_zero_rat))) (forall ((N2 tptp.nat)) (not (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat tptp.suc N2)) tptp.zero_zero_int))) (forall ((N2 tptp.nat)) (not (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat tptp.suc N2)) tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (not (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat tptp.suc N2)) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B)) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) B)) B)) (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) B))) (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (tptp.minus_7197305767214868737atural A (tptp.times_2397367101498566445atural (tptp.divide5121882707175180666atural A B) B)) (tptp.modulo8411746178871703098atural A B))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B)) B))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger A) (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) B)) B))) (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (tptp.minus_7197305767214868737atural A (tptp.modulo8411746178871703098atural A B)) (tptp.times_2397367101498566445atural (tptp.divide5121882707175180666atural A B) B))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger A) (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) B)))) (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (tptp.minus_7197305767214868737atural A (tptp.modulo8411746178871703098atural A B)) (tptp.times_2397367101498566445atural B (tptp.divide5121882707175180666atural A B)))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) B))) (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) B))) (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (tptp.minus_7197305767214868737atural A (tptp.times_2397367101498566445atural B (tptp.divide5121882707175180666atural A B))) (tptp.modulo8411746178871703098atural A B))) (forall ((M tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) K)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_nat_int _let_1 M)) K) (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))))))) (forall ((N2 tptp.nat) (I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) (tptp.aa_nat_nat tptp.suc I2))) N2)))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat B) C))) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B)) C))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int B) C))) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) C))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger B) C))) C) (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)) C))) (forall ((A tptp.code_natural) (C tptp.code_natural) (B tptp.code_natural)) (= (tptp.modulo8411746178871703098atural (tptp.times_2397367101498566445atural (tptp.modulo8411746178871703098atural A C) (tptp.modulo8411746178871703098atural B C)) C) (tptp.modulo8411746178871703098atural (tptp.times_2397367101498566445atural A B) C))) (forall ((A tptp.nat) (C tptp.nat) (A2 tptp.nat) (B tptp.nat) (B2 tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A2) C)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat B) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat B2) C)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B)) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A2) B2)) C))))) (forall ((A tptp.int) (C tptp.int) (A2 tptp.int) (B tptp.int) (B2 tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A2) C)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int B) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int B2) C)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A2) B2)) C))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (A2 tptp.code_integer) (B tptp.code_integer) (B2 tptp.code_integer)) (=> (= (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) C) (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A2) C)) (=> (= (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger B) C) (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger B2) C)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)) C) (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A2) B2)) C))))) (forall ((A tptp.code_natural) (C tptp.code_natural) (A2 tptp.code_natural) (B tptp.code_natural) (B2 tptp.code_natural)) (=> (= (tptp.modulo8411746178871703098atural A C) (tptp.modulo8411746178871703098atural A2 C)) (=> (= (tptp.modulo8411746178871703098atural B C) (tptp.modulo8411746178871703098atural B2 C)) (= (tptp.modulo8411746178871703098atural (tptp.times_2397367101498566445atural A B) C) (tptp.modulo8411746178871703098atural (tptp.times_2397367101498566445atural A2 B2) C))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B)) C))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B)) C))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) B)) C))) (forall ((A tptp.code_natural) (C tptp.code_natural) (B tptp.code_natural)) (= (tptp.modulo8411746178871703098atural (tptp.times_2397367101498566445atural A C) (tptp.times_2397367101498566445atural B C)) (tptp.times_2397367101498566445atural (tptp.modulo8411746178871703098atural A B) C))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C))) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) B)) (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger _let_1 A)) (tptp.aa_Cod1783974652533396728nteger _let_1 B))))) (forall ((C tptp.code_natural) (A tptp.code_natural) (B tptp.code_natural)) (= (tptp.times_2397367101498566445atural C (tptp.modulo8411746178871703098atural A B)) (tptp.modulo8411746178871703098atural (tptp.times_2397367101498566445atural C A) (tptp.times_2397367101498566445atural C B)))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) C)) B)) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B)) C))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) C)) B)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) C))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) C)) B)) C) (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)) C))) (forall ((A tptp.code_natural) (C tptp.code_natural) (B tptp.code_natural)) (= (tptp.modulo8411746178871703098atural (tptp.times_2397367101498566445atural (tptp.modulo8411746178871703098atural A C) B) C) (tptp.modulo8411746178871703098atural (tptp.times_2397367101498566445atural A B) C))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat B) C))) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat _let_1 B)) C)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int B) C))) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int _let_1 B)) C)))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger B) C))) C) (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B)) C)))) (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (= (tptp.modulo8411746178871703098atural (tptp.times_2397367101498566445atural A (tptp.modulo8411746178871703098atural B C)) C) (tptp.modulo8411746178871703098atural (tptp.times_2397367101498566445atural A B) C))) (forall ((A tptp.rat) (B tptp.rat) (D2 tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat D2) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat B) D2)))))) (forall ((A tptp.int) (B tptp.int) (D2 tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int D2) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) D2)))))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B)))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.minus_minus_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat B) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) C))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat C) D2)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) D2))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int C) D2)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) D2))))) (forall ((X tptp.nat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat X))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) Y) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) _let_1)))) (forall ((X tptp.nat) (Y tptp.int)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) Y) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) _let_1)))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) Y) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Y) _let_1)))) (forall ((X tptp.nat) (Y tptp.code_integer)) (let ((_let_1 (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger X))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) Y) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger Y) _let_1)))) (forall ((A tptp.rat) (B tptp.rat) (D2 tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat D2) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat B) D2)))))) (forall ((A tptp.int) (B tptp.int) (D2 tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int D2) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) D2)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat C) D2)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) D2))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int C) D2)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) D2))))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B)))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.minus_minus_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat B) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) C))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A))) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger B) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B)) (tptp.aa_Cod1783974652533396728nteger _let_1 C))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat B) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 B)) (tptp.aa_rat_rat _let_1 C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat B) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 B)) (tptp.aa_nat_nat _let_1 C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 B)) (tptp.aa_int_int _let_1 C))))) (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger B) C)) A) (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) A)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) A)))) (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat B) C)) A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) A)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) A)))) (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat B) C)) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) A)))) (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) C)) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) A)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) A)))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A))) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger B) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B)) (tptp.aa_Cod1783974652533396728nteger _let_1 C))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat B) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 B)) (tptp.aa_rat_rat _let_1 C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 B)) (tptp.aa_int_int _let_1 C))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger A) B)) C) (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) B)) C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C)))) (forall ((P tptp.fun_Co8822979462182099027r_bool) (D3 tptp.code_integer) (Q tptp.fun_Co8822979462182099027r_bool)) (=> (forall ((X3 tptp.code_integer) (K2 tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool P X3)) (tptp.pp (tptp.aa_Code_integer_bool P (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger X3) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger K2) D3)))))) (=> (forall ((X3 tptp.code_integer) (K2 tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool Q X3)) (tptp.pp (tptp.aa_Code_integer_bool Q (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger X3) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger K2) D3)))))) (forall ((X5 tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger X5) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger K4) D3)))) (= (and (tptp.pp (tptp.aa_Code_integer_bool P X5)) (tptp.pp (tptp.aa_Code_integer_bool Q X5))) (and (tptp.pp (tptp.aa_Code_integer_bool P _let_1)) (tptp.pp (tptp.aa_Code_integer_bool Q _let_1))))))))) (forall ((P tptp.fun_rat_bool) (D3 tptp.rat) (Q tptp.fun_rat_bool)) (=> (forall ((X3 tptp.rat) (K2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool P X3)) (tptp.pp (tptp.aa_rat_bool P (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat X3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat K2) D3)))))) (=> (forall ((X3 tptp.rat) (K2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool Q X3)) (tptp.pp (tptp.aa_rat_bool Q (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat X3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat K2) D3)))))) (forall ((X5 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat X5) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat K4) D3)))) (= (and (tptp.pp (tptp.aa_rat_bool P X5)) (tptp.pp (tptp.aa_rat_bool Q X5))) (and (tptp.pp (tptp.aa_rat_bool P _let_1)) (tptp.pp (tptp.aa_rat_bool Q _let_1))))))))) (forall ((P tptp.fun_int_bool) (D3 tptp.int) (Q tptp.fun_int_bool)) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K2) D3)))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool Q X3)) (tptp.pp (tptp.aa_int_bool Q (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K2) D3)))))) (forall ((X5 tptp.int) (K4 tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X5) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K4) D3)))) (= (and (tptp.pp (tptp.aa_int_bool P X5)) (tptp.pp (tptp.aa_int_bool Q X5))) (and (tptp.pp (tptp.aa_int_bool P _let_1)) (tptp.pp (tptp.aa_int_bool Q _let_1))))))))) (forall ((P tptp.fun_Co8822979462182099027r_bool) (D3 tptp.code_integer) (Q tptp.fun_Co8822979462182099027r_bool)) (=> (forall ((X3 tptp.code_integer) (K2 tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool P X3)) (tptp.pp (tptp.aa_Code_integer_bool P (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger X3) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger K2) D3)))))) (=> (forall ((X3 tptp.code_integer) (K2 tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool Q X3)) (tptp.pp (tptp.aa_Code_integer_bool Q (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger X3) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger K2) D3)))))) (forall ((X5 tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger X5) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger K4) D3)))) (= (or (tptp.pp (tptp.aa_Code_integer_bool P X5)) (tptp.pp (tptp.aa_Code_integer_bool Q X5))) (or (tptp.pp (tptp.aa_Code_integer_bool P _let_1)) (tptp.pp (tptp.aa_Code_integer_bool Q _let_1))))))))) (forall ((P tptp.fun_rat_bool) (D3 tptp.rat) (Q tptp.fun_rat_bool)) (=> (forall ((X3 tptp.rat) (K2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool P X3)) (tptp.pp (tptp.aa_rat_bool P (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat X3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat K2) D3)))))) (=> (forall ((X3 tptp.rat) (K2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool Q X3)) (tptp.pp (tptp.aa_rat_bool Q (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat X3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat K2) D3)))))) (forall ((X5 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat X5) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat K4) D3)))) (= (or (tptp.pp (tptp.aa_rat_bool P X5)) (tptp.pp (tptp.aa_rat_bool Q X5))) (or (tptp.pp (tptp.aa_rat_bool P _let_1)) (tptp.pp (tptp.aa_rat_bool Q _let_1))))))))) (forall ((P tptp.fun_int_bool) (D3 tptp.int) (Q tptp.fun_int_bool)) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K2) D3)))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool Q X3)) (tptp.pp (tptp.aa_int_bool Q (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K2) D3)))))) (forall ((X5 tptp.int) (K4 tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X5) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K4) D3)))) (= (or (tptp.pp (tptp.aa_int_bool P X5)) (tptp.pp (tptp.aa_int_bool Q X5))) (or (tptp.pp (tptp.aa_int_bool P _let_1)) (tptp.pp (tptp.aa_int_bool Q _let_1))))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N2)) M))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int A)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int B))))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int A)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int B))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2) tptp.zero_zero_nat) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M) tptp.zero_zero_nat) (= M N2)))) (forall ((M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.zero_zero_nat) M)) (forall ((M tptp.nat) (N2 tptp.nat) (L tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat L))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M))) (=> (tptp.pp (tptp.aa_nat_bool _let_2 N2)) (=> (tptp.pp (tptp.aa_nat_bool _let_2 L)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 N2)) (tptp.aa_nat_nat _let_1 M)))))))) (forall ((J tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) N2)) K)))) (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (exists ((M5 tptp.nat)) (= N2 (tptp.aa_nat_nat tptp.suc M5))))) (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (tptp.aa_nat_nat tptp.suc M)))) (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (tptp.aa_nat_nat tptp.suc M)))) (forall ((M tptp.nat)) (not (= (tptp.aa_nat_nat tptp.suc M) tptp.zero_zero_nat))) (forall ((P tptp.fun_nat_bool) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P K)) (=> (forall ((N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc N5))) (tptp.pp (tptp.aa_nat_bool P N5)))) (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat))))) (forall ((P tptp.fun_nat_fun_nat_bool) (M tptp.nat) (N2 tptp.nat)) (=> (forall ((X3 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P X3) tptp.zero_zero_nat))) (=> (forall ((Y3 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P tptp.zero_zero_nat) (tptp.aa_nat_nat tptp.suc Y3)))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P X3) Y3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P (tptp.aa_nat_nat tptp.suc X3)) (tptp.aa_nat_nat tptp.suc Y3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P M) N2)))))) (forall ((P tptp.fun_nat_bool) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat)) (=> (forall ((N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P N5)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc N5))))) (tptp.pp (tptp.aa_nat_bool P N2))))) (forall ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y (tptp.aa_nat_nat tptp.suc Nat3))))))) (forall ((Nat tptp.nat) (X2 tptp.nat)) (=> (= Nat (tptp.aa_nat_nat tptp.suc X2)) (not (= Nat tptp.zero_zero_nat)))) (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (tptp.aa_nat_nat tptp.suc Nat2)))) (forall ((Nat2 tptp.nat)) (not (= (tptp.aa_nat_nat tptp.suc Nat2) tptp.zero_zero_nat))) (forall ((X2 tptp.nat)) (not (= tptp.zero_zero_nat (tptp.aa_nat_nat tptp.suc X2)))) (forall ((I2 tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) K)) (=> (not (= K (tptp.aa_nat_nat tptp.suc I2))) (not (forall ((J2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) J2)) (not (= K (tptp.aa_nat_nat tptp.suc J2))))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc M)) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (forall ((I2 tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc I2)) K)) (not (forall ((J2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) J2)) (not (= K (tptp.aa_nat_nat tptp.suc J2)))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc M))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (=> (not (= _let_1 N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) N2)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat tptp.suc N2))) (=> (not (tptp.pp (tptp.aa_nat_bool _let_1 N2))) (= M N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 N2)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat tptp.suc N2)))))) (forall ((N2 tptp.nat) (P tptp.fun_nat_bool)) (= (exists ((I4 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.aa_nat_nat tptp.suc N2))) (tptp.pp (tptp.aa_nat_bool P I4)))) (or (tptp.pp (tptp.aa_nat_bool P N2)) (exists ((I4 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) N2)) (tptp.pp (tptp.aa_nat_bool P I4))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat tptp.suc N2))) (or (tptp.pp (tptp.aa_nat_bool _let_1 N2)) (= M N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat tptp.suc M))))) (forall ((N2 tptp.nat) (P tptp.fun_nat_bool)) (= (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.aa_nat_nat tptp.suc N2))) (tptp.pp (tptp.aa_nat_bool P I4)))) (and (tptp.pp (tptp.aa_nat_bool P N2)) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) N2)) (tptp.pp (tptp.aa_nat_bool P I4))))))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc N2)) M)) (exists ((M7 tptp.nat)) (and (= M (tptp.aa_nat_nat tptp.suc M7)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M7)))))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2))) (=> (not (tptp.pp (tptp.aa_nat_bool _let_1 M))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat tptp.suc M))) (= M N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc M)) (tptp.aa_nat_nat tptp.suc N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) J)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc I2)) K))))) (forall ((I2 tptp.nat) (J tptp.nat) (P tptp.fun_nat_fun_nat_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) J)) (=> (forall ((I3 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P I3) (tptp.aa_nat_nat tptp.suc I3)))) (=> (forall ((I3 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool P I3))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) J2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J2) K2)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 J2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P J2) K2)) (tptp.pp (tptp.aa_nat_bool _let_1 K2)))))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P I2) J)))))) (forall ((I2 tptp.nat) (J tptp.nat) (P tptp.fun_nat_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) J)) (=> (forall ((I3 tptp.nat)) (=> (= J (tptp.aa_nat_nat tptp.suc I3)) (tptp.pp (tptp.aa_nat_bool P I3)))) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) J)) (=> (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc I3))) (tptp.pp (tptp.aa_nat_bool P I3))))) (tptp.pp (tptp.aa_nat_bool P I2)))))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2))) (=> (not (tptp.pp (tptp.aa_nat_bool _let_1 M))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat tptp.suc M))) (= N2 M))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 M)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 N2)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K)) (= M N2)))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 M)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 N2)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2))))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K))) (=> (tptp.pp (tptp.aa_nat_bool _let_2 M)) (=> (tptp.pp (tptp.aa_nat_bool _let_2 N2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K)) (tptp.aa_nat_nat _let_1 N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (L tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) L)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) L))))) (forall ((M tptp.nat) (N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) M))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) C)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 C)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_2 A)) (tptp.aa_nat_nat _let_2 B))) (tptp.pp (tptp.aa_nat_bool _let_1 A)))))))) (forall ((M tptp.nat) (N2 tptp.nat) (L tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat L))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 N2)) (tptp.aa_nat_nat _let_1 M)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2)) N2) M)) (forall ((N2 tptp.nat) (M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) M)) N2) M)) (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc M)) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M))) (=> (tptp.pp (tptp.aa_nat_bool _let_2 _let_1)) (=> (not (tptp.pp (tptp.aa_nat_bool _let_2 N2))) (= M _let_1)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 N2)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat tptp.suc N2)))))) (forall ((N2 tptp.nat) (M8 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc N2)) M8)) (exists ((M5 tptp.nat)) (= M8 (tptp.aa_nat_nat tptp.suc M5))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M))) (= (tptp.pp (tptp.aa_nat_bool _let_2 _let_1)) (or (tptp.pp (tptp.aa_nat_bool _let_2 N2)) (= M _let_1)))))) (forall ((N2 tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc N2)) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc N2)) M)))) (forall ((P tptp.fun_nat_bool) (N2 tptp.nat)) (=> (forall ((N5 tptp.nat)) (=> (forall ((M4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc M4)) N5)) (tptp.pp (tptp.aa_nat_bool P M4)))) (tptp.pp (tptp.aa_nat_bool P N5)))) (tptp.pp (tptp.aa_nat_bool P N2)))) (forall ((M tptp.nat) (N2 tptp.nat) (P tptp.fun_nat_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (=> (tptp.pp (tptp.aa_nat_bool P M)) (=> (forall ((N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N5)) (=> (tptp.pp (tptp.aa_nat_bool P N5)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc N5)))))) (tptp.pp (tptp.aa_nat_bool P N2)))))) (forall ((M tptp.nat) (N2 tptp.nat) (R tptp.fun_nat_fun_nat_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (=> (forall ((X3 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R X3) X3))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool R X3))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 Y3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R Y3) Z2)) (tptp.pp (tptp.aa_nat_bool _let_1 Z2)))))) (=> (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R N5) (tptp.aa_nat_nat tptp.suc N5)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R M) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat tptp.suc M)) N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) (tptp.aa_nat_nat tptp.suc N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat tptp.suc M)) N2) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2)))) (forall ((A3 tptp.nat) (K tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K))) (=> (= A3 (tptp.aa_nat_nat _let_1 A)) (= (tptp.aa_nat_nat tptp.suc A3) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc A)))))) (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) K)))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N2))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.suc K)))) (= (= (tptp.aa_nat_nat _let_1 M) (tptp.aa_nat_nat _let_1 N2)) (= M N2)))) (forall ((X tptp.nat) (Y tptp.nat) (C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_nat6120813132205607877r_bool tptp.nO_MAT8694959213317031834nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X) Y)) C)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger A) B)) C) (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C))))) (forall ((X tptp.nat) (Y tptp.nat) (C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.nO_MATCH_nat_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X) Y)) C)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) B)) C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C))))) (forall ((X tptp.nat) (Y tptp.nat) (C tptp.int) (A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_nat_fun_int_bool tptp.nO_MATCH_nat_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X) Y)) C)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C))))) (forall ((X tptp.int) (Y tptp.int) (C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_int3865899974016033897r_bool tptp.nO_MAT9066612773553876470nteger (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int X) Y)) C)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger A) B)) C) (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C))))) (forall ((X tptp.int) (Y tptp.int) (C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.nO_MATCH_int_rat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int X) Y)) C)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) B)) C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C))))) (forall ((X tptp.int) (Y tptp.int) (C tptp.int) (A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.nO_MATCH_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int X) Y)) C)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C))))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.nO_MAT8252062027627875367nteger (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger X) Y)) C)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger A) B)) C) (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C))))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.nO_MAT7795273704451493282er_rat (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger X) Y)) C)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) B)) C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C))))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (C tptp.int) (A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_Cod8597349444926882409t_bool tptp.nO_MAT8427913294028938742er_int (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger X) Y)) C)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C))))) (forall ((X tptp.rat) (Y tptp.rat) (C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.nO_MAT243659986023775650nteger (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Y)) C)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger A) B)) C) (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C))))) (forall ((X tptp.nat) (Y tptp.nat) (A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_nat6120813132205607877r_bool tptp.nO_MAT8694959213317031834nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X) Y)) A)) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger B) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B)) (tptp.aa_Cod1783974652533396728nteger _let_1 C)))))) (forall ((X tptp.nat) (Y tptp.nat) (A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.nO_MATCH_nat_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X) Y)) A)) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat B) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 B)) (tptp.aa_rat_rat _let_1 C)))))) (forall ((X tptp.nat) (Y tptp.nat) (A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_nat_fun_int_bool tptp.nO_MATCH_nat_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X) Y)) A)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 B)) (tptp.aa_int_int _let_1 C)))))) (forall ((X tptp.int) (Y tptp.int) (A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_int3865899974016033897r_bool tptp.nO_MAT9066612773553876470nteger (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int X) Y)) A)) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger B) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B)) (tptp.aa_Cod1783974652533396728nteger _let_1 C)))))) (forall ((X tptp.int) (Y tptp.int) (A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.nO_MATCH_int_rat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int X) Y)) A)) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat B) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 B)) (tptp.aa_rat_rat _let_1 C)))))) (forall ((X tptp.int) (Y tptp.int) (A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.nO_MATCH_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int X) Y)) A)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 B)) (tptp.aa_int_int _let_1 C)))))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.nO_MAT8252062027627875367nteger (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger X) Y)) A)) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger B) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B)) (tptp.aa_Cod1783974652533396728nteger _let_1 C)))))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.nO_MAT7795273704451493282er_rat (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger X) Y)) A)) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat B) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 B)) (tptp.aa_rat_rat _let_1 C)))))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_Cod8597349444926882409t_bool tptp.nO_MAT8427913294028938742er_int (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger X) Y)) A)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 B)) (tptp.aa_int_int _let_1 C)))))) (forall ((X tptp.rat) (Y tptp.rat) (A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.nO_MAT243659986023775650nteger (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Y)) A)) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger B) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B)) (tptp.aa_Cod1783974652533396728nteger _let_1 C)))))) (forall ((A tptp.code_natural) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_natural tptp.semiri3763490453095760265atural M))) (let ((_let_2 (tptp.aa_nat_Code_natural tptp.semiri3763490453095760265atural N2))) (= (tptp.modulo8411746178871703098atural A (tptp.times_2397367101498566445atural _let_1 _let_2)) (tptp.plus_p4538020629002901425atural (tptp.times_2397367101498566445atural _let_1 (tptp.modulo8411746178871703098atural (tptp.divide5121882707175180666atural A _let_1) _let_2)) (tptp.modulo8411746178871703098atural A _let_1)))))) (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A))) (let ((_let_3 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) (let ((_let_4 (tptp.aa_int_fun_int_int tptp.times_times_int _let_1))) (= (tptp.aa_int_int _let_2 (tptp.aa_int_int _let_4 _let_3)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) _let_1)) _let_3))) (tptp.aa_int_int _let_2 _let_1)))))))) (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A))) (let ((_let_3 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2))) (let ((_let_4 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1))) (= (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat _let_4 _let_3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1)) _let_3))) (tptp.aa_nat_nat _let_2 _let_1)))))))) (forall ((A tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M))) (let ((_let_2 (tptp.modulo364778990260209775nteger A))) (let ((_let_3 (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) (let ((_let_4 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1))) (= (tptp.aa_Cod1783974652533396728nteger _let_2 (tptp.aa_Cod1783974652533396728nteger _let_4 _let_3)) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger _let_4 (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) _let_1)) _let_3))) (tptp.aa_Cod1783974652533396728nteger _let_2 _let_1)))))))) (forall ((K tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) M)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat K) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) M))))) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= N2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat tptp.suc M)) N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 N2)) (=> (not _let_2) (= _let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat)) N2)))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat) M)) (= (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat))))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) N2)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2))) (let ((_let_2 (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (= N2 tptp.zero_zero_nat)))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) N2)))))))) (forall ((X5 tptp.nat) (Xa3 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X5) Xa3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X5)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Xa3))))) (forall ((X5 tptp.nat) (Xa3 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X5) Xa3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X5)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Xa3))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) B)) A)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B)) A)))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B)) A)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B)) B)))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B)) B)))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) B)) B)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) M)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N2))) M) tptp.one_one_nat))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2)))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2)))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2)))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)))) (forall ((M tptp.nat)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat)))) (forall ((M tptp.nat)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int)))) (forall ((M tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat)))) (forall ((M tptp.nat)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M)) tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int B) C)) (not (forall ((D tptp.int)) (not (= B (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) D)))))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (= (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) C) (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger B) C)) (not (forall ((D tptp.code_integer)) (not (= B (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) D)))))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger A) B)) tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) B)) tptp.zero_zero_rat)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)) tptp.zero_zero_int)))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) N2)))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger A) B)) tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) B)) tptp.zero_zero_rat)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)) tptp.zero_zero_int)))) (forall ((I2 tptp.rat) (K tptp.rat) (N2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat I2) K)) N2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat I2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat N2) K))))) (forall ((I2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) K)) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K))))) (forall ((I2 tptp.int) (K tptp.int) (N2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I2) K)) N2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int N2) K))))) (forall ((I2 tptp.rat) (K tptp.rat) (N2 tptp.rat) (J tptp.rat)) (let ((_let_1 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat N2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat J) K))))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat I2) K)) N2)))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat N2) K)) J))))))))) (forall ((I2 tptp.nat) (K tptp.nat) (N2 tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) K))))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) K)) N2)))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K)) J))))))))) (forall ((I2 tptp.int) (K tptp.int) (N2 tptp.int) (J tptp.int)) (let ((_let_1 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int N2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) K))))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I2) K)) N2)))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int N2) K)) J))))))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) B)) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat C) B))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int C) B))))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat C) B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B)) C)))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int C) B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) C)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat B) A)) A) B))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) C)) A))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat B) A))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C) A)) B))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat B) A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 B)) A))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 B)) A) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat B) A)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat B) A)) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) C)) A)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) C)) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat B) A)) C)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat B) A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C) A)) B)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat B) A)) B))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)))) (=> _let_1 (=> _let_1 (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat B) A) C) (= B (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C) A))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (forall ((I2 tptp.nat) (J tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) J)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger I2)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger J))))) (forall ((I2 tptp.nat) (J tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) J)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat I2)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat J))))) (forall ((I2 tptp.nat) (J tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) J)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat I2)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat J))))) (forall ((I2 tptp.nat) (J tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) J)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int I2)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int J))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat X) Y) tptp.bot_bo2099793752762293965at_nat) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat X) Y)))) (forall ((X tptp.set_bool) (Y tptp.set_bool)) (= (= (tptp.minus_minus_set_bool X Y) tptp.bot_bot_set_bool) (tptp.ord_less_eq_set_bool X Y))) (forall ((X tptp.assn) (Y tptp.assn)) (= (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.minus_minus_assn X) Y) tptp.bot_bot_assn) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn X) Y)))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat X) Y) tptp.bot_bot_set_nat) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat X) Y)))) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int X) Y) tptp.bot_bot_set_int) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X) Y)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) B)) A))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) B)) A))) (forall ((A tptp.int) (B tptp.int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)) A))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) B)) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat C) B))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int C) B))))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat C) B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B)) C)))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int C) B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) C)))) (forall ((A tptp.code_natural) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_natural tptp.semiri3763490453095760265atural N2))) (let ((_let_2 (tptp.aa_nat_Code_natural tptp.semiri3763490453095760265atural M))) (= (tptp.divide5121882707175180666atural A (tptp.times_2397367101498566445atural _let_2 _let_1)) (tptp.divide5121882707175180666atural (tptp.divide5121882707175180666atural A _let_2) _let_1))))) (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) (let ((_let_2 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M))) (let ((_let_3 (tptp.aa_int_fun_int_int tptp.divide_divide_int A))) (= (tptp.aa_int_int _let_3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_2) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int _let_3 _let_2)) _let_1)))))) (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2))) (let ((_let_2 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M))) (let ((_let_3 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A))) (= (tptp.aa_nat_nat _let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_2) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_3 _let_2)) _let_1)))))) (forall ((A tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) (let ((_let_2 (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M))) (let ((_let_3 (tptp.divide6298287555418463151nteger A))) (= (tptp.aa_Cod1783974652533396728nteger _let_3 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_2) _let_1)) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger _let_3 _let_2)) _let_1)))))) (forall ((A tptp.code_integer) (E tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) E)) C) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) E)) D2)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger A) B)) E)) C) D2))) (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) E)) C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) E)) D2)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) B)) E)) C) D2))) (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) E)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) E)) D2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)) E)) C) D2))) (forall ((A tptp.code_integer) (E tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) E)) C) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) E)) D2)) (= C (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger B) A)) E)) D2)))) (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) E)) C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) E)) D2)) (= C (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat B) A)) E)) D2)))) (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) E)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) E)) D2)) (= C (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) A)) E)) D2)))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger X) X)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger Y) Y)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger X) Y)) (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) X)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Y)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat X) Y)))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) Y)))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N2)) N2)))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2)))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_Code_natural_bool (tptp.aa_Cod6910080592713026658l_bool tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural N2)))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat N2)))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat N2)))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_num_int tptp.numeral_numeral_int N2)))) (forall ((N2 tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2)) tptp.zero_z3403309356797280102nteger)))) (forall ((N2 tptp.num)) (not (tptp.pp (tptp.aa_Code_natural_bool (tptp.aa_Cod6910080592713026658l_bool tptp.ord_le1926595141338095240atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural N2)) tptp.zero_z2226904508553997617atural)))) (forall ((N2 tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2)) tptp.zero_zero_rat)))) (forall ((N2 tptp.num)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat N2)) tptp.zero_zero_nat)))) (forall ((N2 tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int tptp.numeral_numeral_int N2)) tptp.zero_zero_int)))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat N2)))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_num_int tptp.numeral_numeral_int N2)))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2)))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat N2)))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_Code_natural_bool (tptp.aa_Cod6910080592713026658l_bool tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural N2)))) (forall ((N2 tptp.num)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_num_nat tptp.numeral_numeral_nat N2)) tptp.zero_zero_nat)))) (forall ((N2 tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_num_int tptp.numeral_numeral_int N2)) tptp.zero_zero_int)))) (forall ((N2 tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2)) tptp.zero_z3403309356797280102nteger)))) (forall ((N2 tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2)) tptp.zero_zero_rat)))) (forall ((N2 tptp.num)) (not (tptp.pp (tptp.aa_Code_natural_bool (tptp.aa_Cod6910080592713026658l_bool tptp.ord_le5570908160329646204atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural N2)) tptp.zero_z2226904508553997617atural)))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2)))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_Code_natural_bool (tptp.aa_Cod6910080592713026658l_bool tptp.ord_le1926595141338095240atural tptp.one_one_Code_natural) (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural N2)))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat N2)))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat N2)))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) (tptp.aa_num_int tptp.numeral_numeral_int N2)))) (forall ((N2 tptp.num)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_num_nat tptp.numeral_numeral_nat N2)) tptp.one_one_nat)))) (forall ((N2 tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_num_int tptp.numeral_numeral_int N2)) tptp.one_one_int)))) (forall ((N2 tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2)) tptp.one_one_Code_integer)))) (forall ((N2 tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2)) tptp.one_one_rat)))) (forall ((N2 tptp.num)) (not (tptp.pp (tptp.aa_Code_natural_bool (tptp.aa_Cod6910080592713026658l_bool tptp.ord_le5570908160329646204atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural N2)) tptp.one_one_Code_natural)))) (forall ((F tptp.fun_nat_assn) (N2 tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_nat_assn F N5)) (tptp.aa_nat_assn F (tptp.aa_nat_nat tptp.suc N5))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) N6)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_nat_assn F N2)) (tptp.aa_nat_assn F N6)))))) (forall ((F tptp.fun_nat_rat) (N2 tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat F N5)) (tptp.aa_nat_rat F (tptp.aa_nat_nat tptp.suc N5))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) N6)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat F N2)) (tptp.aa_nat_rat F N6)))))) (forall ((F tptp.fun_nat_num) (N2 tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_nat_num F N5)) (tptp.aa_nat_num F (tptp.aa_nat_nat tptp.suc N5))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) N6)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_nat_num F N2)) (tptp.aa_nat_num F N6)))))) (forall ((F tptp.fun_nat_nat) (N2 tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat F N5)) (tptp.aa_nat_nat F (tptp.aa_nat_nat tptp.suc N5))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) N6)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat F N2)) (tptp.aa_nat_nat F N6)))))) (forall ((F tptp.fun_nat_int) (N2 tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int F N5)) (tptp.aa_nat_int F (tptp.aa_nat_nat tptp.suc N5))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) N6)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int F N2)) (tptp.aa_nat_int F N6)))))) (forall ((F tptp.fun_nat_assn) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_nat_assn F N5)) (tptp.aa_nat_assn F (tptp.aa_nat_nat tptp.suc N5))))) (= (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_nat_assn F N2)) (tptp.aa_nat_assn F M))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M))))) (forall ((F tptp.fun_nat_rat) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat F N5)) (tptp.aa_nat_rat F (tptp.aa_nat_nat tptp.suc N5))))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat F N2)) (tptp.aa_nat_rat F M))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M))))) (forall ((F tptp.fun_nat_num) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_nat_num F N5)) (tptp.aa_nat_num F (tptp.aa_nat_nat tptp.suc N5))))) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_nat_num F N2)) (tptp.aa_nat_num F M))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M))))) (forall ((F tptp.fun_nat_nat) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat F N5)) (tptp.aa_nat_nat F (tptp.aa_nat_nat tptp.suc N5))))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat F N2)) (tptp.aa_nat_nat F M))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M))))) (forall ((F tptp.fun_nat_int) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int F N5)) (tptp.aa_nat_int F (tptp.aa_nat_nat tptp.suc N5))))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int F N2)) (tptp.aa_nat_int F M))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M))))) (forall ((F tptp.fun_nat_set_int) (N2 tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_nat_set_int F N5)) (tptp.aa_nat_set_int F (tptp.aa_nat_nat tptp.suc N5))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N6)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_nat_set_int F N2)) (tptp.aa_nat_set_int F N6)))))) (forall ((F tptp.fun_nat_rat) (N2 tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F N5)) (tptp.aa_nat_rat F (tptp.aa_nat_nat tptp.suc N5))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N6)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F N2)) (tptp.aa_nat_rat F N6)))))) (forall ((F tptp.fun_nat_num) (N2 tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F N5)) (tptp.aa_nat_num F (tptp.aa_nat_nat tptp.suc N5))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N6)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F N2)) (tptp.aa_nat_num F N6)))))) (forall ((F tptp.fun_nat_nat) (N2 tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat F N5)) (tptp.aa_nat_nat F (tptp.aa_nat_nat tptp.suc N5))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N6)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat F N2)) (tptp.aa_nat_nat F N6)))))) (forall ((F tptp.fun_nat_int) (N2 tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int F N5)) (tptp.aa_nat_int F (tptp.aa_nat_nat tptp.suc N5))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N6)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int F N2)) (tptp.aa_nat_int F N6)))))) (forall ((F tptp.fun_nat_set_int) (N2 tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_nat_set_int F (tptp.aa_nat_nat tptp.suc N5))) (tptp.aa_nat_set_int F N5)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N6)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_nat_set_int F N6)) (tptp.aa_nat_set_int F N2)))))) (forall ((F tptp.fun_nat_rat) (N2 tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F (tptp.aa_nat_nat tptp.suc N5))) (tptp.aa_nat_rat F N5)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N6)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F N6)) (tptp.aa_nat_rat F N2)))))) (forall ((F tptp.fun_nat_num) (N2 tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F (tptp.aa_nat_nat tptp.suc N5))) (tptp.aa_nat_num F N5)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N6)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F N6)) (tptp.aa_nat_num F N2)))))) (forall ((F tptp.fun_nat_nat) (N2 tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat F (tptp.aa_nat_nat tptp.suc N5))) (tptp.aa_nat_nat F N5)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N6)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat F N6)) (tptp.aa_nat_nat F N2)))))) (forall ((F tptp.fun_nat_int) (N2 tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int F (tptp.aa_nat_nat tptp.suc N5))) (tptp.aa_nat_int F N5)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N6)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int F N6)) (tptp.aa_nat_int F N2)))))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 N2)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 M)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) M)))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger A))) (= (tptp.aa_nat_Code_integer _let_1 (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer _let_1 N2)) A)))) (forall ((A tptp.assn) (N2 tptp.nat)) (let ((_let_1 (tptp.power_power_assn A))) (= (tptp.aa_nat_assn _let_1 (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.aa_nat_assn _let_1 N2)) A)))) (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_power_rat A))) (= (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 N2)) A)))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 N2)) A)))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int A))) (= (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_1 N2)) A)))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger A))) (= (tptp.aa_nat_Code_integer _let_1 (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) (tptp.aa_nat_Code_integer _let_1 N2))))) (forall ((A tptp.assn) (N2 tptp.nat)) (let ((_let_1 (tptp.power_power_assn A))) (= (tptp.aa_nat_assn _let_1 (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn A) (tptp.aa_nat_assn _let_1 N2))))) (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_power_rat A))) (= (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) (tptp.aa_nat_rat _let_1 N2))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) (tptp.aa_nat_nat _let_1 N2))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int A))) (= (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) (tptp.aa_nat_int _let_1 N2))))) (forall ((N2 tptp.nat) (P tptp.fun_nat_bool)) (= (exists ((I4 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.aa_nat_nat tptp.suc N2))) (tptp.pp (tptp.aa_nat_bool P I4)))) (or (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat)) (exists ((I4 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) N2)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc I4)))))))) (forall ((N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (exists ((M3 tptp.nat)) (= N2 (tptp.aa_nat_nat tptp.suc M3))))) (forall ((N2 tptp.nat) (P tptp.fun_nat_bool)) (= (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.aa_nat_nat tptp.suc N2))) (tptp.pp (tptp.aa_nat_bool P I4)))) (and (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat)) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) N2)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc I4)))))))) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (exists ((M5 tptp.nat)) (= N2 (tptp.aa_nat_nat tptp.suc M5))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat tptp.suc N2))) (or (= M tptp.zero_zero_nat) (exists ((J3 tptp.nat)) (and (= M (tptp.aa_nat_nat tptp.suc J3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J3) N2))))))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) M)) tptp.zero_zero_nat)) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 M)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 N2)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat B) C)))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) K))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) K)) J)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) M))) (forall ((P tptp.fun_nat_bool) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat)) (=> (forall ((N5 tptp.nat)) (=> (forall ((Nn tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Nn) N5)) (tptp.pp (tptp.aa_nat_bool P Nn)))) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc N5))))) (tptp.pp (tptp.aa_nat_bool P N2))))) (forall ((P tptp.fun_nat_bool) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat)) (=> (forall ((N5 tptp.nat)) (=> (forall ((Nn tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Nn) N5)) (tptp.pp (tptp.aa_nat_bool P Nn)))) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc N5))))) (tptp.pp (tptp.aa_nat_bool P N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2) _let_1) (or (and (= M _let_1) (= N2 tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N2 _let_1)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2)) (or (and (= M _let_1) (= N2 tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N2 _let_1)))))) (forall ((J tptp.nat) (K tptp.nat) (I2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) K)) I2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat J) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) K))))) (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) J)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) K))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) K)) J))))) (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) J)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 J)) K) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) K)))))) (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) J)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) I2)) K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) K)) I2)))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) J)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) I2) K) (= J (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) I2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc M)) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc M)) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (forall ((I2 tptp.nat) (J tptp.nat) (P tptp.fun_nat_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) J)) (=> (tptp.pp (tptp.aa_nat_bool P I2)) (=> (forall ((N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) N5)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N5) J)) (=> (tptp.pp (tptp.aa_nat_bool P N5)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc N5))))))) (tptp.pp (tptp.aa_nat_bool P J)))))) (forall ((I2 tptp.nat) (J tptp.nat) (P tptp.fun_nat_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) J)) (=> (tptp.pp (tptp.aa_nat_bool P J)) (=> (forall ((N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) N5)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N5) J)) (=> (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc N5))) (tptp.pp (tptp.aa_nat_bool P N5)))))) (tptp.pp (tptp.aa_nat_bool P I2)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc M)) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat tptp.suc M))) (= N2 M)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat tptp.suc N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc N2)) M)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat tptp.suc N2))))) (forall ((A tptp.nat) (B tptp.nat)) (= (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) (tptp.aa_nat_nat tptp.suc A)))) (= B A))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc A))) (= (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) _let_1))) (= B _let_1)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (not (forall ((Q4 tptp.nat)) (not (= N2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) Q4)))))))) (forall ((I2 tptp.nat) (M tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) M))))) (forall ((I2 tptp.nat) (M tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) I2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (exists ((K3 tptp.nat)) (= N2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K3)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (exists ((K2 tptp.nat)) (= N2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K2)))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.suc K)))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2))))) (= tptp.one_one_nat _let_41) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.suc K)))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.suc M)) N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N2)))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat tptp.suc N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) tptp.one_one_nat))) (= _let_61 tptp.suc) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat tptp.suc N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc M)) N2)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) B) A)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B) A)))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B) A)))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) B))))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B))))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B))) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B))) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) B))) (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) B))) C) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) C))) (forall ((B tptp.code_natural) (A tptp.code_natural) (C tptp.code_natural)) (= (tptp.plus_p4538020629002901425atural (tptp.plus_p4538020629002901425atural (tptp.times_2397367101498566445atural B (tptp.divide5121882707175180666atural A B)) (tptp.modulo8411746178871703098atural A B)) C) (tptp.plus_p4538020629002901425atural A C))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B)) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B))) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B))) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) B)) B)) (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) B))) C) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) C))) (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (= (tptp.plus_p4538020629002901425atural (tptp.plus_p4538020629002901425atural (tptp.times_2397367101498566445atural (tptp.divide5121882707175180666atural A B) B) (tptp.modulo8411746178871703098atural A B)) C) (tptp.plus_p4538020629002901425atural A C))) (forall ((A tptp.nat) (B tptp.nat)) (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B)) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B)))) (forall ((A tptp.int) (B tptp.int)) (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= A (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) B)) B)) (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) B)))) (forall ((A tptp.code_natural) (B tptp.code_natural)) (= A (tptp.plus_p4538020629002901425atural (tptp.times_2397367101498566445atural (tptp.divide5121882707175180666atural A B) B) (tptp.modulo8411746178871703098atural A B)))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B)) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B)) A)) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B)) A)) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) B)) B)) (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) B)) A)) (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (tptp.plus_p4538020629002901425atural (tptp.times_2397367101498566445atural (tptp.divide5121882707175180666atural A B) B) (tptp.modulo8411746178871703098atural A B)) A)) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B)) B)) A)) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)) B)) A)) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) B)) B)) A)) (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (tptp.plus_p4538020629002901425atural (tptp.modulo8411746178871703098atural A B) (tptp.times_2397367101498566445atural (tptp.divide5121882707175180666atural A B) B)) A)) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B))) A)) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B))) A)) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) B))) A)) (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (tptp.plus_p4538020629002901425atural (tptp.modulo8411746178871703098atural A B) (tptp.times_2397367101498566445atural B (tptp.divide5121882707175180666atural A B))) A)) (forall ((B tptp.nat) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) B)) A)) (forall ((B tptp.int) (A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B)) A)) (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) B))) (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) B)) A)) (forall ((B tptp.code_natural) (A tptp.code_natural)) (= (tptp.plus_p4538020629002901425atural (tptp.times_2397367101498566445atural B (tptp.divide5121882707175180666atural A B)) (tptp.modulo8411746178871703098atural A B)) A)) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 B)) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) C))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat B) C))) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int _let_1 B)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) C))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int B) C))) C))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B)) C) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger B) C))) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger B) C))) C))))) (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (= (tptp.divide5121882707175180666atural (tptp.times_2397367101498566445atural A B) C) (tptp.plus_p4538020629002901425atural (tptp.times_2397367101498566445atural A (tptp.divide5121882707175180666atural B C)) (tptp.divide5121882707175180666atural (tptp.times_2397367101498566445atural A (tptp.modulo8411746178871703098atural B C)) C)))) (forall ((A tptp.code_integer) (E tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) E)) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) E)) D2))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger A) B)) E)) C)) D2)))) (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) E)) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) E)) D2))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) B)) E)) C)) D2)))) (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) E)) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) E)) D2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)) E)) C)) D2)))) (forall ((A tptp.code_integer) (E tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) E)) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) E)) D2))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger C) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger B) A)) E)) D2))))) (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) E)) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) E)) D2))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat B) A)) E)) D2))))) (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) E)) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) E)) D2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) A)) E)) D2))))) (forall ((A tptp.code_integer) (E tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) E)) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) E)) D2))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger A) B)) E)) C)) D2)))) (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) E)) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) E)) D2))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) B)) E)) C)) D2)))) (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) E)) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) E)) D2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)) E)) C)) D2)))) (forall ((A tptp.code_integer) (E tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) E)) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) E)) D2))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger C) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger B) A)) E)) D2))))) (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) E)) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) E)) D2))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat B) A)) E)) D2))))) (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) E)) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) E)) D2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) A)) E)) D2))))) (forall ((X tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger X) X)) tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger X) tptp.one_one_Code_integer)) (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger X) tptp.one_one_Code_integer)))) (forall ((X tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) X)) tptp.one_one_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) tptp.one_one_rat)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat X) tptp.one_one_rat)))) (forall ((X tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) X)) tptp.one_one_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) tptp.one_one_int)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) tptp.one_one_int)))) (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) Z)) B)) Z))))))) (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W2 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Y)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat W2) Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat W2) Y))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Z)))))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat Y) Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Z)) Y)) Z)))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Z)) Y) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Z))) Z)))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N2)) N2)))) (forall ((A tptp.code_integer) (N2 tptp.nat) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc N2))) (=> (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) _let_2) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger B) _let_2)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)) (= A B))))))) (forall ((A tptp.rat) (N2 tptp.nat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc N2))) (=> (= (tptp.aa_nat_rat (tptp.power_power_rat A) _let_2) (tptp.aa_nat_rat (tptp.power_power_rat B) _let_2)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (= A B))))))) (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc N2))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) _let_2)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (= A B))))))) (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc N2))) (=> (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) _let_2) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int B) _let_2)) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (= A B))))))) (forall ((A tptp.code_integer) (N2 tptp.nat) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) _let_1)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger B) _let_1))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B)))))) (forall ((A tptp.rat) (N2 tptp.nat) (B tptp.rat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat A) _let_1)) (tptp.aa_nat_rat (tptp.power_power_rat B) _let_1))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)))))) (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) _let_1))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)))))) (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) _let_1)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int B) _let_1))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)))))) (forall ((B tptp.rat) (C tptp.rat) (W2 tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W2))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C) _let_1) (and (=> (not _let_2) (= B (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))) (forall ((W2 tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W2))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C)) (and (=> (not _let_2) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))) (forall ((M tptp.nat) (Q5 tptp.nat) (N2 tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) Q5) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N2) Q5)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (not (forall ((S5 tptp.nat)) (not (= M (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Q5) S5))))))))) (forall ((M tptp.nat) (Q5 tptp.nat) (N2 tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) Q5) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N2) Q5)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (not (forall ((S5 tptp.nat)) (not (= N2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Q5) S5))))))))) (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X) N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat Y) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)) (exists ((Q4 tptp.nat)) (= X (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Y) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) Q4))))))) (forall ((A3 tptp.nat) (B3 tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A3) B3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A3) N2) tptp.zero_zero_nat) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat B3) N2) tptp.zero_zero_nat) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A3) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B3) N2)))))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) (tptp.aa_nat_nat tptp.suc N2))))))) (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_nat_nat tptp.suc N2))))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) (tptp.aa_nat_nat tptp.suc N2))))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) (tptp.aa_nat_nat tptp.suc N2))))))) (forall ((P tptp.fun_nat_bool) (A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) B))) (and (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat))) (forall ((D5 tptp.nat)) (=> (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) D5)) (tptp.pp (tptp.aa_nat_bool P D5))))))) (forall ((P tptp.fun_nat_bool) (A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) B))) (not (or (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (not (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat)))) (exists ((D5 tptp.nat)) (and (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) D5)) (not (tptp.pp (tptp.aa_nat_bool P D5))))))))) (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) J)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) K)) I2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) K)))))) (forall ((P tptp.fun_nat_bool) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P N2)) (=> (not (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat))) (exists ((K2 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K2) N2)) (forall ((I tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) K2)) (not (tptp.pp (tptp.aa_nat_bool P I))))) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc K2)))))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) M)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) M)))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) M)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N2)))))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 N2)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 M)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N2))))))) (forall ((N2 tptp.nat) (P tptp.fun_nat_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (=> (tptp.pp (tptp.aa_nat_bool P tptp.one_one_nat)) (=> (forall ((N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N5)) (=> (tptp.pp (tptp.aa_nat_bool P N5)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc N5)))))) (tptp.pp (tptp.aa_nat_bool P N2)))))) (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat J) I2)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat I2) U)) M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat J) U)) N2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat I2) J)) U)) M) N2)))) (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) J)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat I2) U)) M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat J) U)) N2)) (= M (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) I2)) U)) N2))))) (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat J) I2)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat I2) U)) M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat J) U)) N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat I2) J)) U)) M)) N2))))) (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) J)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat I2) U)) M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat J) U)) N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) I2)) U)) N2)))))) (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat J) I2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat I2) U)) M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat J) U)) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat I2) J)) U)) M)) N2)))) (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) J)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat I2) U)) M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat J) U)) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) I2)) U)) N2))))) (forall ((N2 tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat N2) K))))) (forall ((I2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 I2)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat I2) N2)))))) (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W2 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Y)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat W2) Z))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat W2) Y))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Z))) tptp.zero_zero_rat)))))) (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W2 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Y)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat W2) Z))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat W2) Y))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Z))) tptp.zero_zero_rat)))))) (forall ((P tptp.fun_nat_bool) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (= N2 tptp.zero_zero_nat))) (= (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N2))) (and (=> _let_1 (tptp.pp (tptp.aa_nat_bool P M))) (=> (not _let_1) (forall ((I4 tptp.nat) (J3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J3) N2)) (=> (= M (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) I4)) J3)) (tptp.pp (tptp.aa_nat_bool P J3)))))))))) (forall ((B tptp.rat) (C tptp.rat) (W2 tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W2))) (let ((_let_2 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_4 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) C))) (let ((_let_5 (tptp.pp (tptp.aa_rat_bool _let_2 C)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C)) _let_1)) (and (=> _let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) _let_4))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_4) B))) (=> (not _let_3) (tptp.pp (tptp.aa_rat_bool _let_2 _let_1))))))))))))) (forall ((W2 tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W2))) (let ((_let_2 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_4 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) C))) (let ((_let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool _let_2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C))) (and (=> _let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_4) B))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) _let_4))) (=> (not _let_3) (tptp.pp (tptp.aa_rat_bool _let_2 tptp.zero_zero_rat))))))))))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) (tptp.aa_nat_nat tptp.suc N2))) A))))) (forall ((A tptp.rat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_nat_nat tptp.suc N2))) A))))) (forall ((A tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) (tptp.aa_nat_nat tptp.suc N2))) A))))) (forall ((A tptp.int) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) (tptp.aa_nat_nat tptp.suc N2))) A))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) (tptp.aa_nat_nat tptp.suc N2))) tptp.one_one_Code_integer))))) (forall ((A tptp.rat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_nat_nat tptp.suc N2))) tptp.one_one_rat))))) (forall ((A tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) (tptp.aa_nat_nat tptp.suc N2))) tptp.one_one_nat))))) (forall ((A tptp.int) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) (tptp.aa_nat_nat tptp.suc N2))) tptp.one_one_int))))) (forall ((A tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (not (= A tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N2))))))) (forall ((A tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int A))) (=> (not (= A tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (= (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_nat_int _let_1 M)) (tptp.aa_nat_int _let_1 N2))))))) (forall ((A tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger A))) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (= (tptp.aa_nat_Code_integer _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_nat_Code_integer _let_1 M)) (tptp.aa_nat_Code_integer _let_1 N2))))))) (forall ((A tptp.rat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.power_power_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (= (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_nat_rat _let_1 M)) (tptp.aa_nat_rat _let_1 N2))))))) (forall ((A tptp.code_natural) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.power_7079662738309270450atural A))) (=> (not (= A tptp.zero_z2226904508553997617atural)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (= (tptp.aa_nat_Code_natural _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) (tptp.divide5121882707175180666atural (tptp.aa_nat_Code_natural _let_1 M) (tptp.aa_nat_Code_natural _let_1 N2))))))) (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat J) I2)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat I2) U)) M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat J) U)) N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat I2) J)) U)) M)) N2))))) (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) J)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat I2) U)) M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat J) U)) N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) I2)) U)) N2)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N2))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat)) N2)))))))) (forall ((N2 tptp.nat) (Q5 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 Q5)) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc Q5)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2) Q5))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.modulo364778990260209775nteger A))) (let ((_let_2 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C)) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger _let_2 C)) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger _let_2 (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) B)) C))) (tptp.aa_Cod1783974652533396728nteger _let_1 B))))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) C)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat _let_2 C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B)) C))) (tptp.aa_nat_nat _let_1 B))))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.times_times_int B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int _let_2 C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)) C))) (tptp.aa_int_int _let_1 B))))))) (forall ((U tptp.rat) (V tptp.rat) (R3 tptp.rat) (S2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat U) V)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) R3)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat R3) S2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat U) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat R3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat V) U))) S2))) V)))))) (forall ((B tptp.rat) (C tptp.rat) (W2 tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W2))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_3 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) C))) (let ((_let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C)) _let_1)) (and (=> _let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) _let_3))) (=> (not _let_4) (and (=> _let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_3) B))) (=> (not _let_2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1)))))))))))) (forall ((E tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) E)) (not (forall ((N5 tptp.nat)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat tptp.one_one_rat) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat tptp.suc N5)))) E))))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) X)) (exists ((N5 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N5)) X)))))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2) (tptp.aa_rat_rat (tptp.semiri7787848453975740701ux_rat tptp.aTP_Lamm_gc N2) tptp.zero_zero_rat))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2) (tptp.aa_int_int (tptp.aa_nat_fun_int_int (tptp.semiri8420488043553186161ux_int tptp.aTP_Lamm_gd) N2) tptp.zero_zero_int))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.semiri8422978514062236437ux_nat tptp.aTP_Lamm_ge) N2) tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2) (tptp.aa_Cod1783974652533396728nteger (tptp.semiri4055485073559036834nteger tptp.aTP_Lamm_gf N2) tptp.zero_z3403309356797280102nteger))) (forall ((P tptp.fun_nat_fun_nat_bool) (M tptp.nat) (N2 tptp.nat)) (=> (forall ((M5 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P M5) tptp.zero_zero_nat))) (=> (forall ((M5 tptp.nat) (N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N5)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P N5) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M5) N5))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P M5) N5))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P M) N2))))) (forall ((X tptp.fun_Pr4403862266400233414at_nat) (X2 tptp.produc3260487557148687353it_nat)) (= (tptp.size_o1731029420616209814it_nat X (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat X2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_Pro545002926299402503at_nat X X2)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (forall ((X tptp.fun_num_nat) (X2 tptp.num)) (= (tptp.aa_option_num_nat (tptp.size_option_num X) (tptp.aa_num_option_num tptp.some_num X2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat X X2)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (forall ((X tptp.fun_Pr367382672041210069at_nat) (X2 tptp.produc8664842809031399944it_nat)) (= (tptp.size_o29782932136985253it_nat X (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat X2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_Pro5228051289423594006at_nat X X2)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (forall ((N2 tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat A) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 (tptp.aa_rat_rat (tptp.set_fo1949268297981939178at_rat (tptp.aTP_Lamm_gg A) tptp.zero_zero_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_rat))))))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int A) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 (tptp.aa_int_int (tptp.aa_nat_fun_int_int (tptp.set_fo2581907887559384638at_int (tptp.aTP_Lamm_gh A) tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_int))))))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger A) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_Code_integer)) (=> (not _let_2) (= _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.set_fo1084959871951514735nteger (tptp.aTP_Lamm_gi A) tptp.zero_zero_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_Code_integer))))))) (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat A) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat (tptp.aTP_Lamm_gj A) tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_nat))))))) (forall ((X tptp.fun_num_nat)) (= (tptp.aa_option_num_nat (tptp.size_option_num X) tptp.none_num) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat A3) A3) tptp.bot_bo2099793752762293965at_nat)) (forall ((A3 tptp.set_bool)) (= (tptp.minus_minus_set_bool A3 A3) tptp.bot_bot_set_bool)) (forall ((A3 tptp.set_int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) A3) tptp.bot_bot_set_int)) (forall ((A3 tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) A3) tptp.bot_bot_set_nat)) (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat tptp.bot_bo2099793752762293965at_nat) A3) tptp.bot_bo2099793752762293965at_nat)) (forall ((A3 tptp.set_bool)) (= (tptp.minus_minus_set_bool tptp.bot_bot_set_bool A3) tptp.bot_bot_set_bool)) (forall ((A3 tptp.set_int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int tptp.bot_bot_set_int) A3) tptp.bot_bot_set_int)) (forall ((A3 tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat tptp.bot_bot_set_nat) A3) tptp.bot_bot_set_nat)) (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat A3) tptp.bot_bo2099793752762293965at_nat) A3)) (forall ((A3 tptp.set_bool)) (= (tptp.minus_minus_set_bool A3 tptp.bot_bot_set_bool) A3)) (forall ((A3 tptp.set_int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) tptp.bot_bot_set_int) A3)) (forall ((A3 tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) tptp.bot_bot_set_nat) A3)) (forall ((B3 tptp.set_Pr8693737435421807431at_nat) (A3 tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.minus_8321449233255521966at_nat B3) A3)) A3) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat B3) A3))) (forall ((B3 tptp.set_Pr8551490117392284871at_nat) (A3 tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.minus_5060654252129873198at_nat B3) A3)) A3) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat B3) A3))) (forall ((B3 tptp.set_Pr4329608150637261639at_nat) (A3 tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.minus_3314409938677909166at_nat B3) A3)) A3) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat B3) A3))) (forall ((B3 tptp.set_nat) (A3 tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat B3) A3)) A3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat B3) A3))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3))) (= (tptp.aa_set5535132180132642428at_nat _let_1 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.minus_8321449233255521966at_nat B3) A3)) (tptp.aa_set5535132180132642428at_nat _let_1 B3)))) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3))) (= (tptp.aa_set6734554978791863420at_nat _let_1 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.minus_5060654252129873198at_nat B3) A3)) (tptp.aa_set6734554978791863420at_nat _let_1 B3)))) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3))) (= (tptp.aa_set4883462369968598652at_nat _let_1 (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.minus_3314409938677909166at_nat B3) A3)) (tptp.aa_set4883462369968598652at_nat _let_1 B3)))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3))) (= (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat B3) A3)) (tptp.aa_set_nat_set_nat _let_1 B3)))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat A3) B3) tptp.bot_bo2099793752762293965at_nat) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A3) B3)))) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool)) (= (= (tptp.minus_minus_set_bool A3 B3) tptp.bot_bot_set_bool) (tptp.ord_less_eq_set_bool A3 B3))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3) tptp.bot_bot_set_nat) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) B3)))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3) tptp.bot_bot_set_int) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat B3) A3)) tptp.bot_bo2099793752762293965at_nat)) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool)) (= (tptp.inf_inf_set_bool A3 (tptp.minus_minus_set_bool B3 A3)) tptp.bot_bot_set_bool)) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int B3) A3)) tptp.bot_bot_set_int)) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat B3) A3)) tptp.bot_bot_set_nat)) (forall ((K tptp.int) (L tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) L)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int K) L) K)))) (forall ((K tptp.int) (L tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int L) K)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int K) L) K)))) (forall ((K tptp.int) (L tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) L)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int K) L) tptp.zero_zero_int)))) (forall ((K tptp.int) (L tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int L) K)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int K) L) tptp.zero_zero_int)))) (forall ((L tptp.int) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) L)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int L) K)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int K) L) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int K) L)) L)) tptp.one_one_int))))) (forall ((A3 tptp.int) (B3 tptp.int) (N2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A3) B3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) N2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A3) N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.if_int (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int B3) N2)) tptp.zero_zero_int)) tptp.one_one_int) tptp.zero_zero_int))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B3) N2)))))) (forall ((A3 tptp.int) (B3 tptp.int) (N2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A3) B3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) N2)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A3) N2) tptp.zero_zero_int) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int B3) N2) tptp.zero_zero_int) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A3) N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B3) N2)))))))) (forall ((K tptp.int) (P tptp.fun_int_fun_int_bool) (N2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) K)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int N2) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int N2) K))) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) J3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int J3) K)) (= N2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) I4)) J3))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P I4) J3))))))) (forall ((K tptp.int) (P tptp.fun_int_fun_int_bool) (N2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int N2) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int N2) K))) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) J3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int J3) tptp.zero_zero_int)) (= N2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) I4)) J3))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P I4) J3))))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.times_times_int B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int _let_2 C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)) C))) (tptp.aa_int_int _let_1 B))))))) (forall ((L tptp.int) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) L)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int K) L))))) (forall ((L tptp.int) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int L) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int K) L)) tptp.zero_zero_int)))) (forall ((L tptp.int) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) L)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int K) L)) L)))) (forall ((L tptp.int) (K tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int L))) (=> (tptp.pp (tptp.aa_int_bool _let_1 tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int K) L)))))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) L))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) K)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_1) tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int K) L) _let_1))))) (forall ((M tptp.int) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) M)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int M) K)) M)))) (forall ((L tptp.int) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) L)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int L) K)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int K) L) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int K) L)) L))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.ord_less_int B))) (=> (tptp.pp (tptp.aa_int_bool _let_2 tptp.zero_zero_int)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_1) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool _let_2 _let_1))))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int _let_1) B)))))) (forall ((I2 tptp.int) (K tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int I2) K) I2) (or (= K tptp.zero_zero_int) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) I2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int I2) K))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I2) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) I2)))))) (forall ((D2 tptp.int) (P4 tptp.fun_int_bool) (P tptp.fun_int_bool)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D2)) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool P4 X3)) (tptp.pp (tptp.aa_int_bool P4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K2) D2)))))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z4) X3)) (= (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P4 X3)))))) (=> (exists ((X_13 tptp.int)) (tptp.pp (tptp.aa_int_bool P4 X_13))) (exists ((X_1 tptp.int)) (tptp.pp (tptp.aa_int_bool P X_1)))))))) (forall ((D2 tptp.int) (P1 tptp.fun_int_bool) (P tptp.fun_int_bool)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D2)) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool P1 X3)) (tptp.pp (tptp.aa_int_bool P1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K2) D2)))))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) Z4)) (= (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P1 X3)))))) (=> (exists ((X_13 tptp.int)) (tptp.pp (tptp.aa_int_bool P1 X_13))) (exists ((X_1 tptp.int)) (tptp.pp (tptp.aa_int_bool P X_1)))))))) (forall ((D2 tptp.int) (P tptp.fun_int_bool) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D2)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X3) D2))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P X5)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X5) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) D2)))))))))) (forall ((A tptp.int) (B tptp.int) (Q5 tptp.int) (R3 tptp.int)) (=> (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) Q5)) R3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) R3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R3) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B) R3))))) (forall ((A tptp.int) (B tptp.int) (Q5 tptp.int) (R3 tptp.int)) (=> (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) Q5)) R3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int R3) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) R3)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B) R3))))) (forall ((P tptp.fun_int_bool) (N2 tptp.int) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int N2) K))) (and (=> (= K tptp.zero_zero_int) (tptp.pp (tptp.aa_int_bool P N2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) K)) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) J3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int J3) K)) (= N2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) I4)) J3))) (tptp.pp (tptp.aa_int_bool P J3))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) J3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int J3) tptp.zero_zero_int)) (= N2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) I4)) J3))) (tptp.pp (tptp.aa_int_bool P J3)))))))) (forall ((B2 tptp.int) (Q7 tptp.int) (R6 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) Q7)) R6))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R6) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)) (tptp.pp (tptp.aa_int_bool _let_1 Q7))))))) (forall ((B tptp.int) (Q5 tptp.int) (R3 tptp.int) (B2 tptp.int) (Q7 tptp.int) (R6 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) Q7)) R6))) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) Q5)) R3) _let_2) (=> (tptp.pp (tptp.aa_int_bool _let_1 _let_2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R6) B2)) (=> (tptp.pp (tptp.aa_int_bool _let_1 R3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Q5) Q7))))))))))) (forall ((D2 tptp.int) (P tptp.fun_int_bool) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D2)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X3) D2))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P X5)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X5) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) D2)))))))))) (forall ((B tptp.int) (Q5 tptp.int) (R3 tptp.int) (B2 tptp.int) (Q7 tptp.int) (R6 tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B2) Q7)) R6))) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) Q5)) R3) _let_1) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int _let_1) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R3) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) R6)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Q7) Q5)))))))))) (forall ((B tptp.int) (Q7 tptp.int) (R6 tptp.int) (Q5 tptp.int) (R3 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_1 Q7)) R6)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_1 Q5)) R3))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) R6)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R6) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R3) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Q7) Q5)))))))) (forall ((B tptp.int) (Q7 tptp.int) (R6 tptp.int) (Q5 tptp.int) (R3 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int B))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.times_times_int B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_2 Q7)) R6)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_2 Q5)) R3))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int R3) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool _let_1 R3)) (=> (tptp.pp (tptp.aa_int_bool _let_1 R6)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Q5) Q7))))))))) (forall ((X tptp.int) (X8 tptp.int) (P tptp.bool) (P4 tptp.bool)) (let ((_let_1 (tptp.pp P4))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_3 (tptp.pp (tptp.aa_int_bool _let_2 X8)))) (let ((_let_4 (tptp.pp P))) (=> (= X X8) (=> (=> _let_3 (= _let_4 _let_1)) (= (=> (tptp.pp (tptp.aa_int_bool _let_2 X)) _let_4) (=> _let_3 _let_1))))))))) (forall ((X tptp.int) (X8 tptp.int) (P tptp.bool) (P4 tptp.bool)) (let ((_let_1 (tptp.pp P4))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_3 (tptp.pp (tptp.aa_int_bool _let_2 X8)))) (let ((_let_4 (tptp.pp P))) (=> (= X X8) (=> (=> _let_3 (= _let_4 _let_1)) (= (and (tptp.pp (tptp.aa_int_bool _let_2 X)) _let_4) (and _let_3 _let_1))))))))) (forall ((A tptp.int) (X tptp.int)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) X)) (= A X) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) A)))) (forall ((P tptp.fun_int_bool) (N2 tptp.int) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int N2) K))) (and (=> (= K tptp.zero_zero_int) (tptp.pp (tptp.aa_int_bool P tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) K)) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) J3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int J3) K)) (= N2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) I4)) J3))) (tptp.pp (tptp.aa_int_bool P I4))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) J3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int J3) tptp.zero_zero_int)) (= N2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) I4)) J3))) (tptp.pp (tptp.aa_int_bool P I4)))))))) (forall ((A tptp.int) (B tptp.int) (Q5 tptp.int) (R3 tptp.int)) (=> (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) Q5)) R3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int R3) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) R3)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B) Q5))))) (forall ((A tptp.int) (B tptp.int) (Q5 tptp.int) (R3 tptp.int)) (=> (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) Q5)) R3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) R3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R3) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B) Q5))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.divide_divide_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) C)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int _let_1 B)) C))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (tptp.pp (tptp.aa_int_bool _let_1 B))))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B))) (tptp.pp (tptp.aa_int_bool _let_1 A)))))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) tptp.zero_zero_int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int))))) (forall ((K tptp.int) (I2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 K)) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int I2) K))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) I2)))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)) tptp.zero_zero_int))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)) tptp.zero_zero_int))))) (forall ((L tptp.int) (K tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int L) K)) (=> (tptp.pp (tptp.aa_int_bool _let_1 L)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int K) L))))))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int K) L))) (or (= K tptp.zero_zero_int) (= L tptp.zero_zero_int) (and (tptp.pp (tptp.aa_int_bool _let_1 K)) (tptp.pp (tptp.aa_int_bool _let_1 L))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int L) tptp.zero_zero_int))))))) (forall ((A tptp.int) (B2 tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.divide_divide_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int _let_1 B2)) (tptp.aa_int_int _let_1 B)))))))) (forall ((A tptp.int) (A2 tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) A2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A2) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)))))) (forall ((I2 tptp.int) (K tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int I2) K) tptp.zero_zero_int) (or (= K tptp.zero_zero_int) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) I2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int I2) K))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I2) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) I2)))))) (forall ((A tptp.int) (B2 tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.divide_divide_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B2) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int _let_1 B)) (tptp.aa_int_int _let_1 B2)))))))) (forall ((A tptp.int) (A2 tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) A2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A2) B)))))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int))))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) tptp.zero_zero_int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) A))))) (forall ((X tptp.int) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) X)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int X) K)) X))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)) tptp.zero_zero_int))))) (forall ((A3 tptp.set_nat) (C3 tptp.set_nat) (D3 tptp.set_nat) (B3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) C3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat D3) B3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat C3) D3)))))) (forall ((A3 tptp.set_int) (C3 tptp.set_int) (D3 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) C3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int D3) B3)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3)) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int C3) D3)))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3)) A3))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3)) A3))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) B3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B3) C3)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat B3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat C3) A3)) A3)))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (C3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) C3)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int B3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int C3) A3)) A3)))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int B))) (let ((_let_2 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int A))) (let ((_let_3 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) B)))) (let ((_let_4 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int _let_2) _let_1)))) (and (=> _let_4 (= _let_3 tptp.zero_zero_int)) (=> (not _let_4) (= _let_3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int _let_2) _let_1))))))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat A3) B3)) C3) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) C3)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat B3) C3)))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C3 tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3)) C3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) C3)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat B3) C3)))) (forall ((C3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat C3))) (= (tptp.aa_set8868280134176360700at_nat _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat A3) B3)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat (tptp.aa_set8868280134176360700at_nat _let_1 A3)) (tptp.aa_set8868280134176360700at_nat _let_1 B3))))) (forall ((C3 tptp.set_nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat C3))) (= (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat (tptp.aa_set_nat_set_nat _let_1 A3)) (tptp.aa_set_nat_set_nat _let_1 B3))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat A3))) (= (tptp.aa_set8868280134176360700at_nat _let_1 (tptp.aa_set8868280134176360700at_nat _let_1 B3)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3)))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3))) (= (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat _let_1 B3)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3)))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (C3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) C3)))) (= (tptp.aa_set8868280134176360700at_nat _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat B3) C3)) (tptp.aa_set8868280134176360700at_nat _let_1 B3)))) (forall ((A3 tptp.set_nat) (C3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) C3)))) (= (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat B3) C3)) (tptp.aa_set_nat_set_nat _let_1 B3)))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3))) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat (tptp.aa_set8868280134176360700at_nat _let_1 B3)) C3) (tptp.aa_set8868280134176360700at_nat _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat B3) C3))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C3 tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3))) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat (tptp.aa_set_nat_set_nat _let_1 B3)) C3) (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat B3) C3))))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (C3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (tptp.aa_set3125807151510273166at_nat tptp.minus_8321449233255521966at_nat A3))) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.minus_8321449233255521966at_nat (tptp.aa_set5535132180132642428at_nat _let_1 B3)) C3) (tptp.aa_set5535132180132642428at_nat _let_1 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat B3) C3))))) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (C3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (tptp.aa_set4622835569371386638at_nat tptp.minus_5060654252129873198at_nat A3))) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.minus_5060654252129873198at_nat (tptp.aa_set6734554978791863420at_nat _let_1 B3)) C3) (tptp.aa_set6734554978791863420at_nat _let_1 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat B3) C3))))) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (C3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (tptp.aa_set7704514097189807246at_nat tptp.minus_3314409938677909166at_nat A3))) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.minus_3314409938677909166at_nat (tptp.aa_set4883462369968598652at_nat _let_1 B3)) C3) (tptp.aa_set4883462369968598652at_nat _let_1 (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat B3) C3))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C3 tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3))) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat (tptp.aa_set_nat_set_nat _let_1 B3)) C3) (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat B3) C3))))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (C3 tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.minus_8321449233255521966at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3) B3)) C3) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.minus_8321449233255521966at_nat A3) C3)) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.minus_8321449233255521966at_nat B3) C3)))) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (C3 tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.minus_5060654252129873198at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3) B3)) C3) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.minus_5060654252129873198at_nat A3) C3)) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.minus_5060654252129873198at_nat B3) C3)))) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (C3 tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.minus_3314409938677909166at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3) B3)) C3) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.minus_3314409938677909166at_nat A3) C3)) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.minus_3314409938677909166at_nat B3) C3)))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C3 tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)) C3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) C3)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat B3) C3)))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le7866589430770878221at_nat A3) B3)) (exists ((B4 tptp.product_prod_nat_nat)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat B4) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat B3) A3)))))) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool)) (=> (tptp.ord_less_set_bool A3 B3) (exists ((B4 tptp.bool)) (tptp.pp (tptp.member_bool B4 (tptp.minus_minus_set_bool B3 A3)))))) (forall ((A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_less_set_set_nat A3) B3)) (exists ((B4 tptp.set_nat)) (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat B4) (tptp.minus_2163939370556025621et_nat B3 A3)))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int A3) B3)) (exists ((B4 tptp.int)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int B4) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int B3) A3)))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat A3) B3)) (exists ((B4 tptp.nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B4) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat B3) A3)))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A3) B3)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat A3) B3) tptp.bot_bo2099793752762293965at_nat))) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool)) (=> (tptp.ord_less_eq_set_bool A3 B3) (= (tptp.minus_minus_set_bool A3 B3) tptp.bot_bot_set_bool))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) B3)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3) tptp.bot_bot_set_nat))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3) tptp.bot_bot_set_int))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (not (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat A3) B3) A3)) (not (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3) tptp.bot_bo2099793752762293965at_nat)))) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool)) (= (not (= (tptp.minus_minus_set_bool A3 B3) A3)) (not (= (tptp.inf_inf_set_bool A3 B3) tptp.bot_bot_set_bool)))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (not (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3) A3)) (not (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3) tptp.bot_bot_set_int)))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (not (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3) A3)) (not (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3) tptp.bot_bot_set_nat)))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat A3) B3) A3) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3) tptp.bot_bo2099793752762293965at_nat))) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool)) (= (= (tptp.minus_minus_set_bool A3 B3) A3) (= (tptp.inf_inf_set_bool A3 B3) tptp.bot_bot_set_bool))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3) A3) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3) tptp.bot_bot_set_int))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3) A3) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3) tptp.bot_bot_set_nat))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat A3) B3)) tptp.bot_bo2099793752762293965at_nat)) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool)) (= (tptp.inf_inf_set_bool (tptp.inf_inf_set_bool A3 B3) (tptp.minus_minus_set_bool A3 B3)) tptp.bot_bot_set_bool)) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3)) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3)) tptp.bot_bot_set_int)) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3)) tptp.bot_bot_set_nat)) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3) tptp.bot_bo2099793752762293965at_nat) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat A3) B3) A3))) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool)) (=> (= (tptp.inf_inf_set_bool A3 B3) tptp.bot_bot_set_bool) (= (tptp.minus_minus_set_bool A3 B3) A3))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3) tptp.bot_bot_set_int) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3) A3))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (=> (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3) tptp.bot_bot_set_nat) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3) A3))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.ord_le3000389064537975527at_nat A3 B3) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.minus_8321449233255521966at_nat B3) A3)) B3))) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.ord_le8081472938463900775at_nat A3 B3) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.minus_5060654252129873198at_nat B3) A3)) B3))) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.ord_le1268244103169919719at_nat A3 B3) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.minus_3314409938677909166at_nat B3) A3)) B3))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) B3)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat B3) A3)) B3))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int B3) A3)) B3))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (C3 tptp.set_Pr8693737435421807431at_nat)) (= (tptp.ord_le3000389064537975527at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.minus_8321449233255521966at_nat A3) B3) C3) (tptp.ord_le3000389064537975527at_nat A3 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat B3) C3)))) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (C3 tptp.set_Pr8551490117392284871at_nat)) (= (tptp.ord_le8081472938463900775at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.minus_5060654252129873198at_nat A3) B3) C3) (tptp.ord_le8081472938463900775at_nat A3 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat B3) C3)))) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (C3 tptp.set_Pr4329608150637261639at_nat)) (= (tptp.ord_le1268244103169919719at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.minus_3314409938677909166at_nat A3) B3) C3) (tptp.ord_le1268244103169919719at_nat A3 (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat B3) C3)))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3)) C3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat B3) C3))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (C3 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3)) C3)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int B3) C3))))) (forall ((X tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 X)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger X) N2)))))) (forall ((X tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 X)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat X) N2)))))) (forall ((X tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 X)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat X) N2)))))) (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int X) N2)))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat A3) B3)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3)) A3)) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.minus_8321449233255521966at_nat A3) B3)) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat A3) B3)) A3)) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.minus_5060654252129873198at_nat A3) B3)) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat A3) B3)) A3)) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.minus_3314409938677909166at_nat A3) B3)) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat A3) B3)) A3)) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3)) A3)) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat A3) B3)) A3)) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat A3) B3)) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.minus_8321449233255521966at_nat A3) B3)) A3)) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat A3) B3)) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.minus_5060654252129873198at_nat A3) B3)) A3)) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat A3) B3)) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.minus_3314409938677909166at_nat A3) B3)) A3)) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3)) A3)) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat A3))) (= (tptp.aa_set8868280134176360700at_nat _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat B3) C3)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat (tptp.aa_set8868280134176360700at_nat _let_1 B3)) (tptp.aa_set8868280134176360700at_nat _let_1 C3))))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (C3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (tptp.aa_set3125807151510273166at_nat tptp.minus_8321449233255521966at_nat A3))) (= (tptp.aa_set5535132180132642428at_nat _let_1 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat B3) C3)) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat (tptp.aa_set5535132180132642428at_nat _let_1 B3)) (tptp.aa_set5535132180132642428at_nat _let_1 C3))))) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (C3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (tptp.aa_set4622835569371386638at_nat tptp.minus_5060654252129873198at_nat A3))) (= (tptp.aa_set6734554978791863420at_nat _let_1 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat B3) C3)) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat (tptp.aa_set6734554978791863420at_nat _let_1 B3)) (tptp.aa_set6734554978791863420at_nat _let_1 C3))))) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (C3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (tptp.aa_set7704514097189807246at_nat tptp.minus_3314409938677909166at_nat A3))) (= (tptp.aa_set4883462369968598652at_nat _let_1 (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat B3) C3)) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat (tptp.aa_set4883462369968598652at_nat _let_1 B3)) (tptp.aa_set4883462369968598652at_nat _let_1 C3))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C3 tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3))) (= (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat B3) C3)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.aa_set_nat_set_nat _let_1 B3)) (tptp.aa_set_nat_set_nat _let_1 C3))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat A3))) (= (tptp.aa_set8868280134176360700at_nat _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat B3) C3)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.aa_set8868280134176360700at_nat _let_1 B3)) (tptp.aa_set8868280134176360700at_nat _let_1 C3))))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (C3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (tptp.aa_set3125807151510273166at_nat tptp.minus_8321449233255521966at_nat A3))) (= (tptp.aa_set5535132180132642428at_nat _let_1 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat B3) C3)) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat (tptp.aa_set5535132180132642428at_nat _let_1 B3)) (tptp.aa_set5535132180132642428at_nat _let_1 C3))))) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (C3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (tptp.aa_set4622835569371386638at_nat tptp.minus_5060654252129873198at_nat A3))) (= (tptp.aa_set6734554978791863420at_nat _let_1 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat B3) C3)) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat (tptp.aa_set6734554978791863420at_nat _let_1 B3)) (tptp.aa_set6734554978791863420at_nat _let_1 C3))))) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (C3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (tptp.aa_set7704514097189807246at_nat tptp.minus_3314409938677909166at_nat A3))) (= (tptp.aa_set4883462369968598652at_nat _let_1 (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat B3) C3)) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat (tptp.aa_set4883462369968598652at_nat _let_1 B3)) (tptp.aa_set4883462369968598652at_nat _let_1 C3))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C3 tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3))) (= (tptp.aa_set_nat_set_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat B3) C3)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.aa_set_nat_set_nat _let_1 B3)) (tptp.aa_set_nat_set_nat _let_1 C3))))) (forall ((A tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.comm_s4028243227959126397er_rat A))) (=> (not (= (tptp.aa_nat_rat _let_1 M) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (not (= (tptp.aa_nat_rat _let_1 N2) tptp.zero_zero_rat)))))) (forall ((A tptp.rat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.comm_s4028243227959126397er_rat A))) (=> (= (tptp.aa_nat_rat _let_1 N2) tptp.zero_zero_rat) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (= (tptp.aa_nat_rat _let_1 M) tptp.zero_zero_rat))))) (forall ((P tptp.fun_int_bool) (X tptp.nat) (Y tptp.nat)) (= (tptp.pp (tptp.aa_int_bool P (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat X) Y)))) (and (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Y))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (tptp.pp (tptp.aa_int_bool P tptp.zero_zero_int)))))) (forall ((X tptp.code_integer) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) X)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger X) N2))))) (forall ((X tptp.rat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat X) N2))))) (forall ((X tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) X)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat X) N2))))) (forall ((X tptp.int) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) X)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int X) N2))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le7866589430770878221at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat A3) B3)) A3)) (not (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3) tptp.bot_bo2099793752762293965at_nat)))) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool)) (= (tptp.ord_less_set_bool (tptp.minus_minus_set_bool A3 B3) A3) (not (= (tptp.inf_inf_set_bool A3 B3) tptp.bot_bot_set_bool)))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3)) A3)) (not (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3) tptp.bot_bot_set_int)))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3)) A3)) (not (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3) tptp.bot_bot_set_nat)))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger A) (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) N2)))) (forall ((A tptp.rat) (N2 tptp.nat)) (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat A) (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) tptp.one_one_rat)) N2)))) (forall ((A tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat A) (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) tptp.one_one_nat)) N2)))) (forall ((A tptp.int) (N2 tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int A) (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) tptp.one_one_int)) N2)))) (forall ((Z tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.comm_s4028243227959126397er_rat Z))) (= (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Z) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))) (tptp.aa_nat_rat _let_1 N2))))) (forall ((Z tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int Z))) (= (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Z) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) (tptp.aa_nat_int _let_1 N2))))) (forall ((Z tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat Z))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Z) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2))) (tptp.aa_nat_nat _let_1 N2))))) (forall ((Z tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.comm_s8582702949713902594nteger Z))) (= (tptp.aa_nat_Code_integer _let_1 (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger Z) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) (tptp.aa_nat_Code_integer _let_1 N2))))) (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.comm_s4028243227959126397er_rat A))) (= (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 N2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2)))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int A))) (= (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_1 N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat A))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2)))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.comm_s8582702949713902594nteger A))) (= (tptp.aa_nat_Code_integer _let_1 (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer _let_1 N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2)))))) (forall ((Z tptp.rat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.comm_s4028243227959126397er_rat Z))) (= (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) M)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 N2)) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Z) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))) M))))) (forall ((Z tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int Z))) (= (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) M)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_1 N2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Z) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) M))))) (forall ((Z tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat Z))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Z) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2))) M))))) (forall ((Z tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.comm_s8582702949713902594nteger Z))) (= (tptp.aa_nat_Code_integer _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) M)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer _let_1 N2)) (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger Z) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) M))))) (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.rat)) (let ((_let_1 (tptp.comm_s4028243227959126397er_rat Z))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_nat_rat _let_1 N2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 M)) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Z) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M))))))) (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int Z))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_nat_int _let_1 N2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_1 M)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Z) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M))))))) (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat Z))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_nat_nat _let_1 N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Z) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M))))))) (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.code_integer)) (let ((_let_1 (tptp.comm_s8582702949713902594nteger Z))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_nat_Code_integer _let_1 N2) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer _let_1 M)) (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger Z) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M))))))) (forall ((X tptp.rat)) (exists ((N5 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N5))))) (forall ((X tptp.rat)) (exists ((N5 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N5))))) (forall ((W2 tptp.int) (Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int W2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Z) tptp.one_one_int))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int W2) Z)))) (forall ((W2 tptp.int) (Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int W2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Z) tptp.one_one_int))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int W2) Z)))) (forall ((K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) K)) (exists ((N5 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N5)) (= K (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N5)))))) (forall ((K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) K)) (not (forall ((N5 tptp.nat)) (=> (= K (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N5)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N5)))))))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int K)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int I2) J)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 I2)) (tptp.aa_int_int _let_1 J))))))) (forall ((K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (not (forall ((N5 tptp.nat)) (not (= K (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N5))))))) (forall ((K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (exists ((N5 tptp.nat)) (= K (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N5))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3))) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat _let_1) B3) _let_1))) (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat C))) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat A3) B3))) (and (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 A3)) (not (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 B3))))))) (forall ((C tptp.bool) (A3 tptp.set_bool) (B3 tptp.set_bool)) (= (tptp.pp (tptp.member_bool C (tptp.minus_minus_set_bool A3 B3))) (and (tptp.pp (tptp.member_bool C A3)) (not (tptp.pp (tptp.member_bool C B3)))))) (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (tptp.member_set_nat C))) (= (tptp.pp (tptp.aa_set_set_nat_bool _let_1 (tptp.minus_2163939370556025621et_nat A3 B3))) (and (tptp.pp (tptp.aa_set_set_nat_bool _let_1 A3)) (not (tptp.pp (tptp.aa_set_set_nat_bool _let_1 B3))))))) (forall ((C tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (tptp.member_int C))) (= (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3))) (and (tptp.pp (tptp.aa_set_int_bool _let_1 A3)) (not (tptp.pp (tptp.aa_set_int_bool _let_1 B3))))))) (forall ((C tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.member_nat C))) (= (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3))) (and (tptp.pp (tptp.aa_set_nat_bool _let_1 A3)) (not (tptp.pp (tptp.aa_set_nat_bool _let_1 B3))))))) (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat C))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 A3)) (=> (not (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 B3))) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat A3) B3))))))) (forall ((C tptp.bool) (A3 tptp.set_bool) (B3 tptp.set_bool)) (=> (tptp.pp (tptp.member_bool C A3)) (=> (not (tptp.pp (tptp.member_bool C B3))) (tptp.pp (tptp.member_bool C (tptp.minus_minus_set_bool A3 B3)))))) (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (tptp.member_set_nat C))) (=> (tptp.pp (tptp.aa_set_set_nat_bool _let_1 A3)) (=> (not (tptp.pp (tptp.aa_set_set_nat_bool _let_1 B3))) (tptp.pp (tptp.aa_set_set_nat_bool _let_1 (tptp.minus_2163939370556025621et_nat A3 B3))))))) (forall ((C tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (tptp.member_int C))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 A3)) (=> (not (tptp.pp (tptp.aa_set_int_bool _let_1 B3))) (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3))))))) (forall ((C tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.member_nat C))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A3)) (=> (not (tptp.pp (tptp.aa_set_nat_bool _let_1 B3))) (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3))))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat A3) B3) (tptp.collec3392354462482085612at_nat (tptp.aa_fun830836278467416944t_bool (tptp.minus_5597117856863188850t_bool (tptp.aTP_Lamm_a A3)) (tptp.aTP_Lamm_a B3))))) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool)) (= (tptp.minus_minus_set_bool A3 B3) (tptp.collect_bool (tptp.minus_4822186092517116124l_bool (tptp.aTP_Lamm_aa A3) (tptp.aTP_Lamm_aa B3))))) (forall ((A3 tptp.set_Pr958786334691620121nt_int) (B3 tptp.set_Pr958786334691620121nt_int)) (= (tptp.minus_1052850069191792384nt_int A3 B3) (tptp.collec213857154873943460nt_int (tptp.minus_7866439474815358650t_bool (tptp.aTP_Lamm_ab A3) (tptp.aTP_Lamm_ab B3))))) (forall ((A3 tptp.set_list_nat) (B3 tptp.set_list_nat)) (= (tptp.minus_7954133019191499631st_nat A3 B3) (tptp.collect_list_nat (tptp.minus_8064998606961450743t_bool (tptp.aTP_Lamm_ac A3) (tptp.aTP_Lamm_ac B3))))) (forall ((A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (= (tptp.minus_2163939370556025621et_nat A3 B3) (tptp.collect_set_nat (tptp.minus_8322047804725131473t_bool (tptp.aTP_Lamm_ad A3) (tptp.aTP_Lamm_ad B3))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3) (tptp.collect_int (tptp.minus_7727386867957376939t_bool (tptp.aTP_Lamm_af A3) (tptp.aTP_Lamm_af B3))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3) (tptp.collect_nat (tptp.minus_1628305797571225351t_bool (tptp.aTP_Lamm_ae A3) (tptp.aTP_Lamm_ae B3))))) (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat C))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat A3) B3))) (not (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 B3)))))) (forall ((C tptp.bool) (A3 tptp.set_bool) (B3 tptp.set_bool)) (=> (tptp.pp (tptp.member_bool C (tptp.minus_minus_set_bool A3 B3))) (not (tptp.pp (tptp.member_bool C B3))))) (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (tptp.member_set_nat C))) (=> (tptp.pp (tptp.aa_set_set_nat_bool _let_1 (tptp.minus_2163939370556025621et_nat A3 B3))) (not (tptp.pp (tptp.aa_set_set_nat_bool _let_1 B3)))))) (forall ((C tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (tptp.member_int C))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3))) (not (tptp.pp (tptp.aa_set_int_bool _let_1 B3)))))) (forall ((C tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.member_nat C))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3))) (not (tptp.pp (tptp.aa_set_nat_bool _let_1 B3)))))) (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat C))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat A3) B3))) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 A3))))) (forall ((C tptp.bool) (A3 tptp.set_bool) (B3 tptp.set_bool)) (=> (tptp.pp (tptp.member_bool C (tptp.minus_minus_set_bool A3 B3))) (tptp.pp (tptp.member_bool C A3)))) (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (tptp.member_set_nat C))) (=> (tptp.pp (tptp.aa_set_set_nat_bool _let_1 (tptp.minus_2163939370556025621et_nat A3 B3))) (tptp.pp (tptp.aa_set_set_nat_bool _let_1 A3))))) (forall ((C tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (tptp.member_int C))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3))) (tptp.pp (tptp.aa_set_int_bool _let_1 A3))))) (forall ((C tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.member_nat C))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3))) (tptp.pp (tptp.aa_set_nat_bool _let_1 A3))))) (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat C))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat A3) B3))) (not (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 A3)) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 B3))))))) (forall ((C tptp.bool) (A3 tptp.set_bool) (B3 tptp.set_bool)) (=> (tptp.pp (tptp.member_bool C (tptp.minus_minus_set_bool A3 B3))) (not (=> (tptp.pp (tptp.member_bool C A3)) (tptp.pp (tptp.member_bool C B3)))))) (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (tptp.member_set_nat C))) (=> (tptp.pp (tptp.aa_set_set_nat_bool _let_1 (tptp.minus_2163939370556025621et_nat A3 B3))) (not (=> (tptp.pp (tptp.aa_set_set_nat_bool _let_1 A3)) (tptp.pp (tptp.aa_set_set_nat_bool _let_1 B3))))))) (forall ((C tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (tptp.member_int C))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3))) (not (=> (tptp.pp (tptp.aa_set_int_bool _let_1 A3)) (tptp.pp (tptp.aa_set_int_bool _let_1 B3))))))) (forall ((C tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.member_nat C))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3))) (not (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A3)) (tptp.pp (tptp.aa_set_nat_bool _let_1 B3))))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat A3) B3) (tptp.collec3392354462482085612at_nat (tptp.aa_set5223363028666124222t_bool (tptp.aTP_Lamm_gk A3) B3)))) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool)) (= (tptp.minus_minus_set_bool A3 B3) (tptp.collect_bool (tptp.aa_set6670506438128111678l_bool (tptp.aTP_Lamm_gl A3) B3)))) (forall ((A3 tptp.set_Pr958786334691620121nt_int) (B3 tptp.set_Pr958786334691620121nt_int)) (= (tptp.minus_1052850069191792384nt_int A3 B3) (tptp.collec213857154873943460nt_int (tptp.aa_set1381271197253378494t_bool (tptp.aTP_Lamm_gm A3) B3)))) (forall ((A3 tptp.set_list_nat) (B3 tptp.set_list_nat)) (= (tptp.minus_7954133019191499631st_nat A3 B3) (tptp.collect_list_nat (tptp.aa_set257547205302447420t_bool (tptp.aTP_Lamm_gn A3) B3)))) (forall ((A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (= (tptp.minus_2163939370556025621et_nat A3 B3) (tptp.collect_set_nat (tptp.aa_set9121396911425987952t_bool (tptp.aTP_Lamm_go A3) B3)))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3) (tptp.collect_int (tptp.aa_set7012339369581096484t_bool (tptp.aTP_Lamm_gp A3) B3)))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3) (tptp.collect_nat (tptp.aa_set3744802623701456604t_bool (tptp.aTP_Lamm_gq A3) B3)))) (forall ((K tptp.int) (I2 tptp.int) (P tptp.fun_int_bool)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) I2)) (=> (tptp.pp (tptp.aa_int_bool P K)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) I3)) (=> (tptp.pp (tptp.aa_int_bool P I3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I3) tptp.one_one_int)))))) (tptp.pp (tptp.aa_int_bool P I2)))))) (forall ((I2 tptp.int) (K tptp.int) (P tptp.fun_int_bool)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I2) K)) (=> (tptp.pp (tptp.aa_int_bool P K)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I3) K)) (=> (tptp.pp (tptp.aa_int_bool P I3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int I3) tptp.one_one_int)))))) (tptp.pp (tptp.aa_int_bool P I2)))))) (forall ((P tptp.fun_int_bool) (K tptp.int) (I2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P K)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) I3)) (=> (tptp.pp (tptp.aa_int_bool P I3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I3) tptp.one_one_int)))))) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I3) K)) (=> (tptp.pp (tptp.aa_int_bool P I3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int I3) tptp.one_one_int)))))) (tptp.pp (tptp.aa_int_bool P I2)))))) (forall ((K tptp.int) (I2 tptp.int) (P tptp.fun_int_bool)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) I2)) (=> (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) tptp.one_one_int))) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) I3)) (=> (tptp.pp (tptp.aa_int_bool P I3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I3) tptp.one_one_int)))))) (tptp.pp (tptp.aa_int_bool P I2)))))) (forall ((W2 tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int W2))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Z) tptp.one_one_int))) (or (tptp.pp (tptp.aa_int_bool _let_1 Z)) (= W2 Z))))) (forall ((I2 tptp.int) (K tptp.int) (P tptp.fun_int_bool)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int I2) K)) (=> (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int K) tptp.one_one_int))) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int I3) K)) (=> (tptp.pp (tptp.aa_int_bool P I3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int I3) tptp.one_one_int)))))) (tptp.pp (tptp.aa_int_bool P I2)))))) _let_60 (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) Z)) Z)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z) tptp.zero_zero_int)))) _let_59 (forall ((I2 tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int K))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int I2) J)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 I2)) (tptp.aa_int_int _let_1 J))))))) (forall ((M tptp.int) (N2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) M)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int M) N2) tptp.one_one_int) (and (= M tptp.one_one_int) (= N2 tptp.one_one_int))))) (forall ((W2 tptp.int) (Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int W2) tptp.one_one_int)) Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int W2) Z)))) (forall ((W2 tptp.int) (Z tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int W2) Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int W2) tptp.one_one_int)) Z)))) (forall ((W2 tptp.int) (Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int W2) Z)) (exists ((N tptp.nat)) (= Z (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int W2) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)))))) (forall ((Z tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) Z))))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Z)))) (forall ((W2 tptp.int) (Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int W2) Z)) (exists ((N tptp.nat)) (= Z (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int W2) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat tptp.suc N))))))) (forall ((N2 tptp.nat) (F tptp.fun_nat_int) (K tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) N2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int F (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I3) tptp.one_one_nat))) (tptp.aa_nat_int F I3)))) tptp.one_one_int)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int F tptp.zero_zero_nat)) K)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) (tptp.aa_nat_int F N2))) (exists ((I3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I3) N2)) (= (tptp.aa_nat_int F I3) K))))))) (forall ((K tptp.int) (L tptp.int) (Q5 tptp.int) (R3 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int L))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool _let_1 tptp.zero_zero_int)))) (let ((_let_3 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) L)))) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int K L) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q5) R3))) (and (= K (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int L) Q5)) R3)) (=> _let_3 (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) R3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R3) L)))) (=> (not _let_3) (and (=> _let_2 (and (tptp.pp (tptp.aa_int_bool _let_1 R3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int R3) tptp.zero_zero_int)))) (=> (not _let_2) (= Q5 tptp.zero_zero_int)))))))))) (forall ((B tptp.rat) (K tptp.nat)) (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat B) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) K)))) (forall ((B tptp.int) (K tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int K))) tptp.one_one_int)) K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) K)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int (tptp.aa_int_int tptp.uminus_uminus_int B)) K)))) (forall ((B tptp.code_integer) (K tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger B) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger K))) tptp.one_one_Code_integer)) K) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) K)) (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) K)))) (forall ((X tptp.assn)) (= (tptp.aa_assn_assn tptp.uminus_uminus_assn (tptp.aa_assn_assn tptp.uminus_uminus_assn X)) X)) (forall ((X tptp.product_unit)) (= (tptp.uminus2952777764628376836t_unit (tptp.uminus2952777764628376836t_unit X)) X)) (forall ((X tptp.assn) (Y tptp.assn)) (= (= (tptp.aa_assn_assn tptp.uminus_uminus_assn X) (tptp.aa_assn_assn tptp.uminus_uminus_assn Y)) (= X Y))) (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (= (tptp.uminus2952777764628376836t_unit X) (tptp.uminus2952777764628376836t_unit Y)) (= X Y))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.uminus1532241313380277803et_int B3)) (tptp.uminus1532241313380277803et_int A3))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.uminus1532241313380277803et_int A3)) (tptp.uminus1532241313380277803et_int B3))) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) A3)))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B)))) (forall ((B tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) (tptp.aa_rat_rat tptp.uminus_uminus_rat A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)))) (forall ((B tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int B)) (tptp.aa_int_int tptp.uminus_uminus_int A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)))) (forall ((X tptp.assn) (Y tptp.assn)) (= (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn (tptp.aa_assn_assn tptp.uminus_uminus_assn X)) (tptp.aa_assn_assn tptp.uminus_uminus_assn Y))) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn Y) X)))) (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit (tptp.uminus2952777764628376836t_unit X)) (tptp.uminus2952777764628376836t_unit Y))) (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit Y) X)))) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.uminus1532241313380277803et_int X)) (tptp.uminus1532241313380277803et_int Y))) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int Y) X)))) (forall ((B tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int B)) (tptp.aa_int_int tptp.uminus_uminus_int A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B)))) (forall ((B tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) (tptp.aa_rat_rat tptp.uminus_uminus_rat A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)))) (forall ((X tptp.assn) (Y tptp.assn)) (= (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_assn_assn tptp.uminus_uminus_assn X)) (tptp.aa_assn_assn tptp.uminus_uminus_assn Y))) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn Y) X)))) (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le361264281704409273t_unit (tptp.uminus2952777764628376836t_unit X)) (tptp.uminus2952777764628376836t_unit Y))) (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le361264281704409273t_unit Y) X)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) B) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) B) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int A)) (tptp.aa_int_int tptp.uminus_uminus_int B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int tptp.uminus_uminus_int B)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int _let_1 B))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A))) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat _let_1 B))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.uminus6524753893492686040at_nat A3)) A3) tptp.bot_bo2099793752762293965at_nat)) (forall ((A3 tptp.set_bool)) (= (tptp.inf_inf_set_bool (tptp.uminus5166143097222041326t_bool A3) A3) tptp.bot_bot_set_bool)) (forall ((A3 tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.uminus5710092332889474511et_nat A3)) A3) tptp.bot_bot_set_nat)) (forall ((A3 tptp.set_int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int (tptp.uminus1532241313380277803et_int A3)) A3) tptp.bot_bot_set_int)) (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) (tptp.uminus6524753893492686040at_nat A3)) tptp.bot_bo2099793752762293965at_nat)) (forall ((A3 tptp.set_bool)) (= (tptp.inf_inf_set_bool A3 (tptp.uminus5166143097222041326t_bool A3)) tptp.bot_bot_set_bool)) (forall ((A3 tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) (tptp.uminus5710092332889474511et_nat A3)) tptp.bot_bot_set_nat)) (forall ((A3 tptp.set_int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) (tptp.uminus1532241313380277803et_int A3)) tptp.bot_bot_set_int)) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer A))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) A)))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.abs_abs_rat A))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) _let_1) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) A)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.abs_abs_int A))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) A)))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) (tptp.uminus6524753893492686040at_nat B3)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat A3) B3))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) (tptp.uminus5710092332889474511et_nat B3)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat A3) (tptp.uminus6524753893492686040at_nat B3)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) (tptp.uminus5710092332889474511et_nat B3)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))) (= (tptp.aa_rat_rat tptp.abs_abs_rat _let_1) _let_1))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) (= (tptp.aa_int_int tptp.abs_abs_int _let_1) _let_1))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) (= (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer _let_1) _let_1))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (= (tptp.uminus4384627049435823934at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.minus_8321449233255521966at_nat A3) B3)) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat (tptp.uminus4384627049435823934at_nat A3)) B3))) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (= (tptp.uminus2330091110623919550at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.minus_5060654252129873198at_nat A3) B3)) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat (tptp.uminus2330091110623919550at_nat A3)) B3))) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (= (tptp.uminus935396558254630718at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.minus_3314409938677909166at_nat A3) B3)) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat (tptp.uminus935396558254630718at_nat A3)) B3))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.uminus5710092332889474511et_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.uminus5710092332889474511et_nat A3)) B3))) (forall ((N2 tptp.nat) (M tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)))) (forall ((P tptp.assn) (H tptp.produc3658429121746597890et_nat)) (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn (tptp.aa_assn_assn tptp.uminus_uminus_assn P)) H)) (and (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range H)) (not (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn P) H)))))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) A)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int A)) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 tptp.zero_z3403309356797280102nteger))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat A))) (tptp.pp (tptp.aa_rat_bool _let_1 tptp.zero_zero_rat))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int tptp.uminus_uminus_int A))) (tptp.pp (tptp.aa_int_bool _let_1 tptp.zero_zero_int))))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int A)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_rat_rat tptp.uminus_uminus_rat A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int tptp.uminus_uminus_int A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int A)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) A)))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int tptp.uminus_uminus_int A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat tptp.uminus_uminus_rat A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int A)) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) A)))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) A)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int A))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int tptp.uminus_uminus_int A))) (tptp.pp (tptp.aa_int_bool _let_1 tptp.zero_zero_int))))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 tptp.zero_z3403309356797280102nteger))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat A))) (tptp.pp (tptp.aa_rat_bool _let_1 tptp.zero_zero_rat))))) (forall ((Z tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Z) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.aa_int_int tptp.uminus_uminus_int Z))) (forall ((Z tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger Z) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger Z))) (forall ((Z tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Z) (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) (tptp.aa_rat_rat tptp.uminus_uminus_rat Z))) (forall ((Z tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) Z) (tptp.aa_int_int tptp.uminus_uminus_int Z))) (forall ((Z tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) Z) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger Z))) (forall ((Z tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) Z) (tptp.aa_rat_rat tptp.uminus_uminus_rat Z))) (forall ((A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)) (= (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer A) A))) (forall ((A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (= (tptp.aa_rat_rat tptp.abs_abs_rat A) A))) (forall ((A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (= (tptp.aa_int_int tptp.abs_abs_int A) A))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer A)) A)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int A)) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger)) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) tptp.zero_zero_rat)) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int A)) tptp.zero_zero_int)) (= A tptp.zero_zero_int))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer A))) (not (= A tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat tptp.abs_abs_rat A))) (not (= A tptp.zero_zero_rat)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int tptp.abs_abs_int A))) (not (= A tptp.zero_zero_int)))) (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X) (tptp.uminus6524753893492686040at_nat X)) tptp.bot_bo2099793752762293965at_nat)) (forall ((X tptp.set_bool)) (= (tptp.inf_inf_set_bool X (tptp.uminus5166143097222041326t_bool X)) tptp.bot_bot_set_bool)) (forall ((X tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X) (tptp.uminus5710092332889474511et_nat X)) tptp.bot_bot_set_nat)) (forall ((X tptp.set_int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int X) (tptp.uminus1532241313380277803et_int X)) tptp.bot_bot_set_int)) (forall ((X tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X) (tptp.aa_assn_assn tptp.uminus_uminus_assn X)) tptp.bot_bot_assn)) (forall ((X tptp.product_unit)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X) (tptp.uminus2952777764628376836t_unit X)) tptp.bot_bot_Product_unit)) (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.uminus6524753893492686040at_nat X)) X) tptp.bot_bo2099793752762293965at_nat)) (forall ((X tptp.set_bool)) (= (tptp.inf_inf_set_bool (tptp.uminus5166143097222041326t_bool X) X) tptp.bot_bot_set_bool)) (forall ((X tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.uminus5710092332889474511et_nat X)) X) tptp.bot_bot_set_nat)) (forall ((X tptp.set_int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int (tptp.uminus1532241313380277803et_int X)) X) tptp.bot_bot_set_int)) (forall ((X tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn (tptp.aa_assn_assn tptp.uminus_uminus_assn X)) X) tptp.bot_bot_assn)) (forall ((X tptp.product_unit)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit (tptp.uminus2952777764628376836t_unit X)) X) tptp.bot_bot_Product_unit)) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat Y) (tptp.uminus6524753893492686040at_nat X))) tptp.bot_bo2099793752762293965at_nat)) (forall ((X tptp.set_bool) (Y tptp.set_bool)) (= (tptp.inf_inf_set_bool X (tptp.inf_inf_set_bool Y (tptp.uminus5166143097222041326t_bool X))) tptp.bot_bot_set_bool)) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat Y) (tptp.uminus5710092332889474511et_nat X))) tptp.bot_bot_set_nat)) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int X) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int Y) (tptp.uminus1532241313380277803et_int X))) tptp.bot_bot_set_int)) (forall ((X tptp.assn) (Y tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn Y) (tptp.aa_assn_assn tptp.uminus_uminus_assn X))) tptp.bot_bot_assn)) (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit Y) (tptp.uminus2952777764628376836t_unit X))) tptp.bot_bot_Product_unit)) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.uminus6524753893492686040at_nat X)) Y)) tptp.bot_bo2099793752762293965at_nat)) (forall ((X tptp.set_bool) (Y tptp.set_bool)) (= (tptp.inf_inf_set_bool X (tptp.inf_inf_set_bool (tptp.uminus5166143097222041326t_bool X) Y)) tptp.bot_bot_set_bool)) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.uminus5710092332889474511et_nat X)) Y)) tptp.bot_bot_set_nat)) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int X) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int (tptp.uminus1532241313380277803et_int X)) Y)) tptp.bot_bot_set_int)) (forall ((X tptp.assn) (Y tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn (tptp.aa_assn_assn tptp.uminus_uminus_assn X)) Y)) tptp.bot_bot_assn)) (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit (tptp.uminus2952777764628376836t_unit X)) Y)) tptp.bot_bot_Product_unit)) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.uminus6524753893492686040at_nat X)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X) Y)) tptp.bot_bo2099793752762293965at_nat)) (forall ((X tptp.set_bool) (Y tptp.set_bool)) (= (tptp.inf_inf_set_bool (tptp.uminus5166143097222041326t_bool X) (tptp.inf_inf_set_bool X Y)) tptp.bot_bot_set_bool)) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.uminus5710092332889474511et_nat X)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X) Y)) tptp.bot_bot_set_nat)) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int (tptp.uminus1532241313380277803et_int X)) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int X) Y)) tptp.bot_bot_set_int)) (forall ((X tptp.assn) (Y tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn (tptp.aa_assn_assn tptp.uminus_uminus_assn X)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X) Y)) tptp.bot_bot_assn)) (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit (tptp.uminus2952777764628376836t_unit X)) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X) Y)) tptp.bot_bot_Product_unit)) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (tptp.uminus6524753893492686040at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat X) Y)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.uminus6524753893492686040at_nat X)) (tptp.uminus6524753893492686040at_nat Y)))) (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat)) (= (tptp.uminus4384627049435823934at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat X) Y)) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat (tptp.uminus4384627049435823934at_nat X)) (tptp.uminus4384627049435823934at_nat Y)))) (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat)) (= (tptp.uminus2330091110623919550at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat X) Y)) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat (tptp.uminus2330091110623919550at_nat X)) (tptp.uminus2330091110623919550at_nat Y)))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (= (tptp.uminus935396558254630718at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat X) Y)) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat (tptp.uminus935396558254630718at_nat X)) (tptp.uminus935396558254630718at_nat Y)))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (tptp.uminus5710092332889474511et_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat X) Y)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.uminus5710092332889474511et_nat X)) (tptp.uminus5710092332889474511et_nat Y)))) (forall ((X tptp.assn) (Y tptp.assn)) (= (tptp.aa_assn_assn tptp.uminus_uminus_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn X) Y)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn (tptp.aa_assn_assn tptp.uminus_uminus_assn X)) (tptp.aa_assn_assn tptp.uminus_uminus_assn Y)))) (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (tptp.uminus2952777764628376836t_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.sup_sup_Product_unit X) Y)) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit (tptp.uminus2952777764628376836t_unit X)) (tptp.uminus2952777764628376836t_unit Y)))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (tptp.uminus6524753893492686040at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X) Y)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat (tptp.uminus6524753893492686040at_nat X)) (tptp.uminus6524753893492686040at_nat Y)))) (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat)) (= (tptp.uminus4384627049435823934at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat X) Y)) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat (tptp.uminus4384627049435823934at_nat X)) (tptp.uminus4384627049435823934at_nat Y)))) (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat)) (= (tptp.uminus2330091110623919550at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat X) Y)) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat (tptp.uminus2330091110623919550at_nat X)) (tptp.uminus2330091110623919550at_nat Y)))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (= (tptp.uminus935396558254630718at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat X) Y)) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat (tptp.uminus935396558254630718at_nat X)) (tptp.uminus935396558254630718at_nat Y)))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (tptp.uminus5710092332889474511et_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X) Y)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.uminus5710092332889474511et_nat X)) (tptp.uminus5710092332889474511et_nat Y)))) (forall ((X tptp.assn) (Y tptp.assn)) (= (tptp.aa_assn_assn tptp.uminus_uminus_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X) Y)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn (tptp.aa_assn_assn tptp.uminus_uminus_assn X)) (tptp.aa_assn_assn tptp.uminus_uminus_assn Y)))) (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (tptp.uminus2952777764628376836t_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X) Y)) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.sup_sup_Product_unit (tptp.uminus2952777764628376836t_unit X)) (tptp.uminus2952777764628376836t_unit Y)))) (forall ((N2 tptp.nat) (M tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat tptp.suc N2)))) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)))) (forall ((A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger)) (= (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)))) (forall ((A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (= (tptp.aa_rat_rat tptp.abs_abs_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat A)))) (forall ((A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (= (tptp.aa_int_int tptp.abs_abs_int A) (tptp.aa_int_int tptp.uminus_uminus_int A)))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A) (tptp.aa_rat_rat tptp.abs_abs_rat B)))) (or (tptp.pp (tptp.aa_rat_bool _let_1 A)) (= B tptp.zero_zero_rat))))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A) (tptp.aa_rat_rat tptp.abs_abs_rat B))) tptp.zero_zero_rat)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (= B tptp.zero_zero_rat)))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) N2)))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int _let_1 A)) A))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2)))) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger _let_1 A)) A))) (forall ((N2 tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) N2)))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat _let_1 A)) A))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) N2))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) _let_1) tptp.one_one_int))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) _let_1) tptp.one_one_Code_integer))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) N2))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) _let_1) tptp.one_one_rat))) (forall ((V tptp.num) (W2 tptp.num) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int W2))) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W2))) Y))) (forall ((V tptp.num) (W2 tptp.num) (Y tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger V))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger W2))) Y)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W2))) Y))) (forall ((V tptp.num) (W2 tptp.num) (Y tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W2))) Y)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W2))) Y))) (forall ((V tptp.num) (W2 tptp.num) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int V)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int W2))) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W2)))) Y))) (forall ((V tptp.num) (W2 tptp.num) (Y tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger V)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger W2))) Y)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W2)))) Y))) (forall ((V tptp.num) (W2 tptp.num) (Y tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W2))) Y)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W2)))) Y))) (forall ((V tptp.num) (W2 tptp.num) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int W2)) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W2)))) Y))) (forall ((V tptp.num) (W2 tptp.num) (Y tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger V))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger W2)) Y)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W2)))) Y))) (forall ((V tptp.num) (W2 tptp.num) (Y tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W2)) Y)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W2)))) Y))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N2))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2))) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2))) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))) (tptp.aa_num_int tptp.numeral_numeral_int N2)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))) (tptp.aa_num_rat tptp.numeral_numeral_rat N2)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N2))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2))) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2))) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2)))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.abs_abs_int Z)) tptp.one_one_int)) (= Z tptp.zero_zero_int))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2)))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num N2) M)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2)))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num N2) M)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N2)))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num N2) M)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N2)))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num N2) M)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2)))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num N2) M)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2)))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num N2) M)))) (forall ((B tptp.rat) (W2 tptp.num) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W2)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) _let_1)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1)) B))))) (forall ((A tptp.rat) (B tptp.rat) (W2 tptp.num)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W2)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) _let_1))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1)))))) (forall ((A tptp.rat) (B tptp.rat) (W2 tptp.num)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W2)))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= A (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) _let_1)) (and (=> (not _let_2) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_rat))))))) (forall ((B tptp.rat) (W2 tptp.num) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W2)))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) _let_1) A) (and (=> (not _let_2) (= B (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1))) (=> _let_2 (= A tptp.zero_zero_rat))))))) (forall ((A tptp.rat) (B tptp.rat) (W2 tptp.num)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W2)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) _let_1))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1)))))) (forall ((B tptp.rat) (W2 tptp.num) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W2)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) _let_1)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1)) B))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer A)) N2))) (or (not (= A tptp.zero_z3403309356797280102nteger)) (= N2 tptp.zero_zero_nat)))) (forall ((A tptp.rat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) N2))) (or (not (= A tptp.zero_zero_rat)) (= N2 tptp.zero_zero_nat)))) (forall ((A tptp.int) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.abs_abs_int A)) N2))) (or (not (= A tptp.zero_zero_int)) (= N2 tptp.zero_zero_nat)))) (forall ((X tptp.product_prod_int_int)) (not (forall ((D tptp.int) (I3 tptp.int)) (not (= X (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int D) I3)))))) (forall ((X tptp.produc6768802789813714928nt_int)) (not (forall ((F2 tptp.fun_in6429348457993719614e_term) (D tptp.int) (I3 tptp.int)) (not (= X (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int F2) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int D) I3))))))) (forall ((X tptp.produc4441460161354545860nt_int)) (not (forall ((F2 tptp.fun_Pr9164807099015279978e_term) (D tptp.int) (I3 tptp.int)) (not (= X (tptp.aa_Pro3513184699142849729nt_int (tptp.aa_fun1388719692539776744nt_int tptp.produc1560874099174258678nt_int F2) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int D) I3))))))) (forall ((A tptp.int) (B tptp.int) (Q5 tptp.int) (R3 tptp.int) (Q7 tptp.int) (R6 tptp.int)) (let ((_let_1 (tptp.eucl_rel_int A B))) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool _let_1 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q5) R3))) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool _let_1 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q7) R6))) (= R3 R6))))) (forall ((A tptp.int) (B tptp.int) (Q5 tptp.int) (R3 tptp.int) (Q7 tptp.int) (R6 tptp.int)) (let ((_let_1 (tptp.eucl_rel_int A B))) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool _let_1 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q5) R3))) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool _let_1 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q7) R6))) (= Q5 Q7))))) (forall ((A tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer A)))) (forall ((A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat A)))) (forall ((A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int A)) (tptp.aa_int_int tptp.abs_abs_int A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer A)) B)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) B))))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) B)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) B))))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int A)) B)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer A)) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) B)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) B)))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int A)) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer A)) B))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) B))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int A)) B))))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.abs_abs_int A)) B)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer A)) B)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) B))))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) B)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) B))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer A) B) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B)) (or (= A B) (= A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)))))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (tptp.aa_rat_rat tptp.abs_abs_rat A) B) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) B)) (or (= A B) (= A (tptp.aa_rat_rat tptp.uminus_uminus_rat B)))))) (forall ((A tptp.int) (B tptp.int)) (= (= (tptp.aa_int_int tptp.abs_abs_int A) B) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) B)) (or (= A B) (= A (tptp.aa_int_int tptp.uminus_uminus_int B)))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer B)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)) (or (= B A) (= B (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)))))) (forall ((A tptp.rat) (B tptp.rat)) (= (= A (tptp.aa_rat_rat tptp.abs_abs_rat B)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (or (= B A) (= B (tptp.aa_rat_rat tptp.uminus_uminus_rat A)))))) (forall ((A tptp.int) (B tptp.int)) (= (= A (tptp.aa_int_int tptp.abs_abs_int B)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (or (= B A) (= B (tptp.aa_int_int tptp.uminus_uminus_int A)))))) (forall ((A tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer A))) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat tptp.abs_abs_rat A))) tptp.zero_zero_rat))) (forall ((A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int tptp.abs_abs_int A))) tptp.zero_zero_int))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.abs_abs_int A))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)))) (and (=> _let_2 (= _let_1 (tptp.aa_int_int tptp.uminus_uminus_int A))) (=> (not _let_2) (= _let_1 A)))))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer A))) (let ((_let_2 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger)))) (and (=> _let_2 (= _let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))) (=> (not _let_2) (= _let_1 A)))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.abs_abs_rat A))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)))) (and (=> _let_2 (= _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat A))) (=> (not _let_2) (= _let_1 A)))))) (forall ((X5 tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.abs_abs_int X5))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X5) tptp.zero_zero_int)))) (and (=> _let_2 (= _let_1 (tptp.aa_int_int tptp.uminus_uminus_int X5))) (=> (not _let_2) (= _let_1 X5)))))) (forall ((X5 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer X5))) (let ((_let_2 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger X5) tptp.zero_z3403309356797280102nteger)))) (and (=> _let_2 (= _let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger X5))) (=> (not _let_2) (= _let_1 X5)))))) (forall ((X5 tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.abs_abs_rat X5))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X5) tptp.zero_zero_rat)))) (and (=> _let_2 (= _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat X5))) (=> (not _let_2) (= _let_1 X5)))))) (forall ((A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)) (= (tptp.aa_int_int tptp.abs_abs_int A) (tptp.aa_int_int tptp.uminus_uminus_int A)))) (forall ((A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger)) (= (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)))) (forall ((A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (= (tptp.aa_rat_rat tptp.abs_abs_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat A)))) (forall ((I2 tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.abs_abs_int I2))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int I2) tptp.zero_zero_int)))) (and (=> _let_2 (= _let_1 (tptp.aa_int_int tptp.uminus_uminus_int I2))) (=> (not _let_2) (= _let_1 I2)))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer A)) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int A)) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)))) (forall ((A tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer A)))) (forall ((A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat tptp.abs_abs_rat A)))) (forall ((A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) (tptp.aa_int_int tptp.abs_abs_int A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer A)) (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat B)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.abs_abs_int A)) (tptp.aa_int_int tptp.abs_abs_int B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) (tptp.aa_rat_rat tptp.uminus_uminus_rat A))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int B)) (tptp.aa_int_int tptp.uminus_uminus_int A))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) A)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) A)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int B)) A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) (tptp.aa_rat_rat tptp.uminus_uminus_rat A))))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) (tptp.aa_int_int tptp.uminus_uminus_int B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) (tptp.aa_int_int tptp.uminus_uminus_int A))))) (forall ((Y tptp.assn) (X tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn (tptp.aa_assn_assn tptp.uminus_uminus_assn Y)) X)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn (tptp.aa_assn_assn tptp.uminus_uminus_assn X)) Y)))) (forall ((Y tptp.product_unit) (X tptp.product_unit)) (=> (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit (tptp.uminus2952777764628376836t_unit Y)) X)) (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit (tptp.uminus2952777764628376836t_unit X)) Y)))) (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.uminus1532241313380277803et_int Y)) X)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.uminus1532241313380277803et_int X)) Y)))) (forall ((Y tptp.assn) (X tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn Y) (tptp.aa_assn_assn tptp.uminus_uminus_assn X))) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn X) (tptp.aa_assn_assn tptp.uminus_uminus_assn Y))))) (forall ((Y tptp.product_unit) (X tptp.product_unit)) (=> (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit Y) (tptp.uminus2952777764628376836t_unit X))) (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit X) (tptp.uminus2952777764628376836t_unit Y))))) (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int Y) (tptp.uminus1532241313380277803et_int X))) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X) (tptp.uminus1532241313380277803et_int Y))))) (forall ((X tptp.assn) (Y tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn X) Y)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn (tptp.aa_assn_assn tptp.uminus_uminus_assn Y)) (tptp.aa_assn_assn tptp.uminus_uminus_assn X))))) (forall ((X tptp.product_unit) (Y tptp.product_unit)) (=> (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit X) Y)) (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit (tptp.uminus2952777764628376836t_unit Y)) (tptp.uminus2952777764628376836t_unit X))))) (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X) Y)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.uminus1532241313380277803et_int Y)) (tptp.uminus1532241313380277803et_int X))))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int B)) A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) A)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) A)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) (tptp.aa_int_int tptp.uminus_uminus_int B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) (tptp.aa_int_int tptp.uminus_uminus_int A))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger B) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) (tptp.aa_rat_rat tptp.uminus_uminus_rat A))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int B)) (tptp.aa_int_int tptp.uminus_uminus_int A))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) (tptp.aa_rat_rat tptp.uminus_uminus_rat A))))) (forall ((Y tptp.assn) (X tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn Y) (tptp.aa_assn_assn tptp.uminus_uminus_assn X))) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn X) (tptp.aa_assn_assn tptp.uminus_uminus_assn Y))))) (forall ((Y tptp.product_unit) (X tptp.product_unit)) (=> (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le361264281704409273t_unit Y) (tptp.uminus2952777764628376836t_unit X))) (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le361264281704409273t_unit X) (tptp.uminus2952777764628376836t_unit Y))))) (forall ((Y tptp.assn) (X tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_assn_assn tptp.uminus_uminus_assn Y)) X)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn (tptp.aa_assn_assn tptp.uminus_uminus_assn X)) Y)))) (forall ((Y tptp.product_unit) (X tptp.product_unit)) (=> (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le361264281704409273t_unit (tptp.uminus2952777764628376836t_unit Y)) X)) (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le361264281704409273t_unit (tptp.uminus2952777764628376836t_unit X)) Y)))) (forall ((A tptp.int) (B tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) B)) (or (= A B) (= A (tptp.aa_int_int tptp.uminus_uminus_int B))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) B)) (or (= A B) (= A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B))))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) B)) (or (= A B) (= A (tptp.aa_rat_rat tptp.uminus_uminus_rat B))))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) (tptp.aa_int_int tptp.uminus_uminus_int B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) B) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat B)))) (forall ((A tptp.assn) (B tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.minus_minus_assn A) B) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn A) (tptp.aa_assn_assn tptp.uminus_uminus_assn B)))) (forall ((P tptp.fun_Pr803113274115125473t_bool) (Q tptp.fun_Pr803113274115125473t_bool)) (= (tptp.collec213857154873943460nt_int (tptp.aa_fun8917503761599146496t_bool (tptp.aTP_Lamm_gr P) Q)) (tptp.sup_su6024340866399070445nt_int (tptp.uminus6221592323253981072nt_int (tptp.collec213857154873943460nt_int P)) (tptp.collec213857154873943460nt_int Q)))) (forall ((P tptp.fun_list_nat_bool) (Q tptp.fun_list_nat_bool)) (= (tptp.collect_list_nat (tptp.aa_fun6009467934925565500t_bool (tptp.aTP_Lamm_gs P) Q)) (tptp.sup_sup_set_list_nat (tptp.uminus3195874150345416415st_nat (tptp.collect_list_nat P)) (tptp.collect_list_nat Q)))) (forall ((P tptp.fun_set_nat_bool) (Q tptp.fun_set_nat_bool)) (= (tptp.collect_set_nat (tptp.aa_fun3565389549526402364t_bool (tptp.aTP_Lamm_gt P) Q)) (tptp.sup_sup_set_set_nat (tptp.uminus613421341184616069et_nat (tptp.collect_set_nat P)) (tptp.collect_set_nat Q)))) (forall ((P tptp.fun_int_bool) (Q tptp.fun_int_bool)) (= (tptp.collect_int (tptp.aa_fun5146555767781538748t_bool (tptp.aTP_Lamm_gu P) Q)) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int (tptp.uminus1532241313380277803et_int (tptp.collect_int P))) (tptp.collect_int Q)))) (forall ((P tptp.fun_Pr446604468264085555t_bool) (Q tptp.fun_Pr446604468264085555t_bool)) (= (tptp.collec7088162979684241874at_nat (tptp.aa_fun3665199231186260388t_bool (tptp.aTP_Lamm_gv P) Q)) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat (tptp.uminus4384627049435823934at_nat (tptp.collec7088162979684241874at_nat P))) (tptp.collec7088162979684241874at_nat Q)))) (forall ((P tptp.fun_Pr3976602594631769267t_bool) (Q tptp.fun_Pr3976602594631769267t_bool)) (= (tptp.collec5204685387357076818at_nat (tptp.aa_fun3556822901603992740t_bool (tptp.aTP_Lamm_gw P) Q)) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat (tptp.uminus2330091110623919550at_nat (tptp.collec5204685387357076818at_nat P))) (tptp.collec5204685387357076818at_nat Q)))) (forall ((P tptp.fun_Pr1607443439640623155t_bool) (Q tptp.fun_Pr1607443439640623155t_bool)) (= (tptp.collec6321179662152712658at_nat (tptp.aa_fun5022828243006652836t_bool (tptp.aTP_Lamm_gx P) Q)) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat (tptp.uminus935396558254630718at_nat (tptp.collec6321179662152712658at_nat P))) (tptp.collec6321179662152712658at_nat Q)))) (forall ((P tptp.fun_nat_bool) (Q tptp.fun_nat_bool)) (= (tptp.collect_nat (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_gy P) Q)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.uminus5710092332889474511et_nat (tptp.collect_nat P))) (tptp.collect_nat Q)))) (forall ((K tptp.int)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int K tptp.zero_zero_int) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) K)))) (forall ((K tptp.int) (L tptp.int) (Q5 tptp.int) (R3 tptp.int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int K L) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q5) R3))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int K) L) Q5))) (forall ((A tptp.int) (B tptp.int) (Q5 tptp.int) (R3 tptp.int)) (let ((_let_1 (tptp.if_int (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int R3) tptp.zero_zero_int)))) (let ((_let_2 (tptp.aa_int_int tptp.uminus_uminus_int Q5))) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int A B) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q5) R3))) (=> (not (= B tptp.zero_zero_int)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int (tptp.aa_int_int tptp.uminus_uminus_int A) B) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int _let_1 _let_2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int _let_2) tptp.one_one_int))) (tptp.aa_int_int (tptp.aa_int_fun_int_int _let_1 tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) R3)))))))))) (forall ((K tptp.int) (L tptp.int) (Q5 tptp.int) (R3 tptp.int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int K L) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q5) R3))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int K) L) R3))) (forall ((A tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer A)))) (forall ((A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_rat_rat tptp.abs_abs_rat A)))) (forall ((A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int tptp.abs_abs_int A)))) (forall ((A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A)) (= (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer A) A))) (forall ((A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (= (tptp.aa_rat_rat tptp.abs_abs_rat A) A))) (forall ((A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) A)) (= (tptp.aa_int_int tptp.abs_abs_int A) A))) (forall ((A tptp.code_integer)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.rat)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) tptp.zero_zero_rat)))) (forall ((A tptp.int)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.abs_abs_int A)) tptp.zero_zero_int)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) B))) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer A)) (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer B))))) (forall ((A tptp.rat) (B tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat B))))) (forall ((A tptp.int) (B tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.abs_abs_int A)) (tptp.aa_int_int tptp.abs_abs_int B))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer A)) (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer B))) (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger A) B))))) (forall ((A tptp.rat) (B tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat B))) (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) B))))) (forall ((A tptp.int) (B tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int tptp.abs_abs_int A)) (tptp.aa_int_int tptp.abs_abs_int B))) (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer A)) (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer B)))) (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger A) B))))) (forall ((A tptp.rat) (B tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat B)))) (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) B))))) (forall ((A tptp.int) (B tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int tptp.abs_abs_int A)) (tptp.aa_int_int tptp.abs_abs_int B)))) (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer A)) (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer B))) (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger B) A))))) (forall ((A tptp.rat) (B tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat B))) (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat B) A))))) (forall ((A tptp.int) (B tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int tptp.abs_abs_int A)) (tptp.aa_int_int tptp.abs_abs_int B))) (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) A))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer B))) (let ((_let_2 (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger _let_2) C)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger _let_1) D2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_2) _let_1)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) D2)))))))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.abs_abs_rat B))) (let ((_let_2 (tptp.aa_rat_rat tptp.abs_abs_rat A))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_2) C)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_1) D2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_2) _let_1)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) D2)))))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.abs_abs_int B))) (let ((_let_2 (tptp.aa_int_int tptp.abs_abs_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int _let_2) C)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int _let_1) D2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_2) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) D2)))))))) (forall ((M tptp.num) (N2 tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2)))) (forall ((M tptp.num) (N2 tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))) (tptp.aa_num_rat tptp.numeral_numeral_rat N2)))) (forall ((M tptp.num) (N2 tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))) (tptp.aa_num_int tptp.numeral_numeral_int N2)))) (forall ((M tptp.num) (N2 tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2)))))) (forall ((M tptp.num) (N2 tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2)))))) (forall ((M tptp.num) (N2 tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N2)))))) (tptp.pp (tptp.aa_Code_integer_bool _let_52 tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_rat_bool _let_51 tptp.one_one_rat)) (tptp.pp (tptp.aa_int_bool _let_50 tptp.one_one_int)) (not (tptp.pp (tptp.aa_Code_integer_bool _let_58 _let_43))) (not (tptp.pp (tptp.aa_rat_bool _let_57 _let_33))) (not (tptp.pp (tptp.aa_int_bool _let_56 _let_32))) (forall ((M tptp.num) (N2 tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))) (tptp.aa_num_int tptp.numeral_numeral_int N2)))) (forall ((M tptp.num) (N2 tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2)))) (forall ((M tptp.num) (N2 tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))) (tptp.aa_num_rat tptp.numeral_numeral_rat N2)))) (forall ((M tptp.num) (N2 tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N2)))))) (forall ((M tptp.num) (N2 tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2)))))) (forall ((M tptp.num) (N2 tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2)))))) (tptp.pp (tptp.aa_int_bool _let_47 tptp.one_one_int)) (tptp.pp (tptp.aa_Code_integer_bool _let_46 tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_rat_bool _let_45 tptp.one_one_rat)) (not (tptp.pp (tptp.aa_int_bool _let_55 _let_32))) (not (tptp.pp (tptp.aa_Code_integer_bool _let_54 _let_43))) (not (tptp.pp (tptp.aa_rat_bool _let_53 _let_33))) (forall ((W2 tptp.num) (X tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int W2))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int tptp.uminus_uminus_int X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) (tptp.aa_int_int tptp.uminus_uminus_int _let_1))))) (forall ((W2 tptp.num) (X tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger W2))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger X)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger X) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger _let_1))))) (forall ((W2 tptp.num) (X tptp.rat)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W2))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) (tptp.aa_rat_rat tptp.uminus_uminus_rat X)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) (tptp.aa_rat_rat tptp.uminus_uminus_rat _let_1))))) (forall ((X tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) X) tptp.one_one_int) (or (= X tptp.one_one_int) (= X (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))))) (forall ((X tptp.code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger X) X) tptp.one_one_Code_integer) (or (= X tptp.one_one_Code_integer) (= X (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))) (forall ((X tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) X) tptp.one_one_rat) (or (= X tptp.one_one_rat) (= X (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat X) Y) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X) (tptp.uminus6524753893492686040at_nat Y)))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat X) Y) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X) (tptp.uminus5710092332889474511et_nat Y)))) (forall ((X tptp.assn) (Y tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.minus_minus_assn X) Y) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X) (tptp.aa_assn_assn tptp.uminus_uminus_assn Y)))) (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.minus_3524152463667985524t_unit X) Y) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X) (tptp.uminus2952777764628376836t_unit Y)))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.uminus6524753893492686040at_nat X)) A)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X) B)) tptp.bot_bo2099793752762293965at_nat)) (forall ((X tptp.set_bool) (A tptp.set_bool) (B tptp.set_bool)) (= (tptp.inf_inf_set_bool (tptp.inf_inf_set_bool (tptp.uminus5166143097222041326t_bool X) A) (tptp.inf_inf_set_bool X B)) tptp.bot_bot_set_bool)) (forall ((X tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.uminus5710092332889474511et_nat X)) A)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X) B)) tptp.bot_bot_set_nat)) (forall ((X tptp.set_int) (A tptp.set_int) (B tptp.set_int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int (tptp.uminus1532241313380277803et_int X)) A)) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int X) B)) tptp.bot_bot_set_int)) (forall ((X tptp.assn) (A tptp.assn) (B tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn (tptp.aa_assn_assn tptp.uminus_uminus_assn X)) A)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X) B)) tptp.bot_bot_assn)) (forall ((X tptp.product_unit) (A tptp.product_unit) (B tptp.product_unit)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit (tptp.uminus2952777764628376836t_unit X)) A)) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X) B)) tptp.bot_bot_Product_unit)) (forall ((X tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X) A)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.uminus6524753893492686040at_nat X)) B)) tptp.bot_bo2099793752762293965at_nat)) (forall ((X tptp.set_bool) (A tptp.set_bool) (B tptp.set_bool)) (= (tptp.inf_inf_set_bool (tptp.inf_inf_set_bool X A) (tptp.inf_inf_set_bool (tptp.uminus5166143097222041326t_bool X) B)) tptp.bot_bot_set_bool)) (forall ((X tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X) A)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.uminus5710092332889474511et_nat X)) B)) tptp.bot_bot_set_nat)) (forall ((X tptp.set_int) (A tptp.set_int) (B tptp.set_int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int X) A)) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int (tptp.uminus1532241313380277803et_int X)) B)) tptp.bot_bot_set_int)) (forall ((X tptp.assn) (A tptp.assn) (B tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X) A)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn (tptp.aa_assn_assn tptp.uminus_uminus_assn X)) B)) tptp.bot_bot_assn)) (forall ((X tptp.product_unit) (A tptp.product_unit) (B tptp.product_unit)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X) A)) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit (tptp.uminus2952777764628376836t_unit X)) B)) tptp.bot_bot_Product_unit)) (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A3) (tptp.uminus6524753893492686040at_nat A3))) (= A3 tptp.bot_bo2099793752762293965at_nat))) (forall ((A3 tptp.set_bool)) (= (tptp.ord_less_eq_set_bool A3 (tptp.uminus5166143097222041326t_bool A3)) (= A3 tptp.bot_bot_set_bool))) (forall ((A3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) (tptp.uminus5710092332889474511et_nat A3))) (= A3 tptp.bot_bot_set_nat))) (forall ((A3 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) (tptp.uminus1532241313380277803et_int A3))) (= A3 tptp.bot_bot_set_int))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.uminus6524753893492686040at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat (tptp.uminus6524753893492686040at_nat A3)) (tptp.uminus6524753893492686040at_nat B3)))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (= (tptp.uminus4384627049435823934at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat A3) B3)) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat (tptp.uminus4384627049435823934at_nat A3)) (tptp.uminus4384627049435823934at_nat B3)))) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (= (tptp.uminus2330091110623919550at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat A3) B3)) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat (tptp.uminus2330091110623919550at_nat A3)) (tptp.uminus2330091110623919550at_nat B3)))) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (= (tptp.uminus935396558254630718at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat A3) B3)) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat (tptp.uminus935396558254630718at_nat A3)) (tptp.uminus935396558254630718at_nat B3)))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.uminus5710092332889474511et_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.uminus5710092332889474511et_nat A3)) (tptp.uminus5710092332889474511et_nat B3)))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.uminus6524753893492686040at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat A3) B3)) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.uminus6524753893492686040at_nat A3)) (tptp.uminus6524753893492686040at_nat B3)))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (= (tptp.uminus4384627049435823934at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3) B3)) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat (tptp.uminus4384627049435823934at_nat A3)) (tptp.uminus4384627049435823934at_nat B3)))) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (= (tptp.uminus2330091110623919550at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3) B3)) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat (tptp.uminus2330091110623919550at_nat A3)) (tptp.uminus2330091110623919550at_nat B3)))) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (= (tptp.uminus935396558254630718at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3) B3)) (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat (tptp.uminus935396558254630718at_nat A3)) (tptp.uminus935396558254630718at_nat B3)))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.uminus5710092332889474511et_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.uminus5710092332889474511et_nat A3)) (tptp.uminus5710092332889474511et_nat B3)))) (forall ((N2 tptp.nat) (M tptp.nat)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)))))) (forall ((X tptp.rat)) (=> (forall ((E2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) E2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat X)) E2)))) (= X tptp.zero_zero_rat))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (and (or (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger))) (or (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger)))) (= (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer A)) (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer B)))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (and (or (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat))) (or (tptp.pp (tptp.aa_rat_bool _let_1 B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) tptp.zero_zero_rat)))) (= (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat B)))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (and (or (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int))) (or (tptp.pp (tptp.aa_int_bool _let_1 B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) tptp.zero_zero_int)))) (= (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.abs_abs_int A)) (tptp.aa_int_int tptp.abs_abs_int B)))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer Y)) X) (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger Y) X))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) X)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.abs_abs_rat Y)) X) (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) X))))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) X)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.abs_abs_int Y)) X) (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) X))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) B)) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger C) D2)))) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger A) C))) (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger B) D2)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat C) D2)))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) C))) (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat B) D2)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int C) D2)))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) C))) (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) D2)))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger A) B))) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer A)) (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer B))))) (forall ((A tptp.rat) (B tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) B))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat B))))) (forall ((A tptp.int) (B tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.abs_abs_int A)) (tptp.aa_int_int tptp.abs_abs_int B))))) (forall ((X tptp.code_integer) (A tptp.code_integer) (R3 tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger X) A))) R3)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger A) R3)) X)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger X) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) R3)))))) (forall ((X tptp.rat) (A tptp.rat) (R3 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat X) A))) R3)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) R3)) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) R3)))))) (forall ((X tptp.int) (A tptp.int) (R3 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) A))) R3)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) R3)) X)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) R3)))))) (forall ((X tptp.code_integer) (A tptp.code_integer) (R3 tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger X) A))) R3)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger A) R3)) X)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger X) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) R3)))))) (forall ((X tptp.rat) (A tptp.rat) (R3 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat X) A))) R3)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) R3)) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) R3)))))) (forall ((X tptp.int) (A tptp.int) (R3 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) A))) R3)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) R3)) X)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) R3)))))) (forall ((Y tptp.rat) (X tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Y)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat tptp.abs_abs_rat X)) Y) (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Y))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer A)) N2)))) (forall ((A tptp.rat) (N2 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) N2)))) (forall ((A tptp.int) (N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.abs_abs_int A)) N2)))) (forall ((N2 tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2)))))) (forall ((N2 tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2)))))) (forall ((N2 tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N2)))))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2))) tptp.zero_z3403309356797280102nteger))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2))) tptp.zero_zero_rat))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N2))) tptp.zero_zero_int))) (tptp.pp (tptp.aa_Code_integer_bool _let_52 tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_rat_bool _let_51 tptp.zero_zero_rat)) (tptp.pp (tptp.aa_int_bool _let_50 tptp.zero_zero_int)) (not (tptp.pp (tptp.aa_Code_integer_bool _let_39 _let_43))) (not (tptp.pp (tptp.aa_rat_bool _let_49 _let_33))) (not (tptp.pp (tptp.aa_int_bool _let_48 _let_32))) (forall ((N2 tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N2)))))) (forall ((N2 tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2)))))) (forall ((N2 tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2)))))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N2))) tptp.zero_zero_int))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2))) tptp.zero_z3403309356797280102nteger))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2))) tptp.zero_zero_rat))) (tptp.pp (tptp.aa_int_bool _let_47 tptp.zero_zero_int)) (tptp.pp (tptp.aa_Code_integer_bool _let_46 tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_rat_bool _let_45 tptp.zero_zero_rat)) (not (tptp.pp (tptp.aa_int_bool _let_44 _let_32))) (not (tptp.pp (tptp.aa_Code_integer_bool _let_37 _let_43))) (not (tptp.pp (tptp.aa_rat_bool _let_42 _let_33))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M)))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)) (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))) (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) (tptp.aa_num_rat tptp.numeral_numeral_rat M)))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.aa_num_int tptp.numeral_numeral_int M)))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))) tptp.one_one_rat))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))) tptp.one_one_int))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M)))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M)))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)) (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat))))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.aa_num_int tptp.numeral_numeral_int M)))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) (tptp.aa_num_rat tptp.numeral_numeral_rat M)))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))) tptp.one_one_int))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))) tptp.one_one_rat))) (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= C (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A) B))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) B) (tptp.aa_rat_rat tptp.uminus_uminus_rat A))))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A) B)) C) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) B))))) (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C)) A) (and (=> (not _let_1) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C))) (=> _let_1 (= A tptp.zero_zero_rat)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= A (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C))) (and (=> (not _let_1) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C) (tptp.aa_rat_rat tptp.uminus_uminus_rat B))) (=> _let_1 (= A tptp.zero_zero_rat)))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X) Y) tptp.bot_bo2099793752762293965at_nat) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat X) (tptp.uminus6524753893492686040at_nat Y))))) (forall ((X tptp.set_bool) (Y tptp.set_bool)) (= (= (tptp.inf_inf_set_bool X Y) tptp.bot_bot_set_bool) (tptp.ord_less_eq_set_bool X (tptp.uminus5166143097222041326t_bool Y)))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X) Y) tptp.bot_bot_set_nat) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat X) (tptp.uminus5710092332889474511et_nat Y))))) (forall ((X tptp.assn) (Y tptp.assn)) (= (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X) Y) tptp.bot_bot_assn) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn X) (tptp.aa_assn_assn tptp.uminus_uminus_assn Y))))) (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X) Y) tptp.bot_bot_Product_unit) (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit X) (tptp.uminus2952777764628376836t_unit Y))))) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int X) Y) tptp.bot_bot_set_int) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X) (tptp.uminus1532241313380277803et_int Y))))) (forall ((P3 tptp.set_Pr1261947904930325089at_nat) (Q5 tptp.set_Pr1261947904930325089at_nat) (R3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat P3) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat Q5) R3))) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat P3) (tptp.uminus6524753893492686040at_nat Q5))) R3)))) (forall ((P3 tptp.set_Pr8693737435421807431at_nat) (Q5 tptp.set_Pr8693737435421807431at_nat) (R3 tptp.set_Pr8693737435421807431at_nat)) (= (tptp.ord_le3000389064537975527at_nat P3 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat Q5) R3)) (tptp.ord_le3000389064537975527at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat P3) (tptp.uminus4384627049435823934at_nat Q5)) R3))) (forall ((P3 tptp.set_Pr8551490117392284871at_nat) (Q5 tptp.set_Pr8551490117392284871at_nat) (R3 tptp.set_Pr8551490117392284871at_nat)) (= (tptp.ord_le8081472938463900775at_nat P3 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat Q5) R3)) (tptp.ord_le8081472938463900775at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat P3) (tptp.uminus2330091110623919550at_nat Q5)) R3))) (forall ((P3 tptp.set_Pr4329608150637261639at_nat) (Q5 tptp.set_Pr4329608150637261639at_nat) (R3 tptp.set_Pr4329608150637261639at_nat)) (= (tptp.ord_le1268244103169919719at_nat P3 (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat Q5) R3)) (tptp.ord_le1268244103169919719at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat P3) (tptp.uminus935396558254630718at_nat Q5)) R3))) (forall ((P3 tptp.set_nat) (Q5 tptp.set_nat) (R3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat P3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat Q5) R3))) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat P3) (tptp.uminus5710092332889474511et_nat Q5))) R3)))) (forall ((P3 tptp.assn) (Q5 tptp.assn) (R3 tptp.assn)) (= (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn P3) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn Q5) R3))) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn P3) (tptp.aa_assn_assn tptp.uminus_uminus_assn Q5))) R3)))) (forall ((P3 tptp.product_unit) (Q5 tptp.product_unit) (R3 tptp.product_unit)) (= (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit P3) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.sup_sup_Product_unit Q5) R3))) (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit P3) (tptp.uminus2952777764628376836t_unit Q5))) R3)))) (forall ((P3 tptp.set_int) (Q5 tptp.set_int) (R3 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int P3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int Q5) R3))) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int P3) (tptp.uminus1532241313380277803et_int Q5))) R3)))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X) (tptp.uminus6524753893492686040at_nat Y))) Z)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat X) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat Y) Z))))) (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (= (tptp.ord_le3000389064537975527at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat X) (tptp.uminus4384627049435823934at_nat Y)) Z) (tptp.ord_le3000389064537975527at_nat X (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat Y) Z)))) (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat)) (= (tptp.ord_le8081472938463900775at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat X) (tptp.uminus2330091110623919550at_nat Y)) Z) (tptp.ord_le8081472938463900775at_nat X (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat Y) Z)))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (= (tptp.ord_le1268244103169919719at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat X) (tptp.uminus935396558254630718at_nat Y)) Z) (tptp.ord_le1268244103169919719at_nat X (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat Y) Z)))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X) (tptp.uminus5710092332889474511et_nat Y))) Z)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat X) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat Y) Z))))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (= (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X) (tptp.aa_assn_assn tptp.uminus_uminus_assn Y))) Z)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn X) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn Y) Z))))) (forall ((X tptp.product_unit) (Y tptp.product_unit) (Z tptp.product_unit)) (= (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X) (tptp.uminus2952777764628376836t_unit Y))) Z)) (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit X) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.sup_sup_Product_unit Y) Z))))) (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int X) (tptp.uminus1532241313380277803et_int Y))) Z)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int Y) Z))))) (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat X) Y)) Z)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat X) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat (tptp.uminus6524753893492686040at_nat Y)) Z))))) (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (= (tptp.ord_le3000389064537975527at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat X) Y) Z) (tptp.ord_le3000389064537975527at_nat X (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat (tptp.uminus4384627049435823934at_nat Y)) Z)))) (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat)) (= (tptp.ord_le8081472938463900775at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat X) Y) Z) (tptp.ord_le8081472938463900775at_nat X (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat (tptp.uminus2330091110623919550at_nat Y)) Z)))) (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (= (tptp.ord_le1268244103169919719at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat X) Y) Z) (tptp.ord_le1268244103169919719at_nat X (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat (tptp.uminus935396558254630718at_nat Y)) Z)))) (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat X) Y)) Z)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat X) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.uminus5710092332889474511et_nat Y)) Z))))) (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (= (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn X) Y)) Z)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn X) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.sup_sup_assn (tptp.aa_assn_assn tptp.uminus_uminus_assn Y)) Z))))) (forall ((X tptp.product_unit) (Y tptp.product_unit) (Z tptp.product_unit)) (= (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit X) Y)) Z)) (tptp.pp (tptp.aa_Product_unit_bool (tptp.aa_Pro1095446373910179038t_bool tptp.ord_le3221252021190050221t_unit X) (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.sup_sup_Product_unit (tptp.uminus2952777764628376836t_unit Y)) Z))))) (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int X) Y)) Z)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int (tptp.uminus1532241313380277803et_int Y)) Z))))) (forall ((A tptp.int) (N2 tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int A)) N2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) N2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2)))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) N2) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2)))) (forall ((A tptp.rat) (N2 tptp.nat)) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) N2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) N2)) (tptp.aa_nat_rat (tptp.power_power_rat A) N2)))) (forall ((L tptp.int) (K tptp.int) (Q5 tptp.int)) (=> (not (= L tptp.zero_zero_int)) (=> (= K (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Q5) L)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int K L) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q5) tptp.zero_zero_int)))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3) tptp.bot_bo2099793752762293965at_nat) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A3) (tptp.uminus6524753893492686040at_nat B3))))) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool)) (= (= (tptp.inf_inf_set_bool A3 B3) tptp.bot_bot_set_bool) (tptp.ord_less_eq_set_bool A3 (tptp.uminus5166143097222041326t_bool B3)))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3) tptp.bot_bot_set_nat) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) (tptp.uminus5710092332889474511et_nat B3))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3) tptp.bot_bot_set_int) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) (tptp.uminus1532241313380277803et_int B3))))) (forall ((L tptp.int) (K tptp.int)) (=> (not (= L tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int K) L))) (tptp.aa_int_int tptp.abs_abs_int L))))) (forall ((M tptp.int)) (=> (forall ((N5 tptp.nat)) (not (= M (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N5)))) (not (forall ((N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N5)) (not (= M (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N5))))))))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)))) (and (= N2 tptp.zero_zero_nat) (= M tptp.zero_zero_nat)))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) tptp.zero_zero_int))) (forall ((K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) tptp.zero_zero_int)) (not (forall ((N5 tptp.nat)) (not (= K (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N5)))))))) (forall ((K tptp.int) (L tptp.int)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int K L) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int K) L)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int K) L))))) (forall ((X tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer X))))) (forall ((X tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat tptp.one_one_rat) (tptp.aa_rat_rat tptp.abs_abs_rat X))))) (forall ((X tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.aa_int_int tptp.abs_abs_int X))))) (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C))) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat tptp.uminus_uminus_rat B)))))) (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C))) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat tptp.uminus_uminus_rat B)))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)))))) (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_3 (tptp.aa_rat_rat tptp.uminus_uminus_rat B))) (let ((_let_4 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C))) (let ((_let_5 (tptp.pp (tptp.aa_rat_bool _let_1 C)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C))) A)) (and (=> _let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_3) _let_4))) (=> (not _let_5) (and (=> _let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_4) _let_3))) (=> (not _let_2) (tptp.pp (tptp.aa_rat_bool _let_1 A))))))))))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_3 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C))) (let ((_let_4 (tptp.aa_rat_rat tptp.uminus_uminus_rat B))) (let ((_let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C)))) (and (=> _let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_3) _let_4))) (=> (not _let_5) (and (=> _let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_4) _let_3))) (=> (not _let_2) (tptp.pp (tptp.aa_rat_bool _let_1 tptp.zero_zero_rat))))))))))))) (forall ((B tptp.rat) (C tptp.rat) (W2 tptp.num)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W2)))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C) _let_1) (and (=> (not _let_2) (= B (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))) (forall ((W2 tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W2)))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C)) (and (=> (not _let_2) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))) (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) Z))) Z))))))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Z))) Y) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat X)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Z))) Z)))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat X) Z))) Y) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat X)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) Z))) Z)))) (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat B))) (=> (not _let_2) (= _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) Z))) Z))))))) (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat B))) (=> (not _let_2) (= _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) Z))) Z))))))) (forall ((P tptp.assn)) (= (tptp.aa_assn_assn tptp.uminus_uminus_assn P) (tptp.abs_assn (tptp.aTP_Lamm_gz P)))) (forall ((K tptp.int)) (=> (not (= K tptp.zero_zero_int)) (=> (forall ((N5 tptp.nat)) (=> (= K (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N5)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N5))))) (not (forall ((N5 tptp.nat)) (=> (= K (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N5))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N5))))))))) (forall ((N2 tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) K)) (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))) K) tptp.zero_zero_rat))) (forall ((N2 tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) K)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) K) tptp.zero_zero_int))) (forall ((N2 tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) K)) (= (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) K) tptp.zero_z3403309356797280102nteger))) (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))) K) tptp.zero_zero_rat) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) K)))) (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) K) tptp.zero_zero_int) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) K)))) (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) K) tptp.zero_z3403309356797280102nteger) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) K)))) (forall ((A tptp.rat) (N2 tptp.nat)) (= (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat A) N2) tptp.zero_zero_rat) (exists ((K3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K3) N2)) (= A (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K3))))))) (forall ((N2 tptp.nat)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat tptp.suc N2))))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (not (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))) K) tptp.zero_zero_rat)))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (not (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) K) tptp.zero_zero_int)))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (not (= (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) K) tptp.zero_z3403309356797280102nteger)))) (forall ((X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) tptp.zero_zero_int)) (exists ((N5 tptp.nat)) (= X (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat tptp.suc N5))))))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat tptp.suc N2)))) tptp.zero_zero_int))) (forall ((A3 tptp.int) (B3 tptp.int) (N2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A3) B3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int tptp.uminus_uminus_int N2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B3) N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A3) N2)))))) (forall ((B tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int _let_1) B) _let_1)))) (forall ((X tptp.int) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.nO_MATCH_int_int tptp.one_one_int) X)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int X)) N2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) N2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int X) N2))))) (forall ((X tptp.code_integer) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.nO_MAT8252062027627875367nteger tptp.one_one_Code_integer) X)) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger X)) N2) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) N2))))) (forall ((X tptp.rat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.nO_MATCH_rat_rat tptp.one_one_rat) X)) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat X)) N2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) N2)) (tptp.aa_nat_rat (tptp.power_power_rat X) N2))))) (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C))) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat tptp.uminus_uminus_rat B)))))) (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C))) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat tptp.uminus_uminus_rat B)))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)))))) (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_2 (tptp.aa_rat_rat tptp.uminus_uminus_rat B))) (let ((_let_3 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C))) (let ((_let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C))) A)) (and (=> _let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_2) _let_3))) (=> (not _let_4) (and (=> _let_1 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_3) _let_2))) (=> (not _let_1) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)))))))))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_3 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C))) (let ((_let_4 (tptp.aa_rat_rat tptp.uminus_uminus_rat B))) (let ((_let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C)))) (and (=> _let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_3) _let_4))) (=> (not _let_5) (and (=> _let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_4) _let_3))) (=> (not _let_2) (tptp.pp (tptp.aa_rat_bool _let_1 tptp.zero_zero_rat))))))))))))) (forall ((W2 tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W2)))) (let ((_let_2 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_4 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) C))) (let ((_let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool _let_2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C))) (and (=> _let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_4) B))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) _let_4))) (=> (not _let_3) (tptp.pp (tptp.aa_rat_bool _let_2 tptp.zero_zero_rat))))))))))))) (forall ((B tptp.rat) (C tptp.rat) (W2 tptp.num)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W2)))) (let ((_let_2 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_4 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) C))) (let ((_let_5 (tptp.pp (tptp.aa_rat_bool _let_2 C)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C)) _let_1)) (and (=> _let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) _let_4))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_4) B))) (=> (not _let_3) (tptp.pp (tptp.aa_rat_bool _let_2 _let_1))))))))))))) (forall ((K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)) (not (forall ((N5 tptp.nat)) (=> (= K (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N5))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N5)))))))) (forall ((L tptp.int) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) L)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int tptp.uminus_uminus_int K)) L) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int L) tptp.one_one_int)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int K) tptp.one_one_int)) L))))) (forall ((B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) tptp.one_one_int)))) (forall ((B tptp.rat) (C tptp.rat) (W2 tptp.num)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W2)))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_3 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) C))) (let ((_let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C)) _let_1)) (and (=> _let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) _let_3))) (=> (not _let_4) (and (=> _let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_3) B))) (=> (not _let_2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1)))))))))))) (forall ((W2 tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W2)))) (let ((_let_2 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_4 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) C))) (let ((_let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool _let_2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) C))) (and (=> _let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_4) B))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) _let_4))) (=> (not _let_3) (tptp.pp (tptp.aa_rat_bool _let_2 tptp.zero_zero_rat))))))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (F tptp.fun_nat_int) (K tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) I3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) N2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int F (tptp.aa_nat_nat tptp.suc I3))) (tptp.aa_nat_int F I3)))) tptp.one_one_int)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int F M)) K)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) (tptp.aa_nat_int F N2))) (exists ((I3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) I3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I3) N2)) (= (tptp.aa_nat_int F I3) K)))))))) (forall ((D2 tptp.int) (Z tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) Z))) tptp.one_one_int)) D2)))))) (forall ((D2 tptp.int) (X tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.minus_minus_int X))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int _let_1 Z))) tptp.one_one_int)) D2))) Z))))) (forall ((R3 tptp.rat) (K tptp.nat)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat R3))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat R3) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat _let_1) K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat R3) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat _let_1) tptp.one_one_rat)) K))))) (forall ((R3 tptp.int) (K tptp.nat)) (let ((_let_1 (tptp.aa_int_int tptp.uminus_uminus_int R3))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int R3) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int K))) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int _let_1) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int R3) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int)) K))))) (forall ((R3 tptp.code_integer) (K tptp.nat)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger R3))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger R3) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger K))) (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger _let_1) K)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger R3) (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) K))))) (forall ((K tptp.int) (L tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) K)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) L)) tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int K) L) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))))) (forall ((N2 tptp.nat) (F tptp.fun_nat_int) (K tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) N2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int F (tptp.aa_nat_nat tptp.suc I3))) (tptp.aa_nat_int F I3)))) tptp.one_one_int)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int F tptp.zero_zero_nat)) K)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) (tptp.aa_nat_int F N2))) (exists ((I3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I3) N2)) (= (tptp.aa_nat_int F I3) K))))))) (forall ((B tptp.rat) (K tptp.nat)) (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) K) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat B) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K)))) (forall ((B tptp.int) (K tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int (tptp.aa_int_int tptp.uminus_uminus_int B)) K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) K)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int K))) tptp.one_one_int)) K)))) (forall ((B tptp.code_integer) (K tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) K) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) K)) (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger B) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger K))) tptp.one_one_Code_integer)) K)))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (= (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) K)) (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K)))))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (= (tptp.aa_nat_Code_integer _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) K)) (tptp.aa_nat_Code_integer _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K)))))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (= (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) K)) (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K)))))) (forall ((A0 tptp.int) (A1 tptp.int) (P tptp.fun_int_fun_int_bool)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A0) A1))) (=> (forall ((I3 tptp.int) (J2 tptp.int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int I3) J2))) (=> (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I3) J2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I3) tptp.one_one_int)) J2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P I3) J2))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A0) A1))))) (forall ((X tptp.nat)) (= (tptp.bezw X tptp.zero_zero_nat) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (forall ((V tptp.num) (X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V))) (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V))) tptp.one_one_rat)) X)))) (forall ((X tptp.rat) (V tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V))) tptp.one_one_rat))))) (= (tptp.aa_option_num_nat tptp.size_size_option_num tptp.none_num) _let_41) (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat C))) (=> (not (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 A3))) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.uminus6524753893492686040at_nat A3)))))) (forall ((C tptp.bool) (A3 tptp.set_bool)) (=> (not (tptp.pp (tptp.member_bool C A3))) (tptp.pp (tptp.member_bool C (tptp.uminus5166143097222041326t_bool A3))))) (forall ((C tptp.set_nat) (A3 tptp.set_set_nat)) (let ((_let_1 (tptp.member_set_nat C))) (=> (not (tptp.pp (tptp.aa_set_set_nat_bool _let_1 A3))) (tptp.pp (tptp.aa_set_set_nat_bool _let_1 (tptp.uminus613421341184616069et_nat A3)))))) (forall ((C tptp.nat) (A3 tptp.set_nat)) (let ((_let_1 (tptp.member_nat C))) (=> (not (tptp.pp (tptp.aa_set_nat_bool _let_1 A3))) (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.uminus5710092332889474511et_nat A3)))))) (forall ((C tptp.int) (A3 tptp.set_int)) (let ((_let_1 (tptp.member_int C))) (=> (not (tptp.pp (tptp.aa_set_int_bool _let_1 A3))) (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.uminus1532241313380277803et_int A3)))))) (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat C))) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.uminus6524753893492686040at_nat A3))) (not (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 A3)))))) (forall ((C tptp.bool) (A3 tptp.set_bool)) (= (tptp.pp (tptp.member_bool C (tptp.uminus5166143097222041326t_bool A3))) (not (tptp.pp (tptp.member_bool C A3))))) (forall ((C tptp.set_nat) (A3 tptp.set_set_nat)) (let ((_let_1 (tptp.member_set_nat C))) (= (tptp.pp (tptp.aa_set_set_nat_bool _let_1 (tptp.uminus613421341184616069et_nat A3))) (not (tptp.pp (tptp.aa_set_set_nat_bool _let_1 A3)))))) (forall ((C tptp.nat) (A3 tptp.set_nat)) (let ((_let_1 (tptp.member_nat C))) (= (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.uminus5710092332889474511et_nat A3))) (not (tptp.pp (tptp.aa_set_nat_bool _let_1 A3)))))) (forall ((C tptp.int) (A3 tptp.set_int)) (let ((_let_1 (tptp.member_int C))) (= (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.uminus1532241313380277803et_int A3))) (not (tptp.pp (tptp.aa_set_int_bool _let_1 A3)))))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) tptp.zero_zero_rat)))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) X)))) (forall ((X tptp.rat) (V tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X)) (tptp.aa_num_int tptp.numeral_numeral_int V))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_num_rat tptp.numeral_numeral_rat V))))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X)) tptp.one_one_int)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) tptp.zero_zero_rat)))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) X)))) (forall ((V tptp.num) (X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_num_int tptp.numeral_numeral_int V)) (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V)) X)))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X)) tptp.one_one_int)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) tptp.one_one_rat)))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) X)))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat))))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) X)))) (forall ((X tptp.rat) (V tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X)) (tptp.aa_num_int tptp.numeral_numeral_int V))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V)) tptp.one_one_rat))))) (forall ((V tptp.num) (X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int tptp.numeral_numeral_int V)) (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V)) tptp.one_one_rat)) X)))) (forall ((X tptp.rat) (V tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V)))))) (forall ((V tptp.num) (X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V))) (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V))) X)))) (forall ((P tptp.fun_Pr803113274115125473t_bool)) (= (tptp.collec213857154873943460nt_int (tptp.aTP_Lamm_ha P)) (tptp.uminus6221592323253981072nt_int (tptp.collec213857154873943460nt_int P)))) (forall ((P tptp.fun_list_nat_bool)) (= (tptp.collect_list_nat (tptp.aTP_Lamm_hb P)) (tptp.uminus3195874150345416415st_nat (tptp.collect_list_nat P)))) (forall ((P tptp.fun_set_nat_bool)) (= (tptp.collect_set_nat (tptp.aTP_Lamm_hc P)) (tptp.uminus613421341184616069et_nat (tptp.collect_set_nat P)))) (forall ((P tptp.fun_nat_bool)) (= (tptp.collect_nat (tptp.aTP_Lamm_hd P)) (tptp.uminus5710092332889474511et_nat (tptp.collect_nat P)))) (forall ((P tptp.fun_int_bool)) (= (tptp.collect_int (tptp.aTP_Lamm_he P)) (tptp.uminus1532241313380277803et_int (tptp.collect_int P)))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.uminus6524753893492686040at_nat A3) (tptp.collec3392354462482085612at_nat (tptp.aTP_Lamm_hf A3)))) (forall ((A3 tptp.set_bool)) (= (tptp.uminus5166143097222041326t_bool A3) (tptp.collect_bool (tptp.aTP_Lamm_hg A3)))) (forall ((A3 tptp.set_Pr958786334691620121nt_int)) (= (tptp.uminus6221592323253981072nt_int A3) (tptp.collec213857154873943460nt_int (tptp.aTP_Lamm_hh A3)))) (forall ((A3 tptp.set_list_nat)) (= (tptp.uminus3195874150345416415st_nat A3) (tptp.collect_list_nat (tptp.aTP_Lamm_hi A3)))) (forall ((A3 tptp.set_set_nat)) (= (tptp.uminus613421341184616069et_nat A3) (tptp.collect_set_nat (tptp.aTP_Lamm_hj A3)))) (forall ((A3 tptp.set_nat)) (= (tptp.uminus5710092332889474511et_nat A3) (tptp.collect_nat (tptp.aTP_Lamm_hk A3)))) (forall ((A3 tptp.set_int)) (= (tptp.uminus1532241313380277803et_int A3) (tptp.collect_int (tptp.aTP_Lamm_hl A3)))) (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat C))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.uminus6524753893492686040at_nat A3))) (not (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 A3)))))) (forall ((C tptp.bool) (A3 tptp.set_bool)) (=> (tptp.pp (tptp.member_bool C (tptp.uminus5166143097222041326t_bool A3))) (not (tptp.pp (tptp.member_bool C A3))))) (forall ((C tptp.set_nat) (A3 tptp.set_set_nat)) (let ((_let_1 (tptp.member_set_nat C))) (=> (tptp.pp (tptp.aa_set_set_nat_bool _let_1 (tptp.uminus613421341184616069et_nat A3))) (not (tptp.pp (tptp.aa_set_set_nat_bool _let_1 A3)))))) (forall ((C tptp.nat) (A3 tptp.set_nat)) (let ((_let_1 (tptp.member_nat C))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.uminus5710092332889474511et_nat A3))) (not (tptp.pp (tptp.aa_set_nat_bool _let_1 A3)))))) (forall ((C tptp.int) (A3 tptp.set_int)) (let ((_let_1 (tptp.member_int C))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.uminus1532241313380277803et_int A3))) (not (tptp.pp (tptp.aa_set_int_bool _let_1 A3)))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.uminus6524753893492686040at_nat A3) (tptp.collec3392354462482085612at_nat (tptp.aa_fun830836278467416944t_bool tptp.uminus6270006169978340066t_bool (tptp.aTP_Lamm_a A3))))) (forall ((A3 tptp.set_bool)) (= (tptp.uminus5166143097222041326t_bool A3) (tptp.collect_bool (tptp.uminus215040010513443916l_bool (tptp.aTP_Lamm_aa A3))))) (forall ((A3 tptp.set_Pr958786334691620121nt_int)) (= (tptp.uminus6221592323253981072nt_int A3) (tptp.collec213857154873943460nt_int (tptp.uminus8539327787930509866t_bool (tptp.aTP_Lamm_ab A3))))) (forall ((A3 tptp.set_list_nat)) (= (tptp.uminus3195874150345416415st_nat A3) (tptp.collect_list_nat (tptp.uminus5119773305880778631t_bool (tptp.aTP_Lamm_ac A3))))) (forall ((A3 tptp.set_set_nat)) (= (tptp.uminus613421341184616069et_nat A3) (tptp.collect_set_nat (tptp.uminus6226608070181861729t_bool (tptp.aTP_Lamm_ad A3))))) (forall ((A3 tptp.set_nat)) (= (tptp.uminus5710092332889474511et_nat A3) (tptp.collect_nat (tptp.uminus1995910650241132439t_bool (tptp.aTP_Lamm_ae A3))))) (forall ((A3 tptp.set_int)) (= (tptp.uminus1532241313380277803et_int A3) (tptp.collect_int (tptp.uminus8094991720627284027t_bool (tptp.aTP_Lamm_af A3))))) (forall ((X tptp.list_nat) (Y tptp.list_nat)) (=> (not (= (tptp.aa_list_nat_nat tptp.size_size_list_nat X) (tptp.aa_list_nat_nat tptp.size_size_list_nat Y))) (not (= X Y)))) (forall ((X tptp.list_bool) (Y tptp.list_bool)) (=> (not (= (tptp.size_size_list_bool X) (tptp.size_size_list_bool Y))) (not (= X Y)))) (forall ((Y tptp.rat) (X tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat Y)) (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X)) (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X)) (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat Y))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat A)) (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat B)))))))) (forall ((X2 tptp.produc3260487557148687353it_nat)) (= (tptp.size_s2363601347547812957it_nat (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat X2)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (forall ((X2 tptp.num)) (= (tptp.aa_option_num_nat tptp.size_size_option_num (tptp.aa_num_option_num tptp.some_num X2)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (forall ((X2 tptp.produc8664842809031399944it_nat)) (= (tptp.size_s8766407808098229740it_nat (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat X2)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N2)))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int tptp.ring_1_of_int_int A))) (tptp.pp (tptp.aa_int_bool _let_1 A))))) (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger X))) N2)) (tptp.aa_int_Code_integer tptp.ring_18347121197199848620nteger A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N2)) A)))) (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat X))) N2)) (tptp.aa_int_rat tptp.ring_1_of_int_rat A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N2)) A)))) (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N2))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.ring_1_of_int_int A)) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) _let_1))))) (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_int_Code_integer tptp.ring_18347121197199848620nteger A)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger X))) N2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N2))))) (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat A)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat X))) N2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N2))))) (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger X))) N2)) (tptp.aa_int_Code_integer tptp.ring_18347121197199848620nteger A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N2)) A)))) (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat X))) N2)) (tptp.aa_int_rat tptp.ring_1_of_int_rat A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N2)) A)))) (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N2)))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int tptp.ring_1_of_int_int A))) (tptp.pp (tptp.aa_int_bool _let_1 A))))) (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_int_Code_integer tptp.ring_18347121197199848620nteger A)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger X))) N2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N2))))) (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat A)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat X))) N2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N2))))) (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int X))) N2))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.ring_1_of_int_int A)) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) _let_1))))) (forall ((X tptp.rat) (V tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V))) tptp.one_one_rat))))) (forall ((V tptp.num) (X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V))) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V))) tptp.one_one_rat)) X)))) (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat tptp.nat2 A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N2))))) (forall ((W2 tptp.int) (Z tptp.int)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat W2)) (tptp.aa_int_rat tptp.ring_1_of_int_rat Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int W2) Z)))) (forall ((W2 tptp.int) (Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.ring_1_of_int_int W2)) (tptp.aa_int_int tptp.ring_1_of_int_int Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int W2) Z)))) (forall ((W2 tptp.int) (Z tptp.int)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat W2)) (tptp.aa_int_rat tptp.ring_1_of_int_rat Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int W2) Z)))) (forall ((W2 tptp.int) (Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.ring_1_of_int_int W2)) (tptp.aa_int_int tptp.ring_1_of_int_int Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int W2) Z)))) (forall ((W2 tptp.int) (Z tptp.int)) (= (tptp.aa_int_Code_integer tptp.ring_18347121197199848620nteger (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int W2) Z)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_int_Code_integer tptp.ring_18347121197199848620nteger W2)) (tptp.aa_int_Code_integer tptp.ring_18347121197199848620nteger Z)))) (forall ((W2 tptp.int) (Z tptp.int)) (= (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int W2) Z)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat W2)) (tptp.aa_int_rat tptp.ring_1_of_int_rat Z)))) (forall ((W2 tptp.int) (Z tptp.int)) (= (tptp.aa_int_int tptp.ring_1_of_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int W2) Z)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.ring_1_of_int_int W2)) (tptp.aa_int_int tptp.ring_1_of_int_int Z)))) (forall ((Z tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z) tptp.zero_zero_int)) (= (tptp.aa_int_nat tptp.nat2 Z) tptp.zero_zero_nat))) (forall ((I2 tptp.int)) (= (= (tptp.aa_int_nat tptp.nat2 I2) tptp.zero_zero_nat) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I2) tptp.zero_zero_int)))) (forall ((W2 tptp.int) (Z tptp.int)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_int_nat tptp.nat2 W2)) (tptp.aa_int_nat tptp.nat2 Z))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int W2) Z))))) (forall ((Z tptp.int)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_int_nat tptp.nat2 Z)))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)))) (and (=> _let_2 (= _let_1 Z)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_int_Code_integer tptp.ring_18347121197199848620nteger Z)) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z) tptp.zero_zero_int)))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat Z)) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z) tptp.zero_zero_int)))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.ring_1_of_int_int Z)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z) tptp.zero_zero_int)))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_int_Code_integer tptp.ring_18347121197199848620nteger Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_int_rat tptp.ring_1_of_int_rat Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)))) (forall ((Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int tptp.ring_1_of_int_int Z))) (tptp.pp (tptp.aa_int_bool _let_1 Z))))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_int_Code_integer tptp.ring_18347121197199848620nteger Z)) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z) tptp.zero_zero_int)))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat Z)) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z) tptp.zero_zero_int)))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.ring_1_of_int_int Z)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z) tptp.zero_zero_int)))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_int_Code_integer tptp.ring_18347121197199848620nteger Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Z)))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_int_rat tptp.ring_1_of_int_rat Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Z)))) (forall ((Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int tptp.ring_1_of_int_int Z))) (tptp.pp (tptp.aa_int_bool _let_1 Z))))) (forall ((N2 tptp.num) (Z tptp.int)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2)) (tptp.aa_int_Code_integer tptp.ring_18347121197199848620nteger Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int tptp.numeral_numeral_int N2)) Z)))) (forall ((N2 tptp.num) (Z tptp.int)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2)) (tptp.aa_int_rat tptp.ring_1_of_int_rat Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int tptp.numeral_numeral_int N2)) Z)))) (forall ((N2 tptp.num) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int tptp.numeral_numeral_int N2)))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int tptp.ring_1_of_int_int Z))) (tptp.pp (tptp.aa_int_bool _let_1 Z))))) (forall ((Z tptp.int) (N2 tptp.num)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_int_Code_integer tptp.ring_18347121197199848620nteger Z)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z) (tptp.aa_num_int tptp.numeral_numeral_int N2))))) (forall ((Z tptp.int) (N2 tptp.num)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat Z)) (tptp.aa_num_rat tptp.numeral_numeral_rat N2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z) (tptp.aa_num_int tptp.numeral_numeral_int N2))))) (forall ((Z tptp.int) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N2))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.ring_1_of_int_int Z)) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z) _let_1))))) (forall ((N2 tptp.num) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_num_int tptp.numeral_numeral_int N2)))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int tptp.ring_1_of_int_int Z))) (tptp.pp (tptp.aa_int_bool _let_1 Z))))) (forall ((N2 tptp.num) (Z tptp.int)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2)) (tptp.aa_int_Code_integer tptp.ring_18347121197199848620nteger Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_num_int tptp.numeral_numeral_int N2)) Z)))) (forall ((N2 tptp.num) (Z tptp.int)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2)) (tptp.aa_int_rat tptp.ring_1_of_int_rat Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_num_int tptp.numeral_numeral_int N2)) Z)))) (forall ((Z tptp.int) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N2))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.ring_1_of_int_int Z)) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z) _let_1))))) (forall ((Z tptp.int) (N2 tptp.num)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_int_Code_integer tptp.ring_18347121197199848620nteger Z)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z) (tptp.aa_num_int tptp.numeral_numeral_int N2))))) (forall ((Z tptp.int) (N2 tptp.num)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat Z)) (tptp.aa_num_rat tptp.numeral_numeral_rat N2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z) (tptp.aa_num_int tptp.numeral_numeral_int N2))))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_int_Code_integer tptp.ring_18347121197199848620nteger Z)) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z) tptp.one_one_int)))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z) tptp.one_one_int)))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.ring_1_of_int_int Z)) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z) tptp.one_one_int)))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (tptp.aa_int_Code_integer tptp.ring_18347121197199848620nteger Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) Z)))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_int_rat tptp.ring_1_of_int_rat Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) Z)))) (forall ((Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int tptp.ring_1_of_int_int Z))) (tptp.pp (tptp.aa_int_bool _let_1 Z))))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_int_Code_integer tptp.ring_18347121197199848620nteger Z)) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z) tptp.one_one_int)))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z) tptp.one_one_int)))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.ring_1_of_int_int Z)) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z) tptp.one_one_int)))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (tptp.aa_int_Code_integer tptp.ring_18347121197199848620nteger Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) Z)))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.aa_int_rat tptp.ring_1_of_int_rat Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) Z)))) (forall ((Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int tptp.ring_1_of_int_int Z))) (tptp.pp (tptp.aa_int_bool _let_1 Z))))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) X)))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) tptp.zero_zero_rat)))) (forall ((V tptp.num) (X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int tptp.numeral_numeral_int V)) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V)) X)))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) X)))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_int_nat tptp.nat2 Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Z)))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) tptp.one_one_rat)))) (forall ((X tptp.rat) (V tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X)) (tptp.aa_num_int tptp.numeral_numeral_int V))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.aa_num_rat tptp.numeral_numeral_rat V))))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) X)))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X)) tptp.one_one_int)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) tptp.one_one_rat)))) (forall ((Z tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_int_nat tptp.nat2 Z)) (tptp.aa_int_rat tptp.ring_1_of_int_rat Z)))) (forall ((Z tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_int_nat tptp.nat2 Z)) (tptp.aa_int_int tptp.ring_1_of_int_int Z)))) (forall ((Z tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_int_nat tptp.nat2 Z)) (tptp.aa_int_Code_integer tptp.ring_18347121197199848620nteger Z)))) (forall ((X tptp.int) (B tptp.int) (W2 tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat X)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat B)) W2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int B) W2))))) (forall ((X tptp.int) (B tptp.int) (W2 tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.ring_1_of_int_int X)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.ring_1_of_int_int B)) W2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int B) W2))))) (forall ((B tptp.int) (W2 tptp.nat) (X tptp.int)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat B)) W2)) (tptp.aa_int_rat tptp.ring_1_of_int_rat X))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int B) W2)) X)))) (forall ((B tptp.int) (W2 tptp.nat) (X tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.ring_1_of_int_int B)) W2)) (tptp.aa_int_int tptp.ring_1_of_int_int X))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int B) W2)) X)))) (forall ((X tptp.int) (B tptp.int) (W2 tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat X)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat B)) W2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int B) W2))))) (forall ((X tptp.int) (B tptp.int) (W2 tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.ring_1_of_int_int X)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.ring_1_of_int_int B)) W2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int B) W2))))) (forall ((B tptp.int) (W2 tptp.nat) (X tptp.int)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat B)) W2)) (tptp.aa_int_rat tptp.ring_1_of_int_rat X))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int B) W2)) X)))) (forall ((B tptp.int) (W2 tptp.nat) (X tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.ring_1_of_int_int B)) W2)) (tptp.aa_int_int tptp.ring_1_of_int_int X))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int B) W2)) X)))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_int_nat tptp.nat2 Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) Z)))) (forall ((V tptp.num) (X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_num_int tptp.numeral_numeral_int V)) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V)) tptp.one_one_rat)) X)))) (forall ((X tptp.rat) (V tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X)) (tptp.aa_num_int tptp.numeral_numeral_int V))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V)) tptp.one_one_rat))))) (forall ((V tptp.num) (X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V))) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V))) X)))) (forall ((X tptp.rat) (V tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V)))))) (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_int_Code_integer tptp.ring_18347121197199848620nteger A)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger X)) N2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N2))))) (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat A)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat X)) N2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N2))))) (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N2))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.ring_1_of_int_int A)) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) _let_1))))) (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger X)) N2)) (tptp.aa_int_Code_integer tptp.ring_18347121197199848620nteger A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N2)) A)))) (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat X)) N2)) (tptp.aa_int_rat tptp.ring_1_of_int_rat A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N2)) A)))) (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N2)))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int tptp.ring_1_of_int_int A))) (tptp.pp (tptp.aa_int_bool _let_1 A))))) (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N2))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.ring_1_of_int_int A)) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) _let_1))))) (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_int_Code_integer tptp.ring_18347121197199848620nteger A)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger X)) N2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N2))))) (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat A)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat X)) N2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N2))))) (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N2)))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int tptp.ring_1_of_int_int A))) (tptp.pp (tptp.aa_int_bool _let_1 A))))) (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger X)) N2)) (tptp.aa_int_Code_integer tptp.ring_18347121197199848620nteger A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N2)) A)))) (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat X)) N2)) (tptp.aa_int_rat tptp.ring_1_of_int_rat A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N2)) A)))) (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N2)) (tptp.aa_int_nat tptp.nat2 A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N2)) A)))) (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_int_nat tptp.nat2 A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N2))))) (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N2)) (tptp.aa_int_nat tptp.nat2 A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N2)) A)))) (forall ((X tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X))) X))) (forall ((Z tptp.int) (X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat Z)) X)))) (forall ((X tptp.rat) (Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X)) Z)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.aa_int_rat tptp.ring_1_of_int_rat Z))))) (forall ((X tptp.rat)) (exists ((Z2 tptp.int)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_int_rat tptp.ring_1_of_int_rat Z2))))) (forall ((X tptp.rat)) (exists ((Z2 tptp.int)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.aa_int_rat tptp.ring_1_of_int_rat Z2))))) (forall ((X tptp.rat)) (exists ((Z2 tptp.int)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat Z2)) X)))) (forall ((X tptp.int) (Y tptp.code_integer)) (let ((_let_1 (tptp.aa_int_Code_integer tptp.ring_18347121197199848620nteger X))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) Y) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger Y) _let_1)))) (forall ((X tptp.int) (Y tptp.rat)) (let ((_let_1 (tptp.aa_int_rat tptp.ring_1_of_int_rat X))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) Y) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) _let_1)))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.ring_1_of_int_int X))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) Y) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) _let_1)))) (forall ((P tptp.fun_list_nat_bool) (Xs tptp.list_nat)) (=> (forall ((Xs2 tptp.list_nat)) (=> (forall ((Ys tptp.list_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_list_nat_nat tptp.size_size_list_nat Ys)) (tptp.aa_list_nat_nat tptp.size_size_list_nat Xs2))) (tptp.pp (tptp.aa_list_nat_bool P Ys)))) (tptp.pp (tptp.aa_list_nat_bool P Xs2)))) (tptp.pp (tptp.aa_list_nat_bool P Xs)))) (forall ((P tptp.fun_list_bool_bool) (Xs tptp.list_bool)) (=> (forall ((Xs2 tptp.list_bool)) (=> (forall ((Ys tptp.list_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.size_size_list_bool Ys)) (tptp.size_size_list_bool Xs2))) (tptp.pp (tptp.aa_list_bool_bool P Ys)))) (tptp.pp (tptp.aa_list_bool_bool P Xs2)))) (tptp.pp (tptp.aa_list_bool_bool P Xs)))) (forall ((R3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) R3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_int_nat tptp.nat2 (tptp.aa_rat_int tptp.archim3151403230148437115or_rat R3)))) R3)))) (forall ((Z tptp.int) (X tptp.rat)) (let ((_let_1 (tptp.aa_int_rat tptp.ring_1_of_int_rat Z))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1) X)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat _let_1) tptp.one_one_rat))) (= (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X) Z))))) (forall ((X tptp.rat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_rat tptp.ring_1_of_int_rat A))) (= (= (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X) A) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat _let_1) tptp.one_one_rat))))))) (forall ((P tptp.fun_int_bool) (T5 tptp.rat)) (= (tptp.pp (tptp.aa_int_bool P (tptp.aa_rat_int tptp.archim3151403230148437115or_rat T5))) (forall ((I4 tptp.int)) (let ((_let_1 (tptp.aa_int_rat tptp.ring_1_of_int_rat I4))) (=> (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1) T5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat T5) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat _let_1) tptp.one_one_rat)))) (tptp.pp (tptp.aa_int_bool P I4))))))) (forall ((Z tptp.int) (X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)) X)))) (forall ((X tptp.rat) (Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X)) Z)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat Z)) tptp.one_one_rat))))) (forall ((X tptp.rat)) (let ((_let_1 (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat _let_1)) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int))))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X)) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat Y))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X)) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat tptp.nat2 X)) (tptp.aa_int_nat tptp.nat2 Y))))) (forall ((Z tptp.int) (Z6 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 Z)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Z6)) (= (= (tptp.aa_int_nat tptp.nat2 Z) (tptp.aa_int_nat tptp.nat2 Z6)) (= Z Z6)))))) (forall ((P tptp.fun_nat_bool)) (= (forall ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool P X_12))) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) X4)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_int_nat tptp.nat2 X4))))))) (forall ((P tptp.fun_nat_bool)) (= (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool P X_12))) (exists ((X4 tptp.int)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) X4)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_int_nat tptp.nat2 X4))))))) (forall ((X tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X))))) (forall ((X tptp.rat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X)) (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X)))) (forall ((Q5 tptp.rat) (P3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Q5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_rat_int tptp.archim3151403230148437115or_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat P3) Q5)))) Q5)) P3)))) (forall ((K tptp.int)) (let ((_let_1 (tptp.aa_int_rat tptp.ring_1_of_int_rat K))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)))) (and (=> _let_2 (= _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.uminus_uminus_int K)))))) (=> (not _let_2) (= _let_1 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_int_nat tptp.nat2 K)))))))) (forall ((K tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.ring_1_of_int_int K))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)))) (and (=> _let_2 (= _let_1 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.uminus_uminus_int K)))))) (=> (not _let_2) (= _let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_int_nat tptp.nat2 K)))))))) (forall ((K tptp.int)) (let ((_let_1 (tptp.aa_int_Code_integer tptp.ring_18347121197199848620nteger K))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)))) (and (=> _let_2 (= _let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.uminus_uminus_int K)))))) (=> (not _let_2) (= _let_1 (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_int_nat tptp.nat2 K)))))))) (forall ((Q5 tptp.rat) (P3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Q5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat P3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_rat_int tptp.archim3151403230148437115or_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat P3) Q5)))) tptp.one_one_rat)) Q5))))) (forall ((Z tptp.int) (W2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Z)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_int_nat tptp.nat2 W2)) (tptp.aa_int_nat tptp.nat2 Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int W2) Z))))) (forall ((X tptp.rat) (Y tptp.rat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X)) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat Y))) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y))))) (forall ((M tptp.nat) (Z tptp.int)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_int_nat tptp.nat2 Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) Z)))) (forall ((X tptp.int) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat tptp.nat2 X)) N2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))))) (forall ((Z tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_int_nat tptp.nat2 Z)) Z))) (forall ((M tptp.nat) (Z tptp.int)) (= (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M) Z) (and (= M (tptp.aa_int_nat tptp.nat2 Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z))))) (forall ((R3 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat R3) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_int_nat tptp.nat2 (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat R3)))))) (forall ((X tptp.rat) (Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X)) Z)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_int_rat tptp.ring_1_of_int_rat Z))))) (forall ((Z tptp.int) (X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z) (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat Z)) X)))) (forall ((X5 tptp.nat) (Xa3 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X5) Xa3) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X5)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Xa3))))) (forall ((X5 tptp.nat) (Xa3 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat X5) Xa3) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X5)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Xa3))))) (forall ((X5 tptp.nat) (Xa3 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat X5) Xa3) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X5)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Xa3))))) (forall ((X5 tptp.nat) (Xa3 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X5) Xa3) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X5)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Xa3))))) (forall ((X5 tptp.nat) (Xa3 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X5) Xa3) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X5)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Xa3))))) (forall ((Z tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_int_Code_integer tptp.ring_18347121197199848620nteger Z))))) (forall ((Z tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_int_rat tptp.ring_1_of_int_rat Z))))) (forall ((Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 Z)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int tptp.ring_1_of_int_int Z)))))) (forall ((Z tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Z)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_int_Code_integer tptp.ring_18347121197199848620nteger Z))))) (forall ((Z tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Z)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_int_rat tptp.ring_1_of_int_rat Z))))) (forall ((Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 Z)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int tptp.ring_1_of_int_int Z)))))) (forall ((N2 tptp.int) (X tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer (tptp.aa_int_Code_integer tptp.ring_18347121197199848620nteger N2))) X)) (or (= N2 tptp.zero_zero_int) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) X))))) (forall ((N2 tptp.int) (X tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat N2))) X)) (or (= N2 tptp.zero_zero_int) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) X))))) (forall ((N2 tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int tptp.ring_1_of_int_int N2))) X)) (or (= N2 tptp.zero_zero_int) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) X))))) (forall ((N2 tptp.int) (X tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer (tptp.aa_int_Code_integer tptp.ring_18347121197199848620nteger N2))) X)) (or (= N2 tptp.zero_zero_int) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) X))))) (forall ((N2 tptp.int) (X tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat N2))) X)) (or (= N2 tptp.zero_zero_int) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) X))))) (forall ((N2 tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int tptp.ring_1_of_int_int N2))) X)) (or (= N2 tptp.zero_zero_int) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) X))))) (forall ((X tptp.rat)) (exists ((Z2 tptp.int)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat Z2)) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Z2) tptp.one_one_int))))))) (forall ((X tptp.rat)) (exists ((X3 tptp.int)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat X3)) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X3) tptp.one_one_int)))) (forall ((Y4 tptp.int)) (=> (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat Y4)) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Y4) tptp.one_one_int))))) (= Y4 X3)))))) (forall ((W2 tptp.int) (Z tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) W2)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_int_nat tptp.nat2 W2)) (tptp.aa_int_nat tptp.nat2 Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int W2) Z))))) (forall ((W2 tptp.int) (Z tptp.int)) (=> (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) W2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat tptp.nat2 W2)) (tptp.aa_int_nat tptp.nat2 Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int W2) Z))))) (forall ((W2 tptp.int) (M tptp.nat)) (let ((_let_1 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) W2)))) (= (= (tptp.aa_int_nat tptp.nat2 W2) M) (and (=> _let_1 (= W2 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))) (forall ((M tptp.nat) (W2 tptp.int)) (let ((_let_1 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) W2)))) (= (= M (tptp.aa_int_nat tptp.nat2 W2)) (and (=> _let_1 (= W2 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))) (forall ((N2 tptp.nat) (X tptp.int)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2)) (tptp.aa_int_rat tptp.ring_1_of_int_rat X))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)) X)))) (forall ((N2 tptp.nat) (X tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int tptp.ring_1_of_int_int X))) (tptp.pp (tptp.aa_int_bool _let_1 X))))) (forall ((N2 tptp.nat) (X tptp.int)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2)) (tptp.aa_int_Code_integer tptp.ring_18347121197199848620nteger X))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)) X)))) (forall ((P tptp.fun_nat_bool) (I2 tptp.int)) (= (tptp.pp (tptp.aa_nat_bool P (tptp.aa_int_nat tptp.nat2 I2))) (and (forall ((N tptp.nat)) (=> (= I2 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) (tptp.pp (tptp.aa_nat_bool P N)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int I2) tptp.zero_zero_int)) (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat)))))) (forall ((K tptp.int) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) (tptp.aa_int_nat tptp.nat2 K))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)) K))))) (forall ((Z tptp.int) (Z6 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 Z)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Z6)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Z) Z6)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_int_nat tptp.nat2 Z)) (tptp.aa_int_nat tptp.nat2 Z6))))))) (forall ((Z tptp.int) (Z6 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Z) Z6)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_int_nat tptp.nat2 Z)) (tptp.aa_int_nat tptp.nat2 Z6))))) (forall ((Z6 tptp.int) (Z tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z6)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z6) Z)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Z) Z6)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_int_nat tptp.nat2 Z)) (tptp.aa_int_nat tptp.nat2 Z6)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) Y)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_int_nat tptp.nat2 X)) (tptp.aa_int_nat tptp.nat2 Y))))))) (forall ((K tptp.int) (L tptp.int)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) L)))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.abs_abs_int K))) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.abs_abs_int L)))))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) X)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int X) Y)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_int_nat tptp.nat2 X)) (tptp.aa_int_nat tptp.nat2 Y))))) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int X) Y)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_int_nat tptp.nat2 X)) (tptp.aa_int_nat tptp.nat2 Y))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int X) Y)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_int_nat tptp.nat2 X)) (tptp.aa_int_nat tptp.nat2 Y))))))) (forall ((X tptp.rat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X)) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X))) tptp.one_one_int))) (forall ((Z tptp.int) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Z) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_int_nat tptp.nat2 Z)) N2)))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat A)) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat B))) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)))))))) (forall ((X tptp.rat)) (let ((_let_1 (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X)))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) _let_1))))) (forall ((Z tptp.int) (X tptp.rat)) (let ((_let_1 (tptp.aa_int_rat tptp.ring_1_of_int_rat Z))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) _let_1)) (= (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X) Z))))) (forall ((X tptp.rat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_rat tptp.ring_1_of_int_rat A))) (= (= (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X) A) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) _let_1)))))) (forall ((P tptp.fun_int_bool) (T5 tptp.rat)) (= (tptp.pp (tptp.aa_int_bool P (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat T5))) (forall ((I4 tptp.int)) (let ((_let_1 (tptp.aa_int_rat tptp.ring_1_of_int_rat I4))) (=> (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat _let_1) tptp.one_one_rat)) T5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat T5) _let_1))) (tptp.pp (tptp.aa_int_bool P I4))))))) (forall ((X tptp.rat) (Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X)) Z)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat Z)) tptp.one_one_rat))))) (forall ((Z tptp.int) (X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z) (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)) X)))) (forall ((Z tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (= (tptp.aa_nat_nat tptp.suc (tptp.aa_int_nat tptp.nat2 Z)) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) Z))))) (forall ((W2 tptp.int) (M tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) W2)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_int_nat tptp.nat2 W2)) M)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int W2) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)))))) (forall ((Z tptp.int) (Z6 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z) tptp.zero_zero_int)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Z) Z6)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.uminus_uminus_int Z))) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.uminus_uminus_int Z6)))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int A)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int B)))))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)))) (and (=> _let_2 (= _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat B) A))) (=> (not _let_2) (= _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) B))))))) (forall ((Z6 tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Z) Z6))) (let ((_let_2 (tptp.aa_int_nat tptp.nat2 Z))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat _let_2) (tptp.aa_int_nat tptp.nat2 Z6)))) (let ((_let_4 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z6) tptp.zero_zero_int)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int _let_1) tptp.zero_zero_int)) tptp.zero_zero_nat) (tptp.aa_int_nat tptp.nat2 _let_1)))))))))) (forall ((Q5 tptp.rat) (P3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Q5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat P3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat P3) Q5)))) Q5))))) (forall ((Q5 tptp.rat) (P3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Q5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat P3) Q5)))) tptp.one_one_rat)) Q5)) P3)))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X)) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat Y)))) (let ((_let_2 (tptp.aa_rat_int tptp.archim3151403230148437115or_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y)))) (let ((_let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.archimedean_frac_rat X)) (tptp.aa_rat_rat tptp.archimedean_frac_rat Y))) tptp.one_one_rat)))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int)))))))) (forall ((A1 tptp.int) (A22 tptp.int) (A32 tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int A1 A22) A32)) (or (exists ((K3 tptp.int)) (and (= A1 K3) (= A22 tptp.zero_zero_int) (= A32 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) K3)))) (exists ((L2 tptp.int) (K3 tptp.int) (Q6 tptp.int)) (and (= A1 K3) (= A22 L2) (= A32 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q6) tptp.zero_zero_int)) (not (= L2 tptp.zero_zero_int)) (= K3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Q6) L2)))) (exists ((R4 tptp.int) (L2 tptp.int) (K3 tptp.int) (Q6 tptp.int)) (and (= A1 K3) (= A22 L2) (= A32 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q6) R4)) (= (tptp.aa_int_int tptp.sgn_sgn_int R4) (tptp.aa_int_int tptp.sgn_sgn_int L2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.abs_abs_int R4)) (tptp.aa_int_int tptp.abs_abs_int L2))) (= K3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Q6) L2)) R4))))))) (forall ((A1 tptp.int) (A22 tptp.int) (A32 tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int A1 A22) A32)) (=> (=> (= A22 tptp.zero_zero_int) (not (= A32 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) A1)))) (=> (forall ((Q4 tptp.int)) (=> (= A32 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q4) tptp.zero_zero_int)) (=> (not (= A22 tptp.zero_zero_int)) (not (= A1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Q4) A22)))))) (not (forall ((R2 tptp.int) (Q4 tptp.int)) (=> (= A32 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q4) R2)) (=> (= (tptp.aa_int_int tptp.sgn_sgn_int R2) (tptp.aa_int_int tptp.sgn_sgn_int A22)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.abs_abs_int R2)) (tptp.aa_int_int tptp.abs_abs_int A22))) (not (= A1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Q4) A22)) R2)))))))))))) (forall ((S tptp.multis2468970476368604999at_nat)) (= (not (= S tptp.zero_z1048942125864253310at_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.size_s8510653225128441779at_nat S))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (=> (tptp.member_rat A tptp.ring_1_Ints_rat) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)))) (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat A)) (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat B)))))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (=> (tptp.member_rat A tptp.ring_1_Ints_rat) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.ring_1_of_int_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)))) (tptp.aa_int_int tptp.ring_1_of_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat A)) (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat B)))))))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer A)) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.sgn_sgn_rat A)) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.sgn_sgn_int A)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer A))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 A))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat tptp.sgn_sgn_rat A))) (tptp.pp (tptp.aa_rat_bool _let_1 A))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int tptp.sgn_sgn_int A))) (tptp.pp (tptp.aa_int_bool _let_1 A))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.sgn_sgn_rat B))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A) _let_1) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_1)))) (forall ((A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A)) (= (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer A) tptp.one_one_Code_integer))) (forall ((A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (= (tptp.aa_rat_rat tptp.sgn_sgn_rat A) tptp.one_one_rat))) (forall ((A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) A)) (= (tptp.aa_int_int tptp.sgn_sgn_int A) tptp.one_one_int))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat tptp.archimedean_frac_rat X))) (not (tptp.member_rat X tptp.ring_1_Ints_rat)))) (forall ((A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)) (= (tptp.aa_int_int tptp.sgn_sgn_int A) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)))) (forall ((A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger)) (= (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (forall ((A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (= (tptp.aa_rat_rat tptp.sgn_sgn_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)))) (forall ((C3 tptp.multis2468970476368604999at_nat) (B3 tptp.multis2468970476368604999at_nat) (A3 tptp.multis2468970476368604999at_nat)) (let ((_let_1 (tptp.plus_p7104986032573967614at_nat A3))) (=> (= (tptp.minus_4286766774447292334at_nat C3 B3) tptp.zero_z1048942125864253310at_nat) (= (tptp.minus_4286766774447292334at_nat (tptp.aa_mul5754855110707352700at_nat _let_1 B3) C3) (tptp.aa_mul5754855110707352700at_nat _let_1 (tptp.minus_4286766774447292334at_nat B3 C3)))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer A)) (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat tptp.sgn_sgn_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.sgn_sgn_rat A)) (tptp.aa_rat_rat tptp.sgn_sgn_rat B)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int tptp.sgn_sgn_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.sgn_sgn_int A)) (tptp.aa_int_int tptp.sgn_sgn_int B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A) tptp.ring_11222124179247155820nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer B) tptp.ring_11222124179247155820nteger)) (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)) tptp.ring_11222124179247155820nteger))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.member_rat A tptp.ring_1_Ints_rat) (=> (tptp.member_rat B tptp.ring_1_Ints_rat) (tptp.member_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B) tptp.ring_1_Ints_rat)))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A) tptp.ring_1_Ints_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int B) tptp.ring_1_Ints_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) tptp.ring_1_Ints_int))))) (forall ((K tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer K) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger K) (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer K)))) (forall ((K tptp.rat)) (= (tptp.aa_rat_rat tptp.abs_abs_rat K) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat K) (tptp.aa_rat_rat tptp.sgn_sgn_rat K)))) (forall ((K tptp.int)) (= (tptp.aa_int_int tptp.abs_abs_int K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) (tptp.aa_int_int tptp.sgn_sgn_int K)))) (forall ((A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer A)) (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer A)) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) (tptp.aa_rat_rat tptp.sgn_sgn_rat A)) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.abs_abs_int A)) (tptp.aa_int_int tptp.sgn_sgn_int A)) A)) (forall ((A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer A)) (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer A)) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.sgn_sgn_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat A)) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.sgn_sgn_int A)) (tptp.aa_int_int tptp.abs_abs_int A)) A)) (forall ((X tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer X)) (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer X)) X)) (forall ((X tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.sgn_sgn_rat X)) (tptp.aa_rat_rat tptp.abs_abs_rat X)) X)) (forall ((X tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.sgn_sgn_int X)) (tptp.aa_int_int tptp.abs_abs_int X)) X)) (forall ((X tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_rat_rat tptp.archimedean_frac_rat X)))) (forall ((X tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.archimedean_frac_rat X)) tptp.one_one_rat))) (forall ((X tptp.rat) (A tptp.rat)) (= (= (tptp.aa_rat_rat tptp.archimedean_frac_rat X) A) (and (tptp.member_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat X) A) tptp.ring_1_Ints_rat) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.one_one_rat))))) (forall ((A tptp.code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer A) tptp.one_one_Code_integer) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A)))) (forall ((A tptp.rat)) (= (= (tptp.aa_rat_rat tptp.sgn_sgn_rat A) tptp.one_one_rat) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)))) (forall ((A tptp.int)) (= (= (tptp.aa_int_int tptp.sgn_sgn_int A) tptp.one_one_int) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) A)))) (forall ((I2 tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.sgn_sgn_int I2))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) I2)))) (let ((_let_3 (= I2 tptp.zero_zero_int))) (and (=> _let_3 (= _let_1 tptp.zero_zero_int)) (=> (not _let_3) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)))))))))) (forall ((A tptp.int)) (= (= (tptp.aa_int_int tptp.sgn_sgn_int A) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)))) (forall ((A tptp.code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.rat)) (= (= (tptp.aa_rat_rat tptp.sgn_sgn_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)))) (forall ((X tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.sgn_sgn_int X))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) X)))) (let ((_let_3 (= X tptp.zero_zero_int))) (and (=> _let_3 (= _let_1 tptp.zero_zero_int)) (=> (not _let_3) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)))))))))) (forall ((X tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer X))) (let ((_let_2 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) X)))) (let ((_let_3 (= X tptp.zero_z3403309356797280102nteger))) (and (=> _let_3 (= _let_1 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (and (=> _let_2 (= _let_1 tptp.one_one_Code_integer)) (=> (not _let_2) (= _let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))))))) (forall ((X tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.sgn_sgn_rat X))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) X)))) (let ((_let_3 (= X tptp.zero_zero_rat))) (and (=> _let_3 (= _let_1 tptp.zero_zero_rat)) (=> (not _let_3) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)))))))))) (forall ((A tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A) tptp.ring_11222124179247155820nteger)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) A)) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))) (forall ((A tptp.rat)) (=> (tptp.member_rat A tptp.ring_1_Ints_rat) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat tptp.one_one_rat) A)) A)) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat))))) (forall ((A tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A) tptp.ring_1_Ints_int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) A)) A)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int))))) (forall ((X tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X) tptp.ring_11222124179247155820nteger)) (=> (not (= X tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer X)))))) (forall ((X tptp.rat)) (=> (tptp.member_rat X tptp.ring_1_Ints_rat) (=> (not (= X tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_rat_rat tptp.abs_abs_rat X)))))) (forall ((X tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X) tptp.ring_1_Ints_int)) (=> (not (= X tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) (tptp.aa_int_int tptp.abs_abs_int X)))))) (forall ((X tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X) tptp.ring_11222124179247155820nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer X)) tptp.one_one_Code_integer)) (= X tptp.zero_z3403309356797280102nteger)))) (forall ((X tptp.rat)) (=> (tptp.member_rat X tptp.ring_1_Ints_rat) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.abs_abs_rat X)) tptp.one_one_rat)) (= X tptp.zero_zero_rat)))) (forall ((X tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X) tptp.ring_1_Ints_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.abs_abs_int X)) tptp.one_one_int)) (= X tptp.zero_zero_int)))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X) tptp.ring_11222124179247155820nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Y) tptp.ring_11222124179247155820nteger)) (= (= X Y) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger X) Y))) tptp.one_one_Code_integer)))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.member_rat X tptp.ring_1_Ints_rat) (=> (tptp.member_rat Y tptp.ring_1_Ints_rat) (= (= X Y) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat X) Y))) tptp.one_one_rat)))))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X) tptp.ring_1_Ints_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Y) tptp.ring_1_Ints_int)) (= (= X Y) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) Y))) tptp.one_one_int)))))) (forall ((X tptp.rat)) (= (= (tptp.aa_rat_rat tptp.archimedean_frac_rat X) X) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) tptp.one_one_rat))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat tptp.archimedean_frac_rat X)) (tptp.aa_rat_rat tptp.archimedean_frac_rat Y)))) (let ((_let_2 (tptp.aa_rat_rat tptp.archimedean_frac_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y)))) (let ((_let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_1) tptp.one_one_rat)))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat _let_1) tptp.one_one_rat)))))))) (forall ((R3 tptp.int) (L tptp.int) (K tptp.int) (Q5 tptp.int)) (=> (= (tptp.aa_int_int tptp.sgn_sgn_int R3) (tptp.aa_int_int tptp.sgn_sgn_int L)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.abs_abs_int R3)) (tptp.aa_int_int tptp.abs_abs_int L))) (=> (= K (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Q5) L)) R3)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int K L) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q5) R3))))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (=> (tptp.member_rat A tptp.ring_1_Ints_rat) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat A)) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat B)))) (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_rat_int tptp.archim3151403230148437115or_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)))))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (=> (tptp.member_rat A tptp.ring_1_Ints_rat) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.ring_1_of_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat A)) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat B)))) (tptp.aa_int_int tptp.ring_1_of_int_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)))))))) (forall ((From tptp.nat) (To tptp.nat) (Xs tptp.list_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat From) To)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat To) (tptp.aa_list_nat_nat tptp.size_size_list_nat Xs))) (= (tptp.aa_list_nat_nat tptp.size_size_list_nat (tptp.slice_nat From To Xs)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat To) From))))) (forall ((From tptp.nat) (To tptp.nat) (Xs tptp.list_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat From) To)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat To) (tptp.size_size_list_bool Xs))) (= (tptp.size_size_list_bool (tptp.slice_bool From To Xs)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat To) From))))) (forall ((K tptp.nat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.aa_nat_rat (tptp.gbinomial_rat A) K) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) tptp.one_one_rat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat K) tptp.one_one_nat)))))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))) N2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) N2)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N2)))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) N2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) N2)) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N2)))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) N2) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2)) (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger N2)))) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat)))))) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat)))))) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger N2) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2)) (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat)))))) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat)))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat M))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat))))))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int M))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat))))))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger M))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_Code_integer)) (=> (not _let_2) (= _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M)) (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat))))))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat M))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat))))))))) (forall ((Xs tptp.list_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_list_nat_nat tptp.size_size_list_nat Xs)) tptp.one_one_nat)) (= (tptp.rotate1_nat Xs) Xs))) (forall ((Xs tptp.list_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.size_size_list_bool Xs)) tptp.one_one_nat)) (= (tptp.rotate1_bool Xs) Xs))) (forall ((D3 tptp.int) (P tptp.fun_int_bool) (P4 tptp.fun_int_bool) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D3)) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) Z4)) (= (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P4 X3)))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa3) (tptp.set_or1266510415728281911st_int tptp.one_one_int D3))) (forall ((Xb2 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xb2) B3)) (not (= X3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb2) Xa3))))))) (=> (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X3) D3)))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool P4 X3)) (tptp.pp (tptp.aa_int_bool P4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K2) D3)))))) (= (exists ((X_12 tptp.int)) (tptp.pp (tptp.aa_int_bool P X_12))) (or (exists ((X4 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) (tptp.set_or1266510415728281911st_int tptp.one_one_int D3))) (tptp.pp (tptp.aa_int_bool P4 X4)))) (exists ((X4 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) (tptp.set_or1266510415728281911st_int tptp.one_one_int D3))) (exists ((Xa tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa) B3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xa) X4)))))))))))))) (forall ((L tptp.set_int) (H tptp.set_int) (L3 tptp.set_int) (H3 tptp.set_int)) (= (= (tptp.set_or370866239135849197et_int L H) (tptp.set_or370866239135849197et_int L3 H3)) (or (and (= L L3) (= H H3)) (and (not (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int L) H))) (not (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int L3) H3))))))) (forall ((L tptp.rat) (H tptp.rat) (L3 tptp.rat) (H3 tptp.rat)) (= (= (tptp.set_or633870826150836451st_rat L H) (tptp.set_or633870826150836451st_rat L3 H3)) (or (and (= L L3) (= H H3)) (and (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat L) H))) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat L3) H3))))))) (forall ((L tptp.num) (H tptp.num) (L3 tptp.num) (H3 tptp.num)) (= (= (tptp.set_or7049704709247886629st_num L H) (tptp.set_or7049704709247886629st_num L3 H3)) (or (and (= L L3) (= H H3)) (and (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num L) H))) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num L3) H3))))))) (forall ((L tptp.int) (H tptp.int) (L3 tptp.int) (H3 tptp.int)) (= (= (tptp.set_or1266510415728281911st_int L H) (tptp.set_or1266510415728281911st_int L3 H3)) (or (and (= L L3) (= H H3)) (and (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int L) H))) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int L3) H3))))))) (forall ((L tptp.nat) (H tptp.nat) (L3 tptp.nat) (H3 tptp.nat)) (= (= (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat L) H) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat L3) H3)) (or (and (= L L3) (= H H3)) (and (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat L) H))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat L3) H3))))))) (forall ((L tptp.code_integer) (H tptp.code_integer) (L3 tptp.code_integer) (H3 tptp.code_integer)) (= (= (tptp.set_or189985376899183464nteger L H) (tptp.set_or189985376899183464nteger L3 H3)) (or (and (= L L3) (= H H3)) (and (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger L) H))) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger L3) H3))))))) (forall ((I2 tptp.bool) (L tptp.bool) (U tptp.bool)) (= (tptp.pp (tptp.member_bool I2 (tptp.set_or1454250544011482060t_bool L U))) (and (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.ord_less_eq_bool L) I2)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.ord_less_eq_bool I2) U))))) (forall ((I2 tptp.set_nat) (L tptp.set_nat) (U tptp.set_nat)) (= (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat I2) (tptp.set_or4548717258645045905et_nat L U))) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat L) I2)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat I2) U))))) (forall ((I2 tptp.set_int) (L tptp.set_int) (U tptp.set_int)) (= (tptp.member_set_int I2 (tptp.set_or370866239135849197et_int L U)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int L) I2)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int I2) U))))) (forall ((I2 tptp.rat) (L tptp.rat) (U tptp.rat)) (= (tptp.member_rat I2 (tptp.set_or633870826150836451st_rat L U)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat L) I2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat I2) U))))) (forall ((I2 tptp.num) (L tptp.num) (U tptp.num)) (= (tptp.member_num I2 (tptp.set_or7049704709247886629st_num L U)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num L) I2)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num I2) U))))) (forall ((I2 tptp.int) (L tptp.int) (U tptp.int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I2) (tptp.set_or1266510415728281911st_int L U))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int L) I2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I2) U))))) (forall ((I2 tptp.nat) (L tptp.nat) (U tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I2) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat L) U))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat L) I2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) U))))) (forall ((I2 tptp.code_integer) (L tptp.code_integer) (U tptp.code_integer)) (= (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I2) (tptp.set_or189985376899183464nteger L U))) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger L) I2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger I2) U))))) (forall ((A tptp.bool) (B tptp.bool)) (= (= tptp.bot_bot_set_bool (tptp.set_or1454250544011482060t_bool A B)) (not (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.ord_less_eq_bool A) B))))) (forall ((A tptp.set_int) (B tptp.set_int)) (= (= tptp.bot_bot_set_set_int (tptp.set_or370866239135849197et_int A B)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) B))))) (forall ((A tptp.rat) (B tptp.rat)) (= (= tptp.bot_bot_set_rat (tptp.set_or633870826150836451st_rat A B)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))))) (forall ((A tptp.num) (B tptp.num)) (= (= tptp.bot_bot_set_num (tptp.set_or7049704709247886629st_num A B)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B))))) (forall ((A tptp.int) (B tptp.int)) (= (= tptp.bot_bot_set_int (tptp.set_or1266510415728281911st_int A B)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B))))) (forall ((A tptp.nat) (B tptp.nat)) (= (= tptp.bot_bot_set_nat (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat A) B)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= tptp.bot_bo3990330152332043303nteger (tptp.set_or189985376899183464nteger A B)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B))))) (forall ((A tptp.bool) (B tptp.bool)) (= (= (tptp.set_or1454250544011482060t_bool A B) tptp.bot_bot_set_bool) (not (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.ord_less_eq_bool A) B))))) (forall ((A tptp.set_int) (B tptp.set_int)) (= (= (tptp.set_or370866239135849197et_int A B) tptp.bot_bot_set_set_int) (not (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) B))))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (tptp.set_or633870826150836451st_rat A B) tptp.bot_bot_set_rat) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))))) (forall ((A tptp.num) (B tptp.num)) (= (= (tptp.set_or7049704709247886629st_num A B) tptp.bot_bot_set_num) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B))))) (forall ((A tptp.int) (B tptp.int)) (= (= (tptp.set_or1266510415728281911st_int A B) tptp.bot_bot_set_int) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B))))) (forall ((A tptp.nat) (B tptp.nat)) (= (= (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat A) B) tptp.bot_bot_set_nat) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (tptp.set_or189985376899183464nteger A B) tptp.bot_bo3990330152332043303nteger) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B))))) (forall ((B tptp.bool) (A tptp.bool)) (=> (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.ord_less_bool B) A)) (= (tptp.set_or1454250544011482060t_bool A B) tptp.bot_bot_set_bool))) (forall ((B tptp.assn) (A tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn B) A)) (= (tptp.set_or7959216805967363635t_assn A B) tptp.bot_bot_set_assn))) (forall ((B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (= (tptp.set_or633870826150836451st_rat A B) tptp.bot_bot_set_rat))) (forall ((B tptp.num) (A tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) A)) (= (tptp.set_or7049704709247886629st_num A B) tptp.bot_bot_set_num))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)) (= (tptp.set_or1266510415728281911st_int A B) tptp.bot_bot_set_int))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A)) (= (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat A) B) tptp.bot_bot_set_nat))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger B) A)) (= (tptp.set_or189985376899183464nteger A B) tptp.bot_bo3990330152332043303nteger))) (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int) (D2 tptp.set_int)) (= (tptp.ord_le4403425263959731960et_int (tptp.set_or370866239135849197et_int A B) (tptp.set_or370866239135849197et_int C D2)) (or (not (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) B))) (and (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int C) A)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) D2)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (= (tptp.ord_less_eq_set_rat (tptp.set_or633870826150836451st_rat A B) (tptp.set_or633870826150836451st_rat C D2)) (or (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) D2)))))) (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D2 tptp.num)) (= (tptp.ord_less_eq_set_num (tptp.set_or7049704709247886629st_num A B) (tptp.set_or7049704709247886629st_num C D2)) (or (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B))) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num C) A)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) D2)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.set_or1266510415728281911st_int A B)) (tptp.set_or1266510415728281911st_int C D2))) (or (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) D2)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat A) B)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat C) D2))) (or (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) D2)))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (= (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger (tptp.set_or189985376899183464nteger A B)) (tptp.set_or189985376899183464nteger C D2))) (or (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B))) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger C) A)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) D2)))))) (forall ((Xs tptp.list_nat)) (= (tptp.slice_nat tptp.zero_zero_nat (tptp.aa_list_nat_nat tptp.size_size_list_nat Xs) Xs) Xs)) (forall ((Xs tptp.list_bool)) (= (tptp.slice_bool tptp.zero_zero_nat (tptp.size_size_list_bool Xs) Xs) Xs)) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (= (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat _let_1) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat _let_1)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (= (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int _let_1)) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (= (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger _let_1)) (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (= (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat _let_1)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2))))) (forall ((A3 tptp.multis2468970476368604999at_nat) (B3 tptp.multis2468970476368604999at_nat) (M6 tptp.multis2468970476368604999at_nat) (N7 tptp.multis2468970476368604999at_nat)) (=> (= (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat A3) B3) (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat M6) N7)) (not (forall ((Am tptp.multis2468970476368604999at_nat) (An tptp.multis2468970476368604999at_nat)) (=> (= A3 (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat Am) An)) (forall ((Bm tptp.multis2468970476368604999at_nat) (Bn tptp.multis2468970476368604999at_nat)) (=> (= B3 (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat Bm) Bn)) (=> (= M6 (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat Am) Bm)) (not (= N7 (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat An) Bn))))))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat M)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2))))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2)))) (forall ((L tptp.rat) (M tptp.rat) (U tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat L) M)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat M) U)) (= (tptp.sup_sup_set_rat (tptp.set_or633870826150836451st_rat L M) (tptp.set_or633870826150836451st_rat M U)) (tptp.set_or633870826150836451st_rat L U))))) (forall ((L tptp.num) (M tptp.num) (U tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num L) M)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) U)) (= (tptp.sup_sup_set_num (tptp.set_or7049704709247886629st_num L M) (tptp.set_or7049704709247886629st_num M U)) (tptp.set_or7049704709247886629st_num L U))))) (forall ((L tptp.int) (M tptp.int) (U tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int L) M)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int M) U)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int (tptp.set_or1266510415728281911st_int L M)) (tptp.set_or1266510415728281911st_int M U)) (tptp.set_or1266510415728281911st_int L U))))) (forall ((L tptp.nat) (M tptp.nat) (U tptp.nat)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat L))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat L) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) U)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.aa_nat_set_nat _let_1 M)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) U)) (tptp.aa_nat_set_nat _let_1 U)))))) (forall ((L tptp.code_integer) (M tptp.code_integer) (U tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger L) M)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger M) U)) (= (tptp.sup_su848401254843788991nteger (tptp.set_or189985376899183464nteger L M) (tptp.set_or189985376899183464nteger M U)) (tptp.set_or189985376899183464nteger L U))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat M)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2)))))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger N2)))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N2)))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N2)))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2)))) (forall ((N2 tptp.nat)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger N2)) tptp.zero_z3403309356797280102nteger)))) (forall ((N2 tptp.nat)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N2)) tptp.zero_zero_rat)))) (forall ((N2 tptp.nat)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N2)) tptp.zero_zero_int)))) (forall ((N2 tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2)) tptp.zero_zero_nat)))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger N2)))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N2)))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N2)))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2)))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger N2)))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N2)))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N2)))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat M)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int M)) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat M)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2))))) (forall ((A tptp.rat) (K tptp.nat)) (= (tptp.aa_nat_rat (tptp.gbinomial_rat A) K) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) K))) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat K)))) (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat _let_1 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) (tptp.aa_nat_rat (tptp.gbinomial_rat A) K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat _let_1 tptp.one_one_rat)) K))))) (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.gbinomial_rat A))) (let ((_let_3 (tptp.aa_nat_rat _let_2 K))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) _let_3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K)) _let_3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat _let_1)) (tptp.aa_nat_rat _let_2 _let_1)))))))) (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.gbinomial_rat A))) (let ((_let_3 (tptp.aa_nat_rat _let_2 K))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_3) A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K)) _let_3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat _let_1)) (tptp.aa_nat_rat _let_2 _let_1)))))))) (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A) _let_1)) K)) (tptp.aa_nat_rat (tptp.gbinomial_rat A) K)))))) (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn) (D2 tptp.assn)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn C))) (= (tptp.ord_less_set_assn (tptp.set_or7959216805967363635t_assn A B) (tptp.set_or7959216805967363635t_assn C D2)) (and (or (not (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn A) B))) (and (tptp.pp (tptp.aa_assn_bool _let_1 A)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn B) D2)) (or (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn C) A)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn B) D2))))) (tptp.pp (tptp.aa_assn_bool _let_1 D2)))))) (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int) (D2 tptp.set_int)) (let ((_let_1 (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int C))) (= (tptp.ord_less_set_set_int (tptp.set_or370866239135849197et_int A B) (tptp.set_or370866239135849197et_int C D2)) (and (or (not (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) B))) (and (tptp.pp (tptp.aa_set_int_bool _let_1 A)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) D2)) (or (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int C) A)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int B) D2))))) (tptp.pp (tptp.aa_set_int_bool _let_1 D2)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C))) (= (tptp.ord_less_set_rat (tptp.set_or633870826150836451st_rat A B) (tptp.set_or633870826150836451st_rat C D2)) (and (or (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))) (and (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) D2)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) D2))))) (tptp.pp (tptp.aa_rat_bool _let_1 D2)))))) (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D2 tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num C))) (= (tptp.ord_less_set_num (tptp.set_or7049704709247886629st_num A B) (tptp.set_or7049704709247886629st_num C D2)) (and (or (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B))) (and (tptp.pp (tptp.aa_num_bool _let_1 A)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) D2)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num C) A)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) D2))))) (tptp.pp (tptp.aa_num_bool _let_1 D2)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C))) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int (tptp.set_or1266510415728281911st_int A B)) (tptp.set_or1266510415728281911st_int C D2))) (and (or (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B))) (and (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) D2)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) D2))))) (tptp.pp (tptp.aa_int_bool _let_1 D2)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C))) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat A) B)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat C) D2))) (and (or (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B))) (and (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) D2)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) D2))))) (tptp.pp (tptp.aa_nat_bool _let_1 D2)))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger C))) (= (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le1307284697595431911nteger (tptp.set_or189985376899183464nteger A B)) (tptp.set_or189985376899183464nteger C D2))) (and (or (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B))) (and (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) D2)) (or (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger C) A)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger B) D2))))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 D2)))))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat M)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N2)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int M)) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N2)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat M)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N2)) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int M)) tptp.zero_zero_int))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger N2)) (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger M)) tptp.zero_z3403309356797280102nteger))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.modulo8411746178871703098atural (tptp.aa_nat_Code_natural tptp.semiri2447717529341329178atural N2) (tptp.aa_nat_Code_natural tptp.semiri2447717529341329178atural M)) tptp.zero_z2226904508553997617atural))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat M)) tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger N2)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat N2) N2))))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N2)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat N2) N2))))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N2)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat N2) N2))))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat N2) N2))))) (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) tptp.one_one_rat))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat _let_2)) (tptp.aa_nat_rat (tptp.gbinomial_rat _let_1) _let_2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) (tptp.aa_nat_rat (tptp.gbinomial_rat A) K)))))) (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat _let_1)) (tptp.aa_nat_rat (tptp.gbinomial_rat A) _let_1)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) tptp.one_one_rat)) K))))) (forall ((K tptp.nat) (M tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.gbinomial_rat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) M)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 M)) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 K)) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) K))))))) (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.gbinomial_rat A) K))) (let ((_let_2 (= K tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.set_fo1949268297981939178at_rat (tptp.aTP_Lamm_hm A) tptp.zero_zero_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat K) tptp.one_one_nat)) tptp.one_one_rat)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat K)))))))) (forall ((R3 tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat R3) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) R3)))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat N2) R3))))) (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) tptp.one_one_rat))) (= (tptp.aa_nat_rat (tptp.gbinomial_rat _let_2) _let_1) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.gbinomial_rat A) K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat _let_2) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat _let_1))))))) (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) tptp.one_one_rat))) (= (tptp.aa_nat_rat (tptp.gbinomial_rat _let_2) _let_1) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat _let_2) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat _let_1))) (tptp.aa_nat_rat (tptp.gbinomial_rat A) K)))))) (forall ((A tptp.rat) (K tptp.nat)) (= (tptp.aa_nat_rat (tptp.gbinomial_rat A) K) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K)) A)) tptp.one_one_rat)) K)))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 K)) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))) tptp.one_one_rat)) K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 N2)) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) N2))))) (forall ((D2 tptp.int) (P tptp.fun_int_bool)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D2)) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K2) D2)))))) (= (exists ((X_12 tptp.int)) (tptp.pp (tptp.aa_int_bool P X_12))) (exists ((X4 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) (tptp.set_or1266510415728281911st_int tptp.one_one_int D2))) (tptp.pp (tptp.aa_int_bool P X4)))))))) (forall ((D3 tptp.int) (A3 tptp.set_int) (T5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D3)) (forall ((X5 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int T5))) (=> (forall ((Xa4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa4) (tptp.set_or1266510415728281911st_int tptp.one_one_int D3))) (forall ((Xb3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xb3) A3)) (not (= X5 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb3) Xa4))))))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X5)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X5) D3))))))))) (forall ((D3 tptp.int) (T5 tptp.int) (A3 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int T5) A3)) (forall ((X5 tptp.int)) (=> (forall ((Xa4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa4) (tptp.set_or1266510415728281911st_int tptp.one_one_int D3))) (forall ((Xb3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xb3) A3)) (not (= X5 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb3) Xa4))))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X5) T5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X5) D3)) T5)))))))) (forall ((D3 tptp.int) (T5 tptp.int) (A3 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int T5) A3)) (forall ((X5 tptp.int)) (=> (forall ((Xa4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa4) (tptp.set_or1266510415728281911st_int tptp.one_one_int D3))) (forall ((Xb3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xb3) A3)) (not (= X5 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb3) Xa4))))))) (=> (not (= X5 T5)) (not (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X5) D3) T5)))))))) (forall ((D3 tptp.int) (T5 tptp.int) (A3 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int T5) tptp.one_one_int)) A3)) (forall ((X5 tptp.int)) (=> (forall ((Xa4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa4) (tptp.set_or1266510415728281911st_int tptp.one_one_int D3))) (forall ((Xb3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xb3) A3)) (not (= X5 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb3) Xa4))))))) (=> (= X5 T5) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X5) D3) T5))))))) (forall ((D3 tptp.int) (T5 tptp.int) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int T5) B3)) (forall ((X5 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int T5))) (=> (forall ((Xa4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa4) (tptp.set_or1266510415728281911st_int tptp.one_one_int D3))) (forall ((Xb3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xb3) B3)) (not (= X5 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb3) Xa4))))))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X5)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X5) D3)))))))))) (forall ((D3 tptp.int) (B3 tptp.set_int) (T5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D3)) (forall ((X5 tptp.int)) (=> (forall ((Xa4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa4) (tptp.set_or1266510415728281911st_int tptp.one_one_int D3))) (forall ((Xb3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xb3) B3)) (not (= X5 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb3) Xa4))))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X5) T5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X5) D3)) T5))))))) (forall ((D3 tptp.int) (T5 tptp.int) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int T5) B3)) (forall ((X5 tptp.int)) (=> (forall ((Xa4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa4) (tptp.set_or1266510415728281911st_int tptp.one_one_int D3))) (forall ((Xb3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xb3) B3)) (not (= X5 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb3) Xa4))))))) (=> (not (= X5 T5)) (not (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X5) D3) T5)))))))) (forall ((D3 tptp.int) (T5 tptp.int) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int T5) tptp.one_one_int)) B3)) (forall ((X5 tptp.int)) (=> (forall ((Xa4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa4) (tptp.set_or1266510415728281911st_int tptp.one_one_int D3))) (forall ((Xb3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xb3) B3)) (not (= X5 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb3) Xa4))))))) (=> (= X5 T5) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X5) D3) T5))))))) (forall ((A tptp.rat) (K tptp.nat)) (= (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) K) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K)))) (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) tptp.one_one_rat)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.aa_nat_rat (tptp.gbinomial_rat A) K) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat K) tptp.one_one_nat))) (tptp.aa_nat_rat _let_1 K)))))) (forall ((D3 tptp.int) (A3 tptp.set_int) (T5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D3)) (forall ((X5 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int T5))) (=> (forall ((Xa4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa4) (tptp.set_or1266510415728281911st_int tptp.one_one_int D3))) (forall ((Xb3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xb3) A3)) (not (= X5 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb3) Xa4))))))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X5)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X5) D3))))))))) (forall ((D3 tptp.int) (T5 tptp.int) (A3 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int T5) tptp.one_one_int)) A3)) (forall ((X5 tptp.int)) (=> (forall ((Xa4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa4) (tptp.set_or1266510415728281911st_int tptp.one_one_int D3))) (forall ((Xb3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xb3) A3)) (not (= X5 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb3) Xa4))))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X5) T5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X5) D3)) T5)))))))) (forall ((D3 tptp.int) (T5 tptp.int) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int T5) tptp.one_one_int)) B3)) (forall ((X5 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int T5))) (=> (forall ((Xa4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa4) (tptp.set_or1266510415728281911st_int tptp.one_one_int D3))) (forall ((Xb3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xb3) B3)) (not (= X5 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb3) Xa4))))))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X5)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X5) D3)))))))))) (forall ((D3 tptp.int) (B3 tptp.set_int) (T5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D3)) (forall ((X5 tptp.int)) (=> (forall ((Xa4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa4) (tptp.set_or1266510415728281911st_int tptp.one_one_int D3))) (forall ((Xb3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xb3) B3)) (not (= X5 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb3) Xa4))))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X5) T5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X5) D3)) T5))))))) (forall ((D3 tptp.int) (P tptp.fun_int_bool) (P4 tptp.fun_int_bool) (A3 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D3)) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z4) X3)) (= (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P4 X3)))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa3) (tptp.set_or1266510415728281911st_int tptp.one_one_int D3))) (forall ((Xb2 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xb2) A3)) (not (= X3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb2) Xa3))))))) (=> (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X3) D3)))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool P4 X3)) (tptp.pp (tptp.aa_int_bool P4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K2) D3)))))) (= (exists ((X_12 tptp.int)) (tptp.pp (tptp.aa_int_bool P X_12))) (or (exists ((X4 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) (tptp.set_or1266510415728281911st_int tptp.one_one_int D3))) (tptp.pp (tptp.aa_int_bool P4 X4)))) (exists ((X4 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) (tptp.set_or1266510415728281911st_int tptp.one_one_int D3))) (exists ((Xa tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa) A3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xa) X4)))))))))))))) (forall ((From tptp.nat) (To tptp.nat) (Xs tptp.list_int) (I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat From) To)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat To) (tptp.size_size_list_int Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat To) From))) (= (tptp.aa_nat_int (tptp.nth_int (tptp.slice_int From To Xs)) I2) (tptp.aa_nat_int (tptp.nth_int Xs) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat From) I2))))))) (forall ((From tptp.nat) (To tptp.nat) (Xs tptp.list_nat) (I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat From) To)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat To) (tptp.aa_list_nat_nat tptp.size_size_list_nat Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat To) From))) (= (tptp.aa_nat_nat (tptp.nth_nat (tptp.slice_nat From To Xs)) I2) (tptp.aa_nat_nat (tptp.nth_nat Xs) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat From) I2))))))) (forall ((From tptp.nat) (To tptp.nat) (Xs tptp.list_bool) (I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat From) To)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat To) (tptp.size_size_list_bool Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat To) From))) (= (tptp.pp (tptp.aa_nat_bool (tptp.nth_bool (tptp.slice_bool From To Xs)) I2)) (tptp.pp (tptp.aa_nat_bool (tptp.nth_bool Xs) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat From) I2)))))))) (forall ((A tptp.rat) (B tptp.rat) (M tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A) M)) C))) (let ((_let_2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) M)) C))) (let ((_let_3 (tptp.set_or633870826150836451st_rat A B))) (let ((_let_4 (tptp.image_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.aTP_Lamm_hn M) C) _let_3))) (let ((_let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) M)))) (let ((_let_6 (= _let_3 tptp.bot_bot_set_rat))) (and (=> _let_6 (= _let_4 tptp.bot_bot_set_rat)) (=> (not _let_6) (and (=> _let_5 (= _let_4 (tptp.set_or633870826150836451st_rat _let_1 _let_2))) (=> (not _let_5) (= _let_4 (tptp.set_or633870826150836451st_rat _let_2 _let_1))))))))))))) (forall ((A tptp.rat) (B tptp.rat) (M tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A) M)) C))) (let ((_let_2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) M)) C))) (let ((_let_3 (tptp.set_or633870826150836451st_rat A B))) (let ((_let_4 (tptp.image_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.aTP_Lamm_ho M) C) _let_3))) (let ((_let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) M)))) (let ((_let_6 (= _let_3 tptp.bot_bot_set_rat))) (and (=> _let_6 (= _let_4 tptp.bot_bot_set_rat)) (=> (not _let_6) (and (=> _let_5 (= _let_4 (tptp.set_or633870826150836451st_rat _let_1 _let_2))) (=> (not _let_5) (= _let_4 (tptp.set_or633870826150836451st_rat _let_2 _let_1))))))))))))) (forall ((A tptp.rat) (B tptp.rat) (M tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat M))) (let ((_let_2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 A)) C))) (let ((_let_3 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 B)) C))) (let ((_let_4 (tptp.set_or633870826150836451st_rat A B))) (let ((_let_5 (tptp.image_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.aTP_Lamm_hp M) C) _let_4))) (let ((_let_6 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) M)))) (let ((_let_7 (= _let_4 tptp.bot_bot_set_rat))) (and (=> _let_7 (= _let_5 tptp.bot_bot_set_rat)) (=> (not _let_7) (and (=> _let_6 (= _let_5 (tptp.set_or633870826150836451st_rat _let_2 _let_3))) (=> (not _let_6) (= _let_5 (tptp.set_or633870826150836451st_rat _let_3 _let_2)))))))))))))) (forall ((A tptp.rat) (B tptp.rat) (M tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat M))) (let ((_let_2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat _let_1 A)) C))) (let ((_let_3 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat _let_1 B)) C))) (let ((_let_4 (tptp.set_or633870826150836451st_rat A B))) (let ((_let_5 (tptp.image_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.aTP_Lamm_hq M) C) _let_4))) (let ((_let_6 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) M)))) (let ((_let_7 (= _let_4 tptp.bot_bot_set_rat))) (and (=> _let_7 (= _let_5 tptp.bot_bot_set_rat)) (=> (not _let_7) (and (=> _let_6 (= _let_5 (tptp.set_or633870826150836451st_rat _let_2 _let_3))) (=> (not _let_6) (= _let_5 (tptp.set_or633870826150836451st_rat _let_3 _let_2)))))))))))))) (forall ((X tptp.rat) (Y tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.image_rat_rat (tptp.aa_rat_fun_rat_rat tptp.aTP_Lamm_hr C) (tptp.set_or633870826150836451st_rat X Y)))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)))) (let ((_let_3 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) C))) (let ((_let_4 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Y) C))) (let ((_let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (and (=> _let_2 (and (=> _let_5 (= _let_1 (tptp.set_or633870826150836451st_rat _let_3 _let_4))) (=> (not _let_5) (= _let_1 (tptp.set_or633870826150836451st_rat _let_4 _let_3))))) (=> (not _let_2) (= _let_1 tptp.bot_bot_set_rat))))))))) (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc X))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Xa2) X)))) (=> (= (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.nat_prod_decode_aux X) Xa2) Y) (and (=> _let_2 (= Y (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat Xa2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat X) Xa2)))) (=> (not _let_2) (= Y (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.nat_prod_decode_aux _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Xa2) _let_1))))))))) (forall ((B tptp.bool) (F tptp.fun_bool_bool) (X tptp.bool) (A3 tptp.set_bool)) (=> (= (tptp.pp B) (tptp.pp (tptp.aa_bool_bool F X))) (=> (tptp.pp (tptp.member_bool X A3)) (tptp.pp (tptp.member_bool B (tptp.image_bool_bool F A3)))))) (forall ((B tptp.nat) (F tptp.fun_bool_nat) (X tptp.bool) (A3 tptp.set_bool)) (=> (= B (tptp.aa_bool_nat F X)) (=> (tptp.pp (tptp.member_bool X A3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B) (tptp.image_bool_nat F A3)))))) (forall ((B tptp.int) (F tptp.fun_bool_int) (X tptp.bool) (A3 tptp.set_bool)) (=> (= B (tptp.aa_bool_int F X)) (=> (tptp.pp (tptp.member_bool X A3)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int B) (tptp.image_bool_int F A3)))))) (forall ((B tptp.bool) (F tptp.fun_nat_bool) (X tptp.nat) (A3 tptp.set_nat)) (=> (= (tptp.pp B) (tptp.pp (tptp.aa_nat_bool F X))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X) A3)) (tptp.pp (tptp.member_bool B (tptp.image_nat_bool F A3)))))) (forall ((B tptp.nat) (F tptp.fun_nat_nat) (X tptp.nat) (A3 tptp.set_nat)) (=> (= B (tptp.aa_nat_nat F X)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X) A3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B) (tptp.image_nat_nat F A3)))))) (forall ((B tptp.int) (F tptp.fun_nat_int) (X tptp.nat) (A3 tptp.set_nat)) (=> (= B (tptp.aa_nat_int F X)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X) A3)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int B) (tptp.image_nat_int F A3)))))) (forall ((B tptp.bool) (F tptp.fun_int_bool) (X tptp.int) (A3 tptp.set_int)) (=> (= (tptp.pp B) (tptp.pp (tptp.aa_int_bool F X))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X) A3)) (tptp.pp (tptp.member_bool B (tptp.image_int_bool F A3)))))) (forall ((B tptp.nat) (F tptp.fun_int_nat) (X tptp.int) (A3 tptp.set_int)) (=> (= B (tptp.aa_int_nat F X)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X) A3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B) (tptp.image_int_nat F A3)))))) (forall ((B tptp.int) (F tptp.fun_int_int) (X tptp.int) (A3 tptp.set_int)) (=> (= B (tptp.aa_int_int F X)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X) A3)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int B) (tptp.image_int_int F A3)))))) (forall ((B tptp.set_nat) (F tptp.fun_bool_set_nat) (X tptp.bool) (A3 tptp.set_bool)) (=> (= B (tptp.aa_bool_set_nat F X)) (=> (tptp.pp (tptp.member_bool X A3)) (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat B) (tptp.image_bool_set_nat F A3)))))) (forall ((Y6 tptp.set_nat)) (= (tptp.image_nat_nat tptp.aTP_Lamm_fu Y6) Y6)) (forall ((Y6 tptp.set_int)) (= (tptp.image_int_int tptp.aTP_Lamm_fv Y6) Y6)) (forall ((F tptp.fun_bool_bool)) (= (tptp.image_bool_bool F tptp.bot_bot_set_bool) tptp.bot_bot_set_bool)) (forall ((F tptp.fun_bool_nat)) (= (tptp.image_bool_nat F tptp.bot_bot_set_bool) tptp.bot_bot_set_nat)) (forall ((F tptp.fun_bool_int)) (= (tptp.image_bool_int F tptp.bot_bot_set_bool) tptp.bot_bot_set_int)) (forall ((F tptp.fun_nat_bool)) (= (tptp.image_nat_bool F tptp.bot_bot_set_nat) tptp.bot_bot_set_bool)) (forall ((F tptp.fun_nat_nat)) (= (tptp.image_nat_nat F tptp.bot_bot_set_nat) tptp.bot_bot_set_nat)) (forall ((F tptp.fun_nat_int)) (= (tptp.image_nat_int F tptp.bot_bot_set_nat) tptp.bot_bot_set_int)) (forall ((F tptp.fun_int_bool)) (= (tptp.image_int_bool F tptp.bot_bot_set_int) tptp.bot_bot_set_bool)) (forall ((F tptp.fun_int_nat)) (= (tptp.image_int_nat F tptp.bot_bot_set_int) tptp.bot_bot_set_nat)) (forall ((F tptp.fun_int_int)) (= (tptp.image_int_int F tptp.bot_bot_set_int) tptp.bot_bot_set_int)) (forall ((F tptp.fun_nat_set_nat)) (= (tptp.image_nat_set_nat F tptp.bot_bot_set_nat) tptp.bot_bot_set_set_nat)) (forall ((F tptp.fun_bool_bool) (A3 tptp.set_bool)) (= (= tptp.bot_bot_set_bool (tptp.image_bool_bool F A3)) (= A3 tptp.bot_bot_set_bool))) (forall ((F tptp.fun_nat_bool) (A3 tptp.set_nat)) (= (= tptp.bot_bot_set_bool (tptp.image_nat_bool F A3)) (= A3 tptp.bot_bot_set_nat))) (forall ((F tptp.fun_int_bool) (A3 tptp.set_int)) (= (= tptp.bot_bot_set_bool (tptp.image_int_bool F A3)) (= A3 tptp.bot_bot_set_int))) (forall ((F tptp.fun_bool_nat) (A3 tptp.set_bool)) (= (= tptp.bot_bot_set_nat (tptp.image_bool_nat F A3)) (= A3 tptp.bot_bot_set_bool))) (forall ((F tptp.fun_nat_nat) (A3 tptp.set_nat)) (= (= tptp.bot_bot_set_nat (tptp.image_nat_nat F A3)) (= A3 tptp.bot_bot_set_nat))) (forall ((F tptp.fun_int_nat) (A3 tptp.set_int)) (= (= tptp.bot_bot_set_nat (tptp.image_int_nat F A3)) (= A3 tptp.bot_bot_set_int))) (forall ((F tptp.fun_bool_int) (A3 tptp.set_bool)) (= (= tptp.bot_bot_set_int (tptp.image_bool_int F A3)) (= A3 tptp.bot_bot_set_bool))) (forall ((F tptp.fun_nat_int) (A3 tptp.set_nat)) (= (= tptp.bot_bot_set_int (tptp.image_nat_int F A3)) (= A3 tptp.bot_bot_set_nat))) (forall ((F tptp.fun_int_int) (A3 tptp.set_int)) (= (= tptp.bot_bot_set_int (tptp.image_int_int F A3)) (= A3 tptp.bot_bot_set_int))) (forall ((F tptp.fun_nat_set_nat) (A3 tptp.set_nat)) (= (= tptp.bot_bot_set_set_nat (tptp.image_nat_set_nat F A3)) (= A3 tptp.bot_bot_set_nat))) (forall ((F tptp.fun_bool_bool) (A3 tptp.set_bool)) (= (= (tptp.image_bool_bool F A3) tptp.bot_bot_set_bool) (= A3 tptp.bot_bot_set_bool))) (forall ((F tptp.fun_nat_bool) (A3 tptp.set_nat)) (= (= (tptp.image_nat_bool F A3) tptp.bot_bot_set_bool) (= A3 tptp.bot_bot_set_nat))) (forall ((F tptp.fun_int_bool) (A3 tptp.set_int)) (= (= (tptp.image_int_bool F A3) tptp.bot_bot_set_bool) (= A3 tptp.bot_bot_set_int))) (forall ((F tptp.fun_bool_nat) (A3 tptp.set_bool)) (= (= (tptp.image_bool_nat F A3) tptp.bot_bot_set_nat) (= A3 tptp.bot_bot_set_bool))) (forall ((F tptp.fun_nat_nat) (A3 tptp.set_nat)) (= (= (tptp.image_nat_nat F A3) tptp.bot_bot_set_nat) (= A3 tptp.bot_bot_set_nat))) (forall ((F tptp.fun_int_nat) (A3 tptp.set_int)) (= (= (tptp.image_int_nat F A3) tptp.bot_bot_set_nat) (= A3 tptp.bot_bot_set_int))) (forall ((F tptp.fun_bool_int) (A3 tptp.set_bool)) (= (= (tptp.image_bool_int F A3) tptp.bot_bot_set_int) (= A3 tptp.bot_bot_set_bool))) (forall ((F tptp.fun_nat_int) (A3 tptp.set_nat)) (= (= (tptp.image_nat_int F A3) tptp.bot_bot_set_int) (= A3 tptp.bot_bot_set_nat))) (forall ((F tptp.fun_int_int) (A3 tptp.set_int)) (= (= (tptp.image_int_int F A3) tptp.bot_bot_set_int) (= A3 tptp.bot_bot_set_int))) (forall ((F tptp.fun_nat_set_nat) (A3 tptp.set_nat)) (= (= (tptp.image_nat_set_nat F A3) tptp.bot_bot_set_set_nat) (= A3 tptp.bot_bot_set_nat))) (forall ((S tptp.set_Code_integer)) (= (tptp.image_4470545334726330049nteger (tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger) S) S)) (forall ((S tptp.set_mu2057375006010111271at_nat)) (= (tptp.image_2516384619306764229at_nat (tptp.plus_p7104986032573967614at_nat tptp.zero_z1048942125864253310at_nat) S) S)) (forall ((S tptp.set_rat)) (= (tptp.image_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat tptp.zero_zero_rat) S) S)) (forall ((S tptp.set_nat)) (= (tptp.image_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.zero_zero_nat) S) S)) (forall ((S tptp.set_int)) (= (tptp.image_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.zero_zero_int) S) S)) (forall ((K tptp.rat) (I2 tptp.rat) (J tptp.rat)) (= (tptp.image_rat_rat (tptp.aa_rat_fun_rat_rat tptp.aTP_Lamm_hs K) (tptp.set_or633870826150836451st_rat I2 J)) (tptp.set_or633870826150836451st_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat I2) K) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat J) K)))) (forall ((K tptp.int) (I2 tptp.int) (J tptp.int)) (= (tptp.image_int_int (tptp.aa_int_fun_int_int tptp.aTP_Lamm_ht K) (tptp.set_or1266510415728281911st_int I2 J)) (tptp.set_or1266510415728281911st_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I2) K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) K)))) (forall ((K tptp.nat) (I2 tptp.nat) (J tptp.nat)) (= (tptp.image_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_hu K) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat I2) J)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) K)))) (forall ((K tptp.code_integer) (I2 tptp.code_integer) (J tptp.code_integer)) (= (tptp.image_4470545334726330049nteger (tptp.aTP_Lamm_hv K) (tptp.set_or189985376899183464nteger I2 J)) (tptp.set_or189985376899183464nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger I2) K) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger J) K)))) (forall ((D2 tptp.rat) (A tptp.rat) (B tptp.rat)) (= (tptp.image_rat_rat (tptp.aa_rat_fun_rat_rat tptp.aTP_Lamm_hw D2) (tptp.set_or633870826150836451st_rat A B)) (tptp.set_or633870826150836451st_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) D2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat B) D2)))) (forall ((D2 tptp.int) (A tptp.int) (B tptp.int)) (= (tptp.image_int_int (tptp.aa_int_fun_int_int tptp.aTP_Lamm_hx D2) (tptp.set_or1266510415728281911st_int A B)) (tptp.set_or1266510415728281911st_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) D2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) D2)))) (forall ((D2 tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (= (tptp.image_4470545334726330049nteger (tptp.aTP_Lamm_hy D2) (tptp.set_or189985376899183464nteger A B)) (tptp.set_or189985376899183464nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger A) D2) (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger B) D2)))) (forall ((P tptp.fun_int_bool) (F tptp.fun_int_int) (G tptp.fun_int_int) (S tptp.set_int)) (let ((_let_1 (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int S))) (= (tptp.image_int_int (tptp.aa_fun6280345759651049192nt_int (tptp.aa_fun3693603986580398266nt_int (tptp.aTP_Lamm_hz P) F) G) S) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int (tptp.image_int_int F (tptp.aa_set_int_set_int _let_1 (tptp.collect_int P)))) (tptp.image_int_int G (tptp.aa_set_int_set_int _let_1 (tptp.collect_int (tptp.aTP_Lamm_he P)))))))) (forall ((P tptp.fun_nat_bool) (F tptp.fun_nat_int) (G tptp.fun_nat_int) (S tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat S))) (= (tptp.image_nat_int (tptp.aa_fun5565043122120104496at_int (tptp.aa_fun5140708168904641446at_int (tptp.aTP_Lamm_ia P) F) G) S) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int (tptp.image_nat_int F (tptp.aa_set_nat_set_nat _let_1 (tptp.collect_nat P)))) (tptp.image_nat_int G (tptp.aa_set_nat_set_nat _let_1 (tptp.collect_nat (tptp.aTP_Lamm_hd P)))))))) (forall ((P tptp.fun_int_bool) (F tptp.fun_int_nat) (G tptp.fun_int_nat) (S tptp.set_int)) (let ((_let_1 (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int S))) (= (tptp.image_int_nat (tptp.aa_fun6506752150744536624nt_nat (tptp.aa_fun5407591398502139302nt_nat (tptp.aTP_Lamm_ib P) F) G) S) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.image_int_nat F (tptp.aa_set_int_set_int _let_1 (tptp.collect_int P)))) (tptp.image_int_nat G (tptp.aa_set_int_set_int _let_1 (tptp.collect_int (tptp.aTP_Lamm_he P)))))))) (forall ((P tptp.fun_nat_bool) (F tptp.fun_nat_nat) (G tptp.fun_nat_nat) (S tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat S))) (= (tptp.image_nat_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aa_fun6854695580826382482at_nat (tptp.aTP_Lamm_ic P) F) G) S) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.image_nat_nat F (tptp.aa_set_nat_set_nat _let_1 (tptp.collect_nat P)))) (tptp.image_nat_nat G (tptp.aa_set_nat_set_nat _let_1 (tptp.collect_nat (tptp.aTP_Lamm_hd P)))))))) (forall ((P tptp.fun_nat_bool) (F tptp.fun_nat_set_nat) (G tptp.fun_nat_set_nat) (S tptp.set_nat)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat S))) (= (tptp.image_nat_set_nat (tptp.aa_fun850356524293783268et_nat (tptp.aa_fun2558789851993377716et_nat (tptp.aTP_Lamm_id P) F) G) S) (tptp.sup_sup_set_set_nat (tptp.image_nat_set_nat F (tptp.aa_set_nat_set_nat _let_1 (tptp.collect_nat P))) (tptp.image_nat_set_nat G (tptp.aa_set_nat_set_nat _let_1 (tptp.collect_nat (tptp.aTP_Lamm_hd P)))))))) (forall ((P tptp.fun_list_nat_bool) (F tptp.fun_list_nat_nat) (G tptp.fun_list_nat_nat) (S tptp.set_list_nat)) (= (tptp.image_list_nat_nat (tptp.aa_fun8775324257704122008at_nat (tptp.aa_fun7930739032552464066at_nat (tptp.aTP_Lamm_ie P) F) G) S) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.image_list_nat_nat F (tptp.inf_inf_set_list_nat S (tptp.collect_list_nat P)))) (tptp.image_list_nat_nat G (tptp.inf_inf_set_list_nat S (tptp.collect_list_nat (tptp.aTP_Lamm_hb P))))))) (forall ((P tptp.fun_set_nat_bool) (F tptp.fun_set_nat_nat) (G tptp.fun_set_nat_nat) (S tptp.set_set_nat)) (= (tptp.image_set_nat_nat (tptp.aa_fun3386010016858254564at_nat (tptp.aa_fun8118849421014274228at_nat (tptp.aTP_Lamm_if P) F) G) S) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.image_set_nat_nat F (tptp.inf_inf_set_set_nat S (tptp.collect_set_nat P)))) (tptp.image_set_nat_nat G (tptp.inf_inf_set_set_nat S (tptp.collect_set_nat (tptp.aTP_Lamm_hc P))))))) (forall ((P tptp.fun_Pr803113274115125473t_bool) (F tptp.fun_Pr5160692531401422620nt_nat) (G tptp.fun_Pr5160692531401422620nt_nat) (S tptp.set_Pr958786334691620121nt_int)) (= (tptp.image_5044651549707136836nt_nat (tptp.aa_fun6016190284160528700nt_nat (tptp.aa_fun1083184158259774627nt_nat (tptp.aTP_Lamm_ig P) F) G) S) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.image_5044651549707136836nt_nat F (tptp.inf_in2269163501485487111nt_int S (tptp.collec213857154873943460nt_int P)))) (tptp.image_5044651549707136836nt_nat G (tptp.inf_in2269163501485487111nt_int S (tptp.collec213857154873943460nt_int (tptp.aTP_Lamm_ha P))))))) (forall ((P tptp.fun_Pr7757163693017731481t_bool) (F tptp.fun_Pr2602117396471556196at_nat) (G tptp.fun_Pr2602117396471556196at_nat) (S tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat S))) (= (tptp.image_2486076414777270412at_nat (tptp.aa_fun2351638177499875132at_nat (tptp.aa_fun1768432373507419115at_nat (tptp.aTP_Lamm_ih P) F) G) S) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.image_2486076414777270412at_nat F (tptp.aa_set8868280134176360700at_nat _let_1 (tptp.collec3392354462482085612at_nat P)))) (tptp.image_2486076414777270412at_nat G (tptp.aa_set8868280134176360700at_nat _let_1 (tptp.collec3392354462482085612at_nat (tptp.aa_fun830836278467416944t_bool tptp.aTP_Lamm_ii P)))))))) (forall ((P tptp.fun_int_bool) (F tptp.fun_in5957238474111007380at_nat) (G tptp.fun_in5957238474111007380at_nat) (S tptp.set_int)) (let ((_let_1 (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int S))) (= (tptp.image_6031046145702598900at_nat (tptp.aa_fun6444483342604292028at_nat (tptp.aa_fun5672742635520905243at_nat (tptp.aTP_Lamm_ij P) F) G) S) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat (tptp.image_6031046145702598900at_nat F (tptp.aa_set_int_set_int _let_1 (tptp.collect_int P)))) (tptp.image_6031046145702598900at_nat G (tptp.aa_set_int_set_int _let_1 (tptp.collect_int (tptp.aTP_Lamm_he P)))))))) (forall ((D2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat D2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) D2)) (= (tptp.image_rat_rat _let_1 (tptp.set_or633870826150836451st_rat A B)) (tptp.set_or633870826150836451st_rat (tptp.aa_rat_rat _let_1 A) (tptp.aa_rat_rat _let_1 B)))))) (forall ((D2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) D2)) (= (tptp.image_rat_rat (tptp.aa_rat_fun_rat_rat tptp.aTP_Lamm_ik D2) (tptp.set_or633870826150836451st_rat A B)) (tptp.set_or633870826150836451st_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A) D2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat B) D2))))) (forall ((X tptp.bool) (A3 tptp.set_bool) (B tptp.bool) (F tptp.fun_bool_bool)) (=> (tptp.pp (tptp.member_bool X A3)) (=> (= (tptp.pp B) (tptp.pp (tptp.aa_bool_bool F X))) (tptp.pp (tptp.member_bool B (tptp.image_bool_bool F A3)))))) (forall ((X tptp.bool) (A3 tptp.set_bool) (B tptp.nat) (F tptp.fun_bool_nat)) (=> (tptp.pp (tptp.member_bool X A3)) (=> (= B (tptp.aa_bool_nat F X)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B) (tptp.image_bool_nat F A3)))))) (forall ((X tptp.bool) (A3 tptp.set_bool) (B tptp.int) (F tptp.fun_bool_int)) (=> (tptp.pp (tptp.member_bool X A3)) (=> (= B (tptp.aa_bool_int F X)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int B) (tptp.image_bool_int F A3)))))) (forall ((X tptp.nat) (A3 tptp.set_nat) (B tptp.bool) (F tptp.fun_nat_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X) A3)) (=> (= (tptp.pp B) (tptp.pp (tptp.aa_nat_bool F X))) (tptp.pp (tptp.member_bool B (tptp.image_nat_bool F A3)))))) (forall ((X tptp.nat) (A3 tptp.set_nat) (B tptp.nat) (F tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X) A3)) (=> (= B (tptp.aa_nat_nat F X)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B) (tptp.image_nat_nat F A3)))))) (forall ((X tptp.nat) (A3 tptp.set_nat) (B tptp.int) (F tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X) A3)) (=> (= B (tptp.aa_nat_int F X)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int B) (tptp.image_nat_int F A3)))))) (forall ((X tptp.int) (A3 tptp.set_int) (B tptp.bool) (F tptp.fun_int_bool)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X) A3)) (=> (= (tptp.pp B) (tptp.pp (tptp.aa_int_bool F X))) (tptp.pp (tptp.member_bool B (tptp.image_int_bool F A3)))))) (forall ((X tptp.int) (A3 tptp.set_int) (B tptp.nat) (F tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X) A3)) (=> (= B (tptp.aa_int_nat F X)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B) (tptp.image_int_nat F A3)))))) (forall ((X tptp.int) (A3 tptp.set_int) (B tptp.int) (F tptp.fun_int_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X) A3)) (=> (= B (tptp.aa_int_int F X)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int B) (tptp.image_int_int F A3)))))) (forall ((X tptp.bool) (A3 tptp.set_bool) (B tptp.set_nat) (F tptp.fun_bool_set_nat)) (=> (tptp.pp (tptp.member_bool X A3)) (=> (= B (tptp.aa_bool_set_nat F X)) (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat B) (tptp.image_bool_set_nat F A3)))))) (forall ((F tptp.fun_nat_set_nat) (A3 tptp.set_nat) (P tptp.fun_set_nat_bool)) (=> (forall ((X3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat X3) (tptp.image_nat_set_nat F A3))) (tptp.pp (tptp.aa_set_nat_bool P X3)))) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X5) A3)) (tptp.pp (tptp.aa_set_nat_bool P (tptp.aa_nat_set_nat F X5))))))) (forall ((F tptp.fun_nat_nat) (A3 tptp.set_nat) (P tptp.fun_nat_bool)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.image_nat_nat F A3))) (tptp.pp (tptp.aa_nat_bool P X3)))) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X5) A3)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat F X5))))))) (forall ((F tptp.fun_nat_int) (A3 tptp.set_nat) (P tptp.fun_int_bool)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) (tptp.image_nat_int F A3))) (tptp.pp (tptp.aa_int_bool P X3)))) (forall ((X5 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X5) A3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_nat_int F X5))))))) (forall ((F tptp.fun_int_nat) (A3 tptp.set_int) (P tptp.fun_nat_bool)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.image_int_nat F A3))) (tptp.pp (tptp.aa_nat_bool P X3)))) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X5) A3)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_int_nat F X5))))))) (forall ((F tptp.fun_int_int) (A3 tptp.set_int) (P tptp.fun_int_bool)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) (tptp.image_int_int F A3))) (tptp.pp (tptp.aa_int_bool P X3)))) (forall ((X5 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X5) A3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int F X5))))))) (forall ((M6 tptp.set_nat) (N7 tptp.set_nat) (F tptp.fun_nat_set_nat) (G tptp.fun_nat_set_nat)) (=> (= M6 N7) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) N7)) (= (tptp.aa_nat_set_nat F X3) (tptp.aa_nat_set_nat G X3)))) (= (tptp.image_nat_set_nat F M6) (tptp.image_nat_set_nat G N7))))) (forall ((M6 tptp.set_nat) (N7 tptp.set_nat) (F tptp.fun_nat_nat) (G tptp.fun_nat_nat)) (=> (= M6 N7) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) N7)) (= (tptp.aa_nat_nat F X3) (tptp.aa_nat_nat G X3)))) (= (tptp.image_nat_nat F M6) (tptp.image_nat_nat G N7))))) (forall ((M6 tptp.set_nat) (N7 tptp.set_nat) (F tptp.fun_nat_int) (G tptp.fun_nat_int)) (=> (= M6 N7) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) N7)) (= (tptp.aa_nat_int F X3) (tptp.aa_nat_int G X3)))) (= (tptp.image_nat_int F M6) (tptp.image_nat_int G N7))))) (forall ((M6 tptp.set_int) (N7 tptp.set_int) (F tptp.fun_int_nat) (G tptp.fun_int_nat)) (=> (= M6 N7) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) N7)) (= (tptp.aa_int_nat F X3) (tptp.aa_int_nat G X3)))) (= (tptp.image_int_nat F M6) (tptp.image_int_nat G N7))))) (forall ((M6 tptp.set_int) (N7 tptp.set_int) (F tptp.fun_int_int) (G tptp.fun_int_int)) (=> (= M6 N7) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) N7)) (= (tptp.aa_int_int F X3) (tptp.aa_int_int G X3)))) (= (tptp.image_int_int F M6) (tptp.image_int_int G N7))))) (forall ((F tptp.fun_nat_set_nat) (A3 tptp.set_nat) (P tptp.fun_set_nat_bool)) (=> (exists ((X5 tptp.set_nat)) (and (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat X5) (tptp.image_nat_set_nat F A3))) (tptp.pp (tptp.aa_set_nat_bool P X5)))) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (tptp.pp (tptp.aa_set_nat_bool P (tptp.aa_nat_set_nat F X3))))))) (forall ((F tptp.fun_nat_nat) (A3 tptp.set_nat) (P tptp.fun_nat_bool)) (=> (exists ((X5 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X5) (tptp.image_nat_nat F A3))) (tptp.pp (tptp.aa_nat_bool P X5)))) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat F X3))))))) (forall ((F tptp.fun_nat_int) (A3 tptp.set_nat) (P tptp.fun_int_bool)) (=> (exists ((X5 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X5) (tptp.image_nat_int F A3))) (tptp.pp (tptp.aa_int_bool P X5)))) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_nat_int F X3))))))) (forall ((F tptp.fun_int_nat) (A3 tptp.set_int) (P tptp.fun_nat_bool)) (=> (exists ((X5 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X5) (tptp.image_int_nat F A3))) (tptp.pp (tptp.aa_nat_bool P X5)))) (exists ((X3 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_int_nat F X3))))))) (forall ((F tptp.fun_int_int) (A3 tptp.set_int) (P tptp.fun_int_bool)) (=> (exists ((X5 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X5) (tptp.image_int_int F A3))) (tptp.pp (tptp.aa_int_bool P X5)))) (exists ((X3 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int F X3))))))) (forall ((Z tptp.set_nat) (F tptp.fun_nat_set_nat) (A3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat Z) (tptp.image_nat_set_nat F A3))) (exists ((X4 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A3)) (= Z (tptp.aa_nat_set_nat F X4)))))) (forall ((Z tptp.nat) (F tptp.fun_nat_nat) (A3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Z) (tptp.image_nat_nat F A3))) (exists ((X4 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A3)) (= Z (tptp.aa_nat_nat F X4)))))) (forall ((Z tptp.nat) (F tptp.fun_int_nat) (A3 tptp.set_int)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Z) (tptp.image_int_nat F A3))) (exists ((X4 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A3)) (= Z (tptp.aa_int_nat F X4)))))) (forall ((Z tptp.int) (F tptp.fun_nat_int) (A3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Z) (tptp.image_nat_int F A3))) (exists ((X4 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A3)) (= Z (tptp.aa_nat_int F X4)))))) (forall ((Z tptp.int) (F tptp.fun_int_int) (A3 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Z) (tptp.image_int_int F A3))) (exists ((X4 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A3)) (= Z (tptp.aa_int_int F X4)))))) (forall ((X tptp.bool) (A3 tptp.set_bool) (F tptp.fun_bool_bool)) (=> (tptp.pp (tptp.member_bool X A3)) (tptp.pp (tptp.member_bool (tptp.aa_bool_bool F X) (tptp.image_bool_bool F A3))))) (forall ((X tptp.bool) (A3 tptp.set_bool) (F tptp.fun_bool_nat)) (=> (tptp.pp (tptp.member_bool X A3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat (tptp.aa_bool_nat F X)) (tptp.image_bool_nat F A3))))) (forall ((X tptp.bool) (A3 tptp.set_bool) (F tptp.fun_bool_int)) (=> (tptp.pp (tptp.member_bool X A3)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int (tptp.aa_bool_int F X)) (tptp.image_bool_int F A3))))) (forall ((X tptp.nat) (A3 tptp.set_nat) (F tptp.fun_nat_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X) A3)) (tptp.pp (tptp.member_bool (tptp.aa_nat_bool F X) (tptp.image_nat_bool F A3))))) (forall ((X tptp.nat) (A3 tptp.set_nat) (F tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X) A3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat (tptp.aa_nat_nat F X)) (tptp.image_nat_nat F A3))))) (forall ((X tptp.nat) (A3 tptp.set_nat) (F tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X) A3)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int (tptp.aa_nat_int F X)) (tptp.image_nat_int F A3))))) (forall ((X tptp.int) (A3 tptp.set_int) (F tptp.fun_int_bool)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X) A3)) (tptp.pp (tptp.member_bool (tptp.aa_int_bool F X) (tptp.image_int_bool F A3))))) (forall ((X tptp.int) (A3 tptp.set_int) (F tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X) A3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat (tptp.aa_int_nat F X)) (tptp.image_int_nat F A3))))) (forall ((X tptp.int) (A3 tptp.set_int) (F tptp.fun_int_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X) A3)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int (tptp.aa_int_int F X)) (tptp.image_int_int F A3))))) (forall ((X tptp.bool) (A3 tptp.set_bool) (F tptp.fun_bool_set_nat)) (=> (tptp.pp (tptp.member_bool X A3)) (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat (tptp.aa_bool_set_nat F X)) (tptp.image_bool_set_nat F A3))))) (forall ((B tptp.bool) (F tptp.fun_bool_bool) (A3 tptp.set_bool)) (=> (tptp.pp (tptp.member_bool B (tptp.image_bool_bool F A3))) (not (forall ((X3 tptp.bool)) (=> (= (tptp.pp B) (tptp.pp (tptp.aa_bool_bool F X3))) (not (tptp.pp (tptp.member_bool X3 A3)))))))) (forall ((B tptp.bool) (F tptp.fun_nat_bool) (A3 tptp.set_nat)) (=> (tptp.pp (tptp.member_bool B (tptp.image_nat_bool F A3))) (not (forall ((X3 tptp.nat)) (=> (= (tptp.pp B) (tptp.pp (tptp.aa_nat_bool F X3))) (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)))))))) (forall ((B tptp.bool) (F tptp.fun_int_bool) (A3 tptp.set_int)) (=> (tptp.pp (tptp.member_bool B (tptp.image_int_bool F A3))) (not (forall ((X3 tptp.int)) (=> (= (tptp.pp B) (tptp.pp (tptp.aa_int_bool F X3))) (not (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)))))))) (forall ((B tptp.nat) (F tptp.fun_bool_nat) (A3 tptp.set_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B) (tptp.image_bool_nat F A3))) (not (forall ((X3 tptp.bool)) (=> (= B (tptp.aa_bool_nat F X3)) (not (tptp.pp (tptp.member_bool X3 A3)))))))) (forall ((B tptp.nat) (F tptp.fun_nat_nat) (A3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B) (tptp.image_nat_nat F A3))) (not (forall ((X3 tptp.nat)) (=> (= B (tptp.aa_nat_nat F X3)) (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)))))))) (forall ((B tptp.nat) (F tptp.fun_int_nat) (A3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B) (tptp.image_int_nat F A3))) (not (forall ((X3 tptp.int)) (=> (= B (tptp.aa_int_nat F X3)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)))))))) (forall ((B tptp.int) (F tptp.fun_bool_int) (A3 tptp.set_bool)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int B) (tptp.image_bool_int F A3))) (not (forall ((X3 tptp.bool)) (=> (= B (tptp.aa_bool_int F X3)) (not (tptp.pp (tptp.member_bool X3 A3)))))))) (forall ((B tptp.int) (F tptp.fun_nat_int) (A3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int B) (tptp.image_nat_int F A3))) (not (forall ((X3 tptp.nat)) (=> (= B (tptp.aa_nat_int F X3)) (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)))))))) (forall ((B tptp.int) (F tptp.fun_int_int) (A3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int B) (tptp.image_int_int F A3))) (not (forall ((X3 tptp.int)) (=> (= B (tptp.aa_int_int F X3)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)))))))) (forall ((B tptp.bool) (F tptp.fun_set_nat_bool) (A3 tptp.set_set_nat)) (=> (tptp.pp (tptp.member_bool B (tptp.image_set_nat_bool F A3))) (not (forall ((X3 tptp.set_nat)) (=> (= (tptp.pp B) (tptp.pp (tptp.aa_set_nat_bool F X3))) (not (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat X3) A3)))))))) (forall ((F tptp.fun_nat_nat) (G tptp.fun_nat_nat) (A3 tptp.set_nat)) (= (tptp.image_nat_nat F (tptp.image_nat_nat G A3)) (tptp.image_nat_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_il F) G) A3))) (forall ((F tptp.fun_nat_nat) (G tptp.fun_int_nat) (A3 tptp.set_int)) (= (tptp.image_nat_nat F (tptp.image_int_nat G A3)) (tptp.image_int_nat (tptp.aa_fun6506752150744536624nt_nat (tptp.aTP_Lamm_im F) G) A3))) (forall ((F tptp.fun_nat_int) (G tptp.fun_nat_nat) (A3 tptp.set_nat)) (= (tptp.image_nat_int F (tptp.image_nat_nat G A3)) (tptp.image_nat_int (tptp.aa_fun1613598493704395220at_int (tptp.aTP_Lamm_in F) G) A3))) (forall ((F tptp.fun_nat_int) (G tptp.fun_int_nat) (A3 tptp.set_int)) (= (tptp.image_nat_int F (tptp.image_int_nat G A3)) (tptp.image_int_int (tptp.aa_fun2328901131235339916nt_int (tptp.aTP_Lamm_io F) G) A3))) (forall ((F tptp.fun_int_nat) (G tptp.fun_nat_int) (A3 tptp.set_nat)) (= (tptp.image_int_nat F (tptp.image_nat_int G A3)) (tptp.image_nat_nat (tptp.aa_fun519522104774525396at_nat (tptp.aTP_Lamm_ip F) G) A3))) (forall ((F tptp.fun_int_nat) (G tptp.fun_int_int) (A3 tptp.set_int)) (= (tptp.image_int_nat F (tptp.image_int_int G A3)) (tptp.image_int_nat (tptp.aa_fun1234824742305470092nt_nat (tptp.aTP_Lamm_iq F) G) A3))) (forall ((F tptp.fun_int_int) (G tptp.fun_nat_int) (A3 tptp.set_nat)) (= (tptp.image_int_int F (tptp.image_nat_int G A3)) (tptp.image_nat_int (tptp.aa_fun5565043122120104496at_int (tptp.aTP_Lamm_ir F) G) A3))) (forall ((F tptp.fun_int_int) (G tptp.fun_int_int) (A3 tptp.set_int)) (= (tptp.image_int_int F (tptp.image_int_int G A3)) (tptp.image_int_int (tptp.aa_fun6280345759651049192nt_int (tptp.aTP_Lamm_is F) G) A3))) (forall ((F tptp.fun_set_nat_nat) (G tptp.fun_nat_set_nat) (A3 tptp.set_nat)) (= (tptp.image_set_nat_nat F (tptp.image_nat_set_nat G A3)) (tptp.image_nat_nat (tptp.aa_fun4820382421437094446at_nat (tptp.aTP_Lamm_it F) G) A3))) (forall ((F tptp.fun_set_nat_int) (G tptp.fun_nat_set_nat) (A3 tptp.set_nat)) (= (tptp.image_set_nat_int F (tptp.image_nat_set_nat G A3)) (tptp.image_nat_int (tptp.aa_fun642531401927897738at_int (tptp.aTP_Lamm_iu F) G) A3))) (forall ((F tptp.fun_bool_bool) (A3 tptp.set_bool) (P tptp.fun_bool_bool)) (= (tptp.collect_bool (tptp.aa_fun8098540714523660868l_bool (tptp.aa_set6656371295676988350l_bool (tptp.aTP_Lamm_iv F) A3) P)) (tptp.image_bool_bool F (tptp.collect_bool (tptp.aa_fun8098540714523660868l_bool (tptp.aa_set6656371295676988350l_bool (tptp.aTP_Lamm_iw F) A3) P))))) (forall ((F tptp.fun_nat_bool) (A3 tptp.set_nat) (P tptp.fun_bool_bool)) (= (tptp.collect_bool (tptp.aa_fun8098540714523660868l_bool (tptp.aa_set2341586533381200199l_bool (tptp.aTP_Lamm_ix F) A3) P)) (tptp.image_nat_bool F (tptp.collect_nat (tptp.aa_fun5996870036960543647t_bool (tptp.aa_set2681322491556877426t_bool (tptp.aTP_Lamm_iy F) A3) P))))) (forall ((F tptp.fun_int_bool) (A3 tptp.set_int) (P tptp.fun_bool_bool)) (= (tptp.collect_bool (tptp.aa_fun8098540714523660868l_bool (tptp.aa_set8137165717292330403l_bool (tptp.aTP_Lamm_iz F) A3) P)) (tptp.image_int_bool F (tptp.collect_int (tptp.aa_fun2872579070491919427t_bool (tptp.aa_set820588111078594490t_bool (tptp.aTP_Lamm_ja F) A3) P))))) (forall ((F tptp.fun_bool_nat) (A3 tptp.set_bool) (P tptp.fun_nat_bool)) (= (tptp.collect_nat (tptp.aa_fun3878383735219268284t_bool (tptp.aa_set5798912244828377086t_bool (tptp.aTP_Lamm_jb F) A3) P)) (tptp.image_bool_nat F (tptp.collect_bool (tptp.aa_fun6062112079508222567l_bool (tptp.aa_set3283638209543405755l_bool (tptp.aTP_Lamm_jc F) A3) P))))) (forall ((F tptp.fun_nat_nat) (A3 tptp.set_nat) (P tptp.fun_nat_bool)) (= (tptp.collect_nat (tptp.aa_fun3878383735219268284t_bool (tptp.aa_set2548965808111510023t_bool (tptp.aTP_Lamm_jd F) A3) P)) (tptp.image_nat_nat F (tptp.collect_nat (tptp.aa_fun3878383735219268284t_bool (tptp.aa_set2548965808111510023t_bool (tptp.aTP_Lamm_je F) A3) P))))) (forall ((F tptp.fun_int_nat) (A3 tptp.set_int) (P tptp.fun_nat_bool)) (= (tptp.collect_nat (tptp.aa_fun3878383735219268284t_bool (tptp.aa_set527285886755939t_bool (tptp.aTP_Lamm_jf F) A3) P)) (tptp.image_int_nat F (tptp.collect_int (tptp.aa_fun754092768750644064t_bool (tptp.aa_set8763616371094885127t_bool (tptp.aTP_Lamm_jg F) A3) P))))) (forall ((F tptp.fun_bool_int) (A3 tptp.set_bool) (P tptp.fun_int_bool)) (= (tptp.collect_int (tptp.aa_fun5146555767781538748t_bool (tptp.aa_set507720255357849342t_bool (tptp.aTP_Lamm_jh F) A3) P)) (tptp.image_bool_int F (tptp.collect_bool (tptp.aa_fun9099954163972356363l_bool (tptp.aa_set6321480294007539551l_bool (tptp.aTP_Lamm_ji F) A3) P))))) (forall ((F tptp.fun_nat_int) (A3 tptp.set_nat) (P tptp.fun_int_bool)) (= (tptp.collect_int (tptp.aa_fun5146555767781538748t_bool (tptp.aa_set6481145855495758087t_bool (tptp.aTP_Lamm_jj F) A3) P)) (tptp.image_nat_int F (tptp.collect_nat (tptp.aa_fun8270846734250162968t_bool (tptp.aa_set6941428807142404707t_bool (tptp.aTP_Lamm_jk F) A3) P))))) (forall ((F tptp.fun_int_int) (A3 tptp.set_int) (P tptp.fun_int_bool)) (= (tptp.collect_int (tptp.aa_fun5146555767781538748t_bool (tptp.aa_set3932707333271004003t_bool (tptp.aTP_Lamm_jl F) A3) P)) (tptp.image_int_int F (tptp.collect_int (tptp.aa_fun5146555767781538748t_bool (tptp.aa_set3932707333271004003t_bool (tptp.aTP_Lamm_jm F) A3) P))))) (forall ((F tptp.fun_list_nat_bool) (A3 tptp.set_list_nat) (P tptp.fun_bool_bool)) (= (tptp.collect_bool (tptp.aa_fun8098540714523660868l_bool (tptp.aa_set6964050860520458327l_bool (tptp.aTP_Lamm_jn F) A3) P)) (tptp.image_list_nat_bool F (tptp.collect_list_nat (tptp.aa_fun7225089676084268943t_bool (tptp.aa_set4768573287508199762t_bool (tptp.aTP_Lamm_jo F) A3) P))))) (forall ((X tptp.product_prod_nat_nat)) (not (forall ((K2 tptp.nat) (M5 tptp.nat)) (not (= X (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat K2) M5)))))) (forall ((B3 tptp.set_set_nat) (F tptp.fun_nat_set_nat) (A3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat B3) (tptp.image_nat_set_nat F A3))) (exists ((AA tptp.set_nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat AA) A3)) (= B3 (tptp.image_nat_set_nat F AA)))))) (forall ((B3 tptp.set_nat) (F tptp.fun_nat_nat) (A3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B3) (tptp.image_nat_nat F A3))) (exists ((AA tptp.set_nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat AA) A3)) (= B3 (tptp.image_nat_nat F AA)))))) (forall ((B3 tptp.set_nat) (F tptp.fun_int_nat) (A3 tptp.set_int)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B3) (tptp.image_int_nat F A3))) (exists ((AA tptp.set_int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int AA) A3)) (= B3 (tptp.image_int_nat F AA)))))) (forall ((B3 tptp.set_int) (F tptp.fun_nat_int) (A3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) (tptp.image_nat_int F A3))) (exists ((AA tptp.set_nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat AA) A3)) (= B3 (tptp.image_nat_int F AA)))))) (forall ((B3 tptp.set_int) (F tptp.fun_int_int) (A3 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) (tptp.image_int_int F A3))) (exists ((AA tptp.set_int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int AA) A3)) (= B3 (tptp.image_int_int F AA)))))) (forall ((F tptp.fun_nat_set_nat) (A3 tptp.set_nat) (B3 tptp.set_set_nat)) (= (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat (tptp.image_nat_set_nat F A3)) B3)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A3)) (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat (tptp.aa_nat_set_nat F X4)) B3)))))) (forall ((F tptp.fun_nat_nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.image_nat_nat F A3)) B3)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat (tptp.aa_nat_nat F X4)) B3)))))) (forall ((F tptp.fun_int_nat) (A3 tptp.set_int) (B3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.image_int_nat F A3)) B3)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat (tptp.aa_int_nat F X4)) B3)))))) (forall ((F tptp.fun_nat_int) (A3 tptp.set_nat) (B3 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.image_nat_int F A3)) B3)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A3)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int (tptp.aa_nat_int F X4)) B3)))))) (forall ((F tptp.fun_int_int) (A3 tptp.set_int) (B3 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.image_int_int F A3)) B3)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A3)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int (tptp.aa_int_int F X4)) B3)))))) (forall ((B3 tptp.set_set_nat) (F tptp.fun_nat_set_nat) (A3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat B3) (tptp.image_nat_set_nat F A3))) (not (forall ((C5 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat C5) A3)) (not (= B3 (tptp.image_nat_set_nat F C5)))))))) (forall ((B3 tptp.set_nat) (F tptp.fun_nat_nat) (A3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B3) (tptp.image_nat_nat F A3))) (not (forall ((C5 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat C5) A3)) (not (= B3 (tptp.image_nat_nat F C5)))))))) (forall ((B3 tptp.set_nat) (F tptp.fun_int_nat) (A3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B3) (tptp.image_int_nat F A3))) (not (forall ((C5 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int C5) A3)) (not (= B3 (tptp.image_int_nat F C5)))))))) (forall ((B3 tptp.set_int) (F tptp.fun_nat_int) (A3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) (tptp.image_nat_int F A3))) (not (forall ((C5 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat C5) A3)) (not (= B3 (tptp.image_nat_int F C5)))))))) (forall ((B3 tptp.set_int) (F tptp.fun_int_int) (A3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) (tptp.image_int_int F A3))) (not (forall ((C5 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int C5) A3)) (not (= B3 (tptp.image_int_int F C5)))))))) (forall ((A3 tptp.set_bool) (F tptp.fun_bool_bool) (B3 tptp.set_bool)) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 A3)) (tptp.pp (tptp.member_bool (tptp.aa_bool_bool F X3) B3)))) (tptp.ord_less_eq_set_bool (tptp.image_bool_bool F A3) B3))) (forall ((A3 tptp.set_bool) (F tptp.fun_bool_nat) (B3 tptp.set_nat)) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 A3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat (tptp.aa_bool_nat F X3)) B3)))) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.image_bool_nat F A3)) B3)))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_bool) (B3 tptp.set_bool)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (tptp.pp (tptp.member_bool (tptp.aa_nat_bool F X3) B3)))) (tptp.ord_less_eq_set_bool (tptp.image_nat_bool F A3) B3))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_nat) (B3 tptp.set_nat)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat (tptp.aa_nat_nat F X3)) B3)))) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.image_nat_nat F A3)) B3)))) (forall ((A3 tptp.set_int) (F tptp.fun_int_bool) (B3 tptp.set_bool)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (tptp.pp (tptp.member_bool (tptp.aa_int_bool F X3) B3)))) (tptp.ord_less_eq_set_bool (tptp.image_int_bool F A3) B3))) (forall ((A3 tptp.set_int) (F tptp.fun_int_nat) (B3 tptp.set_nat)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat (tptp.aa_int_nat F X3)) B3)))) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.image_int_nat F A3)) B3)))) (forall ((A3 tptp.set_bool) (F tptp.fun_bool_int) (B3 tptp.set_int)) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 A3)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int (tptp.aa_bool_int F X3)) B3)))) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.image_bool_int F A3)) B3)))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_int) (B3 tptp.set_int)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int (tptp.aa_nat_int F X3)) B3)))) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.image_nat_int F A3)) B3)))) (forall ((A3 tptp.set_int) (F tptp.fun_int_int) (B3 tptp.set_int)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int (tptp.aa_int_int F X3)) B3)))) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.image_int_int F A3)) B3)))) (forall ((A3 tptp.set_bool) (F tptp.fun_bool_set_nat) (B3 tptp.set_set_nat)) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 A3)) (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat (tptp.aa_bool_set_nat F X3)) B3)))) (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat (tptp.image_bool_set_nat F A3)) B3)))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (F tptp.fun_nat_set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) B3)) (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat (tptp.image_nat_set_nat F A3)) (tptp.image_nat_set_nat F B3))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (F tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) B3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.image_nat_nat F A3)) (tptp.image_nat_nat F B3))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (F tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) B3)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.image_nat_int F A3)) (tptp.image_nat_int F B3))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (F tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.image_int_nat F A3)) (tptp.image_int_nat F B3))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (F tptp.fun_int_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.image_int_int F A3)) (tptp.image_int_int F B3))))) (forall ((F tptp.fun_int_int) (A3 tptp.set_int) (B3 tptp.set_int)) (= (tptp.image_int_int F (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3)) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int (tptp.image_int_int F A3)) (tptp.image_int_int F B3)))) (forall ((F tptp.fun_int_nat) (A3 tptp.set_int) (B3 tptp.set_int)) (= (tptp.image_int_nat F (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.image_int_nat F A3)) (tptp.image_int_nat F B3)))) (forall ((F tptp.fun_nat_int) (A3 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.image_nat_int F (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int (tptp.image_nat_int F A3)) (tptp.image_nat_int F B3)))) (forall ((F tptp.fun_nat_nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.image_nat_nat F (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.image_nat_nat F A3)) (tptp.image_nat_nat F B3)))) (forall ((F tptp.fun_nat_set_nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.image_nat_set_nat F (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)) (tptp.sup_sup_set_set_nat (tptp.image_nat_set_nat F A3) (tptp.image_nat_set_nat F B3)))) (forall ((F tptp.fun_Pr2871540613828922186at_nat) (A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (= (tptp.image_6160980552072806642at_nat F (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3) B3)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.image_6160980552072806642at_nat F A3)) (tptp.image_6160980552072806642at_nat F B3)))) (forall ((F tptp.fun_na3202795955365919216at_nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.image_3276603626957510736at_nat F (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)) (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat (tptp.image_3276603626957510736at_nat F A3)) (tptp.image_3276603626957510736at_nat F B3)))) (forall ((F tptp.fun_Pr7574179848310716106at_nat) (A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (= (tptp.image_6009382790362589554at_nat F (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3) B3)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.image_6009382790362589554at_nat F A3)) (tptp.image_6009382790362589554at_nat F B3)))) (forall ((F tptp.fun_Pr1253225528153422666at_nat) (A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (= (tptp.image_3198525501578754290at_nat F (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3) B3)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.image_3198525501578754290at_nat F A3)) (tptp.image_3198525501578754290at_nat F B3)))) (forall ((F tptp.fun_na8407688532849143408at_nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.image_5319605298250079696at_nat F (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)) (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat (tptp.image_5319605298250079696at_nat F A3)) (tptp.image_5319605298250079696at_nat F B3)))) (forall ((P tptp.fun_nat_bool) (F tptp.fun_nat_bool) (B3 tptp.set_bool)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P X3)) (tptp.pp (tptp.member_bool (tptp.aa_nat_bool F X3) B3)))) (tptp.ord_less_eq_set_bool (tptp.image_nat_bool F (tptp.collect_nat P)) B3))) (forall ((P tptp.fun_nat_bool) (F tptp.fun_nat_nat) (B3 tptp.set_nat)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P X3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat (tptp.aa_nat_nat F X3)) B3)))) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.image_nat_nat F (tptp.collect_nat P))) B3)))) (forall ((P tptp.fun_int_bool) (F tptp.fun_int_bool) (B3 tptp.set_bool)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.member_bool (tptp.aa_int_bool F X3) B3)))) (tptp.ord_less_eq_set_bool (tptp.image_int_bool F (tptp.collect_int P)) B3))) (forall ((P tptp.fun_int_bool) (F tptp.fun_int_nat) (B3 tptp.set_nat)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat (tptp.aa_int_nat F X3)) B3)))) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.image_int_nat F (tptp.collect_int P))) B3)))) (forall ((P tptp.fun_nat_bool) (F tptp.fun_nat_int) (B3 tptp.set_int)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P X3)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int (tptp.aa_nat_int F X3)) B3)))) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.image_nat_int F (tptp.collect_nat P))) B3)))) (forall ((P tptp.fun_int_bool) (F tptp.fun_int_int) (B3 tptp.set_int)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int (tptp.aa_int_int F X3)) B3)))) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.image_int_int F (tptp.collect_int P))) B3)))) (forall ((P tptp.fun_list_nat_bool) (F tptp.fun_list_nat_bool) (B3 tptp.set_bool)) (=> (forall ((X3 tptp.list_nat)) (=> (tptp.pp (tptp.aa_list_nat_bool P X3)) (tptp.pp (tptp.member_bool (tptp.aa_list_nat_bool F X3) B3)))) (tptp.ord_less_eq_set_bool (tptp.image_list_nat_bool F (tptp.collect_list_nat P)) B3))) (forall ((P tptp.fun_list_nat_bool) (F tptp.fun_list_nat_nat) (B3 tptp.set_nat)) (=> (forall ((X3 tptp.list_nat)) (=> (tptp.pp (tptp.aa_list_nat_bool P X3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat (tptp.aa_list_nat_nat F X3)) B3)))) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.image_list_nat_nat F (tptp.collect_list_nat P))) B3)))) (forall ((P tptp.fun_set_nat_bool) (F tptp.fun_set_nat_bool) (B3 tptp.set_bool)) (=> (forall ((X3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool P X3)) (tptp.pp (tptp.member_bool (tptp.aa_set_nat_bool F X3) B3)))) (tptp.ord_less_eq_set_bool (tptp.image_set_nat_bool F (tptp.collect_set_nat P)) B3))) (forall ((P tptp.fun_set_nat_bool) (F tptp.fun_set_nat_nat) (B3 tptp.set_nat)) (=> (forall ((X3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool P X3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat (tptp.aa_set_nat_nat F X3)) B3)))) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.image_set_nat_nat F (tptp.collect_set_nat P))) B3)))) (forall ((N2 tptp.nat) (P tptp.fun_int_fun_nat_bool)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) N2)) (exists ((Li tptp.int)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool P Li) I3))))) (not (forall ((L4 tptp.list_int)) (=> (= (tptp.size_size_list_int L4) N2) (not (forall ((I tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool P (tptp.aa_nat_int (tptp.nth_int L4) I)) I)))))))))) (forall ((N2 tptp.nat) (P tptp.fun_nat_fun_nat_bool)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) N2)) (exists ((Li tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P Li) I3))))) (not (forall ((L4 tptp.list_nat)) (=> (= (tptp.aa_list_nat_nat tptp.size_size_list_nat L4) N2) (not (forall ((I tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P (tptp.aa_nat_nat (tptp.nth_nat L4) I)) I)))))))))) (forall ((N2 tptp.nat) (P tptp.fun_bo3288154511880838028t_bool)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) N2)) (exists ((Li tptp.bool)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_bool_fun_nat_bool P Li) I3))))) (not (forall ((L4 tptp.list_bool)) (=> (= (tptp.size_size_list_bool L4) N2) (not (forall ((I tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_bool_fun_nat_bool P (tptp.aa_nat_bool (tptp.nth_bool L4) I)) I)))))))))) (forall ((Xs tptp.list_int) (Ys2 tptp.list_int)) (= (= Xs Ys2) (and (= (tptp.size_size_list_int Xs) (tptp.size_size_list_int Ys2)) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.size_size_list_int Xs))) (= (tptp.aa_nat_int (tptp.nth_int Xs) I4) (tptp.aa_nat_int (tptp.nth_int Ys2) I4))))))) (forall ((Xs tptp.list_nat) (Ys2 tptp.list_nat)) (= (= Xs Ys2) (and (= (tptp.aa_list_nat_nat tptp.size_size_list_nat Xs) (tptp.aa_list_nat_nat tptp.size_size_list_nat Ys2)) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.aa_list_nat_nat tptp.size_size_list_nat Xs))) (= (tptp.aa_nat_nat (tptp.nth_nat Xs) I4) (tptp.aa_nat_nat (tptp.nth_nat Ys2) I4))))))) (forall ((Xs tptp.list_bool) (Ys2 tptp.list_bool)) (= (= Xs Ys2) (and (= (tptp.size_size_list_bool Xs) (tptp.size_size_list_bool Ys2)) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) (tptp.size_size_list_bool Xs))) (= (tptp.pp (tptp.aa_nat_bool (tptp.nth_bool Xs) I4)) (tptp.pp (tptp.aa_nat_bool (tptp.nth_bool Ys2) I4)))))))) (forall ((K tptp.nat) (P tptp.fun_nat_fun_int_bool)) (= (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) K)) (exists ((X_12 tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_nat_fun_int_bool P I4) X_12))))) (exists ((Xs3 tptp.list_int)) (and (= (tptp.size_size_list_int Xs3) K) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_nat_fun_int_bool P I4) (tptp.aa_nat_int (tptp.nth_int Xs3) I4))))))))) (forall ((K tptp.nat) (P tptp.fun_nat_fun_nat_bool)) (= (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) K)) (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P I4) X_12))))) (exists ((Xs3 tptp.list_nat)) (and (= (tptp.aa_list_nat_nat tptp.size_size_list_nat Xs3) K) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P I4) (tptp.aa_nat_nat (tptp.nth_nat Xs3) I4))))))))) (forall ((K tptp.nat) (P tptp.fun_na9137082442855928016l_bool)) (= (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) K)) (exists ((X_12 tptp.bool)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_nat_fun_bool_bool P I4) X_12))))) (exists ((Xs3 tptp.list_bool)) (and (= (tptp.size_size_list_bool Xs3) K) (forall ((I4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) K)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_nat_fun_bool_bool P I4) (tptp.aa_nat_bool (tptp.nth_bool Xs3) I4))))))))) (forall ((Xs tptp.list_int) (Ys2 tptp.list_int)) (=> (= (tptp.size_size_list_int Xs) (tptp.size_size_list_int Ys2)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.size_size_list_int Xs))) (= (tptp.aa_nat_int (tptp.nth_int Xs) I3) (tptp.aa_nat_int (tptp.nth_int Ys2) I3)))) (= Xs Ys2)))) (forall ((Xs tptp.list_nat) (Ys2 tptp.list_nat)) (=> (= (tptp.aa_list_nat_nat tptp.size_size_list_nat Xs) (tptp.aa_list_nat_nat tptp.size_size_list_nat Ys2)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.aa_list_nat_nat tptp.size_size_list_nat Xs))) (= (tptp.aa_nat_nat (tptp.nth_nat Xs) I3) (tptp.aa_nat_nat (tptp.nth_nat Ys2) I3)))) (= Xs Ys2)))) (forall ((Xs tptp.list_bool) (Ys2 tptp.list_bool)) (=> (= (tptp.size_size_list_bool Xs) (tptp.size_size_list_bool Ys2)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.size_size_list_bool Xs))) (= (tptp.pp (tptp.aa_nat_bool (tptp.nth_bool Xs) I3)) (tptp.pp (tptp.aa_nat_bool (tptp.nth_bool Ys2) I3))))) (= Xs Ys2)))) (forall ((F tptp.fun_int_nat) (A3 tptp.set_int) (B3 tptp.set_int)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.image_int_nat F (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.image_int_nat F A3)) (tptp.image_int_nat F B3))))) (forall ((F tptp.fun_nat_set_nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat (tptp.image_nat_set_nat F (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3))) (tptp.inf_inf_set_set_nat (tptp.image_nat_set_nat F A3) (tptp.image_nat_set_nat F B3))))) (forall ((F tptp.fun_nat_nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.image_nat_nat F (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3))) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.image_nat_nat F A3)) (tptp.image_nat_nat F B3))))) (forall ((F tptp.fun_na1476630412504255114at_nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat (tptp.image_5846123807819985514at_nat F (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3))) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.image_5846123807819985514at_nat F A3)) (tptp.image_5846123807819985514at_nat F B3))))) (forall ((F tptp.fun_Pr2602117396471556196at_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.image_2486076414777270412at_nat F (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3))) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.image_2486076414777270412at_nat F A3)) (tptp.image_2486076414777270412at_nat F B3))))) (forall ((F tptp.fun_Pr2118491707810114563at_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat (tptp.image_5168914502847457605at_nat F (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3))) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat (tptp.image_5168914502847457605at_nat F A3)) (tptp.image_5168914502847457605at_nat F B3))))) (forall ((F tptp.fun_int_int) (A3 tptp.set_int) (B3 tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.image_int_int F (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int (tptp.image_int_int F A3)) (tptp.image_int_int F B3))))) (forall ((F tptp.fun_nat_int) (A3 tptp.set_nat) (B3 tptp.set_nat)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.image_nat_int F (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3))) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int (tptp.image_nat_int F A3)) (tptp.image_nat_int F B3))))) (forall ((F tptp.fun_Pr7647638413817135296at_int) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.image_2483585944268220136at_int F (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3))) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int (tptp.image_2483585944268220136at_int F A3)) (tptp.image_2483585944268220136at_int F B3))))) (forall ((F tptp.fun_nat_set_nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat (tptp.minus_2163939370556025621et_nat (tptp.image_nat_set_nat F A3) (tptp.image_nat_set_nat F B3))) (tptp.image_nat_set_nat F (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3))))) (forall ((F tptp.fun_int_nat) (A3 tptp.set_int) (B3 tptp.set_int)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat (tptp.image_int_nat F A3)) (tptp.image_int_nat F B3))) (tptp.image_int_nat F (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3))))) (forall ((F tptp.fun_nat_nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat (tptp.image_nat_nat F A3)) (tptp.image_nat_nat F B3))) (tptp.image_nat_nat F (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3))))) (forall ((F tptp.fun_int_int) (A3 tptp.set_int) (B3 tptp.set_int)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int (tptp.image_int_int F A3)) (tptp.image_int_int F B3))) (tptp.image_int_int F (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3))))) (forall ((F tptp.fun_nat_int) (A3 tptp.set_nat) (B3 tptp.set_nat)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int (tptp.image_nat_int F A3)) (tptp.image_nat_int F B3))) (tptp.image_nat_int F (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3))))) (forall ((N2 tptp.nat) (P tptp.fun_nat_bool)) (= (exists ((M3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M3) N2)) (tptp.pp (tptp.aa_nat_bool P M3)))) (exists ((X4 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (tptp.pp (tptp.aa_nat_bool P X4)))))) (forall ((N2 tptp.nat) (P tptp.fun_nat_bool)) (= (forall ((M3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M3) N2)) (tptp.pp (tptp.aa_nat_bool P M3)))) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (tptp.pp (tptp.aa_nat_bool P X4)))))) (forall ((A3 tptp.set_Pr7098220151150636591it_nat)) (not (tptp.member1310632352865511136it_nat tptp.none_P2651198173097904984it_nat (tptp.image_2003495143432273353it_nat tptp.some_P7913643980934408916it_nat A3)))) (forall ((A3 tptp.set_num)) (not (tptp.member_option_num tptp.none_num (tptp.image_num_option_num tptp.some_num A3)))) (forall ((A3 tptp.set_Pr1354866905816374718it_nat)) (not (tptp.member5596548051065438575it_nat tptp.none_P9117596204409417319it_nat (tptp.image_3455408117458022631it_nat tptp.some_P1914260805536162275it_nat A3)))) (forall ((N2 tptp.nat) (Xs tptp.list_int)) (let ((_let_1 (tptp.size_size_list_int Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) _let_1)) (= (tptp.aa_nat_int (tptp.nth_int (tptp.rotate1_int Xs)) N2) (tptp.aa_nat_int (tptp.nth_int Xs) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc N2)) _let_1)))))) (forall ((N2 tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (tptp.aa_list_nat_nat tptp.size_size_list_nat Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) _let_1)) (= (tptp.aa_nat_nat (tptp.nth_nat (tptp.rotate1_nat Xs)) N2) (tptp.aa_nat_nat (tptp.nth_nat Xs) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc N2)) _let_1)))))) (forall ((N2 tptp.nat) (Xs tptp.list_bool)) (let ((_let_1 (tptp.size_size_list_bool Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) _let_1)) (= (tptp.pp (tptp.aa_nat_bool (tptp.nth_bool (tptp.rotate1_bool Xs)) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.nth_bool Xs) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc N2)) _let_1))))))) (forall ((C tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (let ((_let_2 (tptp.image_rat_rat _let_1 (tptp.set_or633870826150836451st_rat X Y)))) (let ((_let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)))) (let ((_let_4 (tptp.aa_rat_rat _let_1 X))) (let ((_let_5 (tptp.aa_rat_rat _let_1 Y))) (let ((_let_6 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (and (=> _let_6 (= _let_2 (tptp.set_or633870826150836451st_rat _let_4 _let_5))) (=> (not _let_6) (and (=> _let_3 (= _let_2 (tptp.set_or633870826150836451st_rat _let_5 _let_4))) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_rat)))))))))))) (forall ((M tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.nat_prod_decode_aux K) M))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) K)))) (and (=> _let_3 (= _let_2 (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat K) M)))) (=> (not _let_3) (= _let_2 (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.nat_prod_decode_aux _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) _let_1))))))))) (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.accp_P4275260045618599050at_nat tptp.nat_pr5047031295181774490ux_rel) (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat X) Xa2))))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc X))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Xa2) X)))) (=> (= (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.nat_prod_decode_aux X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_3 (= Y (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat Xa2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat X) Xa2)))) (=> (not _let_3) (= Y (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.nat_prod_decode_aux _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Xa2) _let_2))))) (not _let_1))))))))) (forall ((N2 tptp.nat) (Xs tptp.list_int) (Ys2 tptp.list_int)) (let ((_let_1 (tptp.size_size_list_int Ys2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_size_list_int Xs)) _let_1))) (= (tptp.nth_Pr4439495888332055232nt_int (tptp.product_int_int Xs Ys2) N2) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_nat_int (tptp.nth_int Xs) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N2) _let_1))) (tptp.aa_nat_int (tptp.nth_int Ys2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs tptp.list_int) (Ys2 tptp.list_nat)) (let ((_let_1 (tptp.aa_list_nat_nat tptp.size_size_list_nat Ys2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_size_list_int Xs)) _let_1))) (= (tptp.nth_Pr8617346907841251940nt_nat (tptp.product_int_nat Xs Ys2) N2) (tptp.product_Pair_int_nat (tptp.aa_nat_int (tptp.nth_int Xs) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N2) _let_1)) (tptp.aa_nat_nat (tptp.nth_nat Ys2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs tptp.list_int) (Ys2 tptp.list_bool)) (let ((_let_1 (tptp.size_size_list_bool Ys2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_size_list_int Xs)) _let_1))) (= (tptp.nth_Pr6495399312670224281t_bool (tptp.product_int_bool Xs Ys2) N2) (tptp.produc788913908665201810t_bool (tptp.aa_nat_int (tptp.nth_int Xs) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N2) _let_1)) (tptp.aa_nat_bool (tptp.nth_bool Ys2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs tptp.list_nat) (Ys2 tptp.list_int)) (let ((_let_1 (tptp.size_size_list_int Ys2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_list_nat_nat tptp.size_size_list_nat Xs)) _let_1))) (= (tptp.nth_Pr3440142176431000676at_int (tptp.product_nat_int Xs Ys2) N2) (tptp.product_Pair_nat_int (tptp.aa_nat_nat (tptp.nth_nat Xs) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N2) _let_1)) (tptp.aa_nat_int (tptp.nth_int Ys2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs tptp.list_nat) (Ys2 tptp.list_nat)) (let ((_let_1 (tptp.aa_list_nat_nat tptp.size_size_list_nat Ys2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_list_nat_nat tptp.size_size_list_nat Xs)) _let_1))) (= (tptp.aa_nat7603221163087113075at_nat (tptp.nth_Pr7617993195940197384at_nat (tptp.product_nat_nat Xs Ys2)) N2) (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat (tptp.aa_nat_nat (tptp.nth_nat Xs) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N2) _let_1))) (tptp.aa_nat_nat (tptp.nth_nat Ys2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs tptp.list_nat) (Ys2 tptp.list_bool)) (let ((_let_1 (tptp.size_size_list_bool Ys2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_list_nat_nat tptp.size_size_list_nat Xs)) _let_1))) (= (tptp.nth_Pr396318242284072693t_bool (tptp.product_nat_bool Xs Ys2) N2) (tptp.produc3913204875133826030t_bool (tptp.aa_nat_nat (tptp.nth_nat Xs) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N2) _let_1)) (tptp.aa_nat_bool (tptp.nth_bool Ys2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs tptp.list_bool) (Ys2 tptp.list_int)) (let ((_let_1 (tptp.size_size_list_int Ys2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_size_list_bool Xs)) _let_1))) (= (tptp.nth_Pr7231943226834047147ol_int (tptp.product_bool_int Xs Ys2) N2) (tptp.produc8871513391732212460ol_int (tptp.aa_nat_bool (tptp.nth_bool Xs) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N2) _let_1)) (tptp.aa_nat_int (tptp.nth_int Ys2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs tptp.list_bool) (Ys2 tptp.list_nat)) (let ((_let_1 (tptp.aa_list_nat_nat tptp.size_size_list_nat Ys2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_size_list_bool Xs)) _let_1))) (= (tptp.nth_Pr2186422209488468047ol_nat (tptp.product_bool_nat Xs Ys2) N2) (tptp.produc8874003862241262736ol_nat (tptp.aa_nat_bool (tptp.nth_bool Xs) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N2) _let_1)) (tptp.aa_nat_nat (tptp.nth_nat Ys2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs tptp.list_bool) (Ys2 tptp.list_bool)) (let ((_let_1 (tptp.size_size_list_bool Ys2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_size_list_bool Xs)) _let_1))) (= (tptp.nth_Pr2856333732135533678l_bool (tptp.product_bool_bool Xs Ys2) N2) (tptp.produc8297744024737662807l_bool (tptp.aa_nat_bool (tptp.nth_bool Xs) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N2) _let_1)) (tptp.aa_nat_bool (tptp.nth_bool Ys2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs tptp.list_a) (Ys2 tptp.list_P131111800688179804it_nat)) (let ((_let_1 (tptp.size_s341701280123345136it_nat Ys2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_size_list_a Xs)) _let_1))) (= (tptp.nth_Pr8687047199098054322it_nat (tptp.produc6966004487978991557it_nat Xs Ys2) N2) (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat (tptp.nth_a Xs (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N2) _let_1))) (tptp.nth_Pr4561283279332054789it_nat Ys2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((A tptp.rat) (T5 tptp.set_rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.aTP_Lamm_hw A))) (= (tptp.image_rat_rat _let_1 (tptp.uminus2201863774496077783et_rat T5)) (tptp.uminus2201863774496077783et_rat (tptp.image_rat_rat _let_1 T5))))) (forall ((A tptp.int) (T5 tptp.set_int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.aTP_Lamm_hx A))) (= (tptp.image_int_int _let_1 (tptp.uminus1532241313380277803et_int T5)) (tptp.uminus1532241313380277803et_int (tptp.image_int_int _let_1 T5))))) (forall ((A tptp.rat) (S2 tptp.set_rat) (T5 tptp.set_rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.aTP_Lamm_hw A))) (= (tptp.image_rat_rat _let_1 (tptp.minus_minus_set_rat S2 T5)) (tptp.minus_minus_set_rat (tptp.image_rat_rat _let_1 S2) (tptp.image_rat_rat _let_1 T5))))) (forall ((A tptp.int) (S2 tptp.set_int) (T5 tptp.set_int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.aTP_Lamm_hx A))) (= (tptp.image_int_int _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int S2) T5)) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int (tptp.image_int_int _let_1 S2)) (tptp.image_int_int _let_1 T5))))) (forall ((A tptp.rat) (S2 tptp.set_rat) (T5 tptp.set_rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.aTP_Lamm_hw A))) (= (tptp.image_rat_rat _let_1 (tptp.inf_inf_set_rat S2 T5)) (tptp.inf_inf_set_rat (tptp.image_rat_rat _let_1 S2) (tptp.image_rat_rat _let_1 T5))))) (forall ((A tptp.int) (S2 tptp.set_int) (T5 tptp.set_int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.aTP_Lamm_hx A))) (= (tptp.image_int_int _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int S2) T5)) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int (tptp.image_int_int _let_1 S2)) (tptp.image_int_int _let_1 T5))))) (forall ((N2 tptp.nat) (M tptp.nat) (X tptp.rat)) (let ((_let_1 (tptp.power_power_rat X))) (let ((_let_2 (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat _let_1) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (= X tptp.one_one_rat))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)))) (and (=> _let_4 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_nat_rat _let_1 M)) (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat tptp.suc N2)))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat tptp.one_one_rat) X)))))))))))) (forall ((F tptp.fun_int_nat) (A3 tptp.set_int)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.groups4541462559716669496nt_nat F A3)) (tptp.groups4538972089207619220nt_int (tptp.aTP_Lamm_jp F) A3))) (forall ((F tptp.fun_nat_nat) (A3 tptp.set_nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A3)) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_jq F)) A3))) (forall ((F tptp.fun_nat_nat) (A3 tptp.set_nat)) (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A3)) (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger (tptp.aTP_Lamm_jr F)) A3))) (forall ((F tptp.fun_nat_nat) (A3 tptp.set_nat)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A3)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_js F)) A3))) (forall ((F tptp.fun_int_int) (A3 tptp.set_int)) (= (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.groups4538972089207619220nt_int F A3)) (tptp.groups3906332499630173760nt_rat (tptp.aTP_Lamm_jt F) A3))) (forall ((F tptp.fun_int_int) (A3 tptp.set_int)) (= (tptp.aa_int_int tptp.ring_1_of_int_int (tptp.groups4538972089207619220nt_int F A3)) (tptp.groups4538972089207619220nt_int (tptp.aTP_Lamm_ju F) A3))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (let ((_let_2 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (tptp.groups7501900531339628137nteger G))) (let ((_let_4 (tptp.aa_set871585252387937313nteger _let_3 (tptp.aa_nat_set_nat _let_2 _let_1)))) (let ((_let_5 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) M)))) (and (=> _let_5 (= _let_4 tptp.zero_z3403309356797280102nteger)) (=> (not _let_5) (= _let_4 (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_set871585252387937313nteger _let_3 (tptp.aa_nat_set_nat _let_2 N2))) (tptp.aa_nat_Code_integer G _let_1))))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_na2338080690716861136at_nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (let ((_let_2 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (tptp.groups6857163185585827899at_nat G (tptp.aa_nat_set_nat _let_2 _let_1)))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) M)))) (and (=> _let_4 (= _let_3 tptp.zero_z1048942125864253310at_nat)) (=> (not _let_4) (= _let_3 (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat (tptp.groups6857163185585827899at_nat G (tptp.aa_nat_set_nat _let_2 N2))) (tptp.aa_nat2240542744625857721at_nat G _let_1)))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (let ((_let_2 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (tptp.groups2906978787729119204at_rat G))) (let ((_let_4 (tptp.aa_set_nat_rat _let_3 (tptp.aa_nat_set_nat _let_2 _let_1)))) (let ((_let_5 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) M)))) (and (=> _let_5 (= _let_4 tptp.zero_zero_rat)) (=> (not _let_5) (= _let_4 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_set_nat_rat _let_3 (tptp.aa_nat_set_nat _let_2 N2))) (tptp.aa_nat_rat G _let_1))))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (let ((_let_2 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (tptp.groups3539618377306564664at_int G))) (let ((_let_4 (tptp.aa_set_nat_int _let_3 (tptp.aa_nat_set_nat _let_2 _let_1)))) (let ((_let_5 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) M)))) (and (=> _let_5 (= _let_4 tptp.zero_zero_int)) (=> (not _let_5) (= _let_4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_set_nat_int _let_3 (tptp.aa_nat_set_nat _let_2 N2))) (tptp.aa_nat_int G _let_1))))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (let ((_let_2 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (tptp.groups3542108847815614940at_nat G))) (let ((_let_4 (tptp.aa_set_nat_nat _let_3 (tptp.aa_nat_set_nat _let_2 _let_1)))) (let ((_let_5 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) M)))) (and (=> _let_5 (= _let_4 tptp.zero_zero_nat)) (=> (not _let_5) (= _let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_set_nat_nat _let_3 (tptp.aa_nat_set_nat _let_2 N2))) (tptp.aa_nat_nat G _let_1))))))))))) (forall ((F tptp.fun_nat_nat) (A tptp.nat) (A3 tptp.set_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_jv F) A)) A3)) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A3)) A))) (forall ((F tptp.fun_int_int) (A tptp.int) (A3 tptp.set_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.groups4538972089207619220nt_int (tptp.aa_int_fun_int_int (tptp.aTP_Lamm_jw F) A) A3)) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.groups4538972089207619220nt_int F A3)) A))) (forall ((G tptp.fun_nat_nat) (M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M)) (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_jx G)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)))) (forall ((G tptp.fun_nat_nat) (M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) K))) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_jy G) K)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)))) (forall ((G tptp.fun_nat_nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat N2) M))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) _let_1) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_nat3783148529270815480at_nat (tptp.aTP_Lamm_jz G) N2) M)) _let_1)))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_na2338080690716861136at_nat)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_2)) (= (tptp.groups6857163185585827899at_nat G (tptp.aa_nat_set_nat _let_1 _let_2)) (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat (tptp.aa_nat2240542744625857721at_nat G _let_2)) (tptp.groups6857163185585827899at_nat G (tptp.aa_nat_set_nat _let_1 N2)))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (tptp.groups2906978787729119204at_rat G))) (let ((_let_3 (tptp.aa_nat_nat tptp.suc N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_3)) (= (tptp.aa_set_nat_rat _let_2 (tptp.aa_nat_set_nat _let_1 _let_3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat G _let_3)) (tptp.aa_set_nat_rat _let_2 (tptp.aa_nat_set_nat _let_1 N2))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (tptp.groups3539618377306564664at_int G))) (let ((_let_3 (tptp.aa_nat_nat tptp.suc N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_3)) (= (tptp.aa_set_nat_int _let_2 (tptp.aa_nat_set_nat _let_1 _let_3)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int G _let_3)) (tptp.aa_set_nat_int _let_2 (tptp.aa_nat_set_nat _let_1 N2))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (tptp.groups3542108847815614940at_nat G))) (let ((_let_3 (tptp.aa_nat_nat tptp.suc N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_3)) (= (tptp.aa_set_nat_nat _let_2 (tptp.aa_nat_set_nat _let_1 _let_3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat G _let_3)) (tptp.aa_set_nat_nat _let_2 (tptp.aa_nat_set_nat _let_1 N2))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_na2338080690716861136at_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.groups6857163185585827899at_nat G (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)) (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat (tptp.aa_nat2240542744625857721at_nat G M)) (tptp.groups6857163185585827899at_nat G (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M)) N2)))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups2906978787729119204at_rat G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_set_nat_rat _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat G M)) (tptp.aa_set_nat_rat _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M)) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.groups3539618377306564664at_int G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_set_nat_int _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int G M)) (tptp.aa_set_nat_int _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M)) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.groups3542108847815614940at_nat G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_set_nat_nat _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat G M)) (tptp.aa_set_nat_nat _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M)) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_na2338080690716861136at_nat)) (let ((_let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat (tptp.groups6857163185585827899at_nat G _let_1)) (tptp.aa_nat2240542744625857721at_nat G (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat (tptp.aa_nat2240542744625857721at_nat G M)) (tptp.groups6857163185585827899at_nat (tptp.aTP_Lamm_ka G) _let_1)))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat G) _let_1)) (tptp.aa_nat_rat G (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat G M)) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_kb G)) _let_1)))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int G) _let_1)) (tptp.aa_nat_int G (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int G M)) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_kc G)) _let_1)))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) _let_1)) (tptp.aa_nat_nat G (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat G M)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_jx G)) _let_1)))))) (forall ((M tptp.nat) (N2 tptp.nat) (F tptp.fun_nat_rat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_1)) (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_kd F)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_nat_rat F _let_1)) (tptp.aa_nat_rat F M)))))) (forall ((M tptp.nat) (N2 tptp.nat) (F tptp.fun_nat_int)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_1)) (= (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_ke F)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int F _let_1)) (tptp.aa_nat_int F M)))))) (forall ((X tptp.code_integer) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger X))) (= (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger (tptp.aa_nat2010205248571845816nteger (tptp.aTP_Lamm_kf X) M)) I5) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer _let_1 M)) (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger _let_1) I5))))) (forall ((X tptp.rat) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (tptp.power_power_rat X))) (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aa_nat_fun_nat_rat (tptp.aTP_Lamm_kg X) M)) I5) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 M)) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat _let_1) I5))))) (forall ((X tptp.int) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int X))) (= (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_kh X) M)) I5) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_1 M)) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int _let_1) I5))))) (forall ((F tptp.fun_nat_Code_integer) (A tptp.nat) (B tptp.nat)) (= (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger F) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat A) B)) (tptp.aa_Cod1783974652533396728nteger (tptp.set_fo1084959871951514735nteger (tptp.aTP_Lamm_ki F) A B) tptp.zero_z3403309356797280102nteger))) (forall ((F tptp.fun_na2338080690716861136at_nat) (A tptp.nat) (B tptp.nat)) (= (tptp.groups6857163185585827899at_nat F (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat A) B)) (tptp.set_fo4497565046347964853at_nat (tptp.aTP_Lamm_kj F) A B tptp.zero_z1048942125864253310at_nat))) (forall ((F tptp.fun_nat_rat) (A tptp.nat) (B tptp.nat)) (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat F) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat A) B)) (tptp.aa_rat_rat (tptp.set_fo1949268297981939178at_rat (tptp.aTP_Lamm_kk F) A B) tptp.zero_zero_rat))) (forall ((F tptp.fun_nat_int) (A tptp.nat) (B tptp.nat)) (= (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int F) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat A) B)) (tptp.aa_int_int (tptp.aa_nat_fun_int_int (tptp.set_fo2581907887559384638at_int (tptp.aTP_Lamm_kl F) A) B) tptp.zero_zero_int))) (forall ((F tptp.fun_nat_nat) (A tptp.nat) (B tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat A) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat (tptp.aTP_Lamm_km F) A) B) tptp.zero_zero_nat))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_na2338080690716861136at_nat) (P3 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2))) (let ((_let_2 (tptp.aa_nat_nat _let_1 P3))) (let ((_let_3 (tptp.aa_nat_nat _let_1 tptp.one_one_nat))) (let ((_let_4 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_3)) (= (tptp.groups6857163185585827899at_nat G (tptp.aa_nat_set_nat _let_4 _let_2)) (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat (tptp.groups6857163185585827899at_nat G (tptp.aa_nat_set_nat _let_4 N2))) (tptp.groups6857163185585827899at_nat G (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat _let_3) _let_2)))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_rat) (P3 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2))) (let ((_let_2 (tptp.aa_nat_nat _let_1 P3))) (let ((_let_3 (tptp.aa_nat_nat _let_1 tptp.one_one_nat))) (let ((_let_4 (tptp.groups2906978787729119204at_rat G))) (let ((_let_5 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_3)) (= (tptp.aa_set_nat_rat _let_4 (tptp.aa_nat_set_nat _let_5 _let_2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_set_nat_rat _let_4 (tptp.aa_nat_set_nat _let_5 N2))) (tptp.aa_set_nat_rat _let_4 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_int) (P3 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2))) (let ((_let_2 (tptp.aa_nat_nat _let_1 P3))) (let ((_let_3 (tptp.aa_nat_nat _let_1 tptp.one_one_nat))) (let ((_let_4 (tptp.groups3539618377306564664at_int G))) (let ((_let_5 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_3)) (= (tptp.aa_set_nat_int _let_4 (tptp.aa_nat_set_nat _let_5 _let_2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_set_nat_int _let_4 (tptp.aa_nat_set_nat _let_5 N2))) (tptp.aa_set_nat_int _let_4 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_nat) (P3 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2))) (let ((_let_2 (tptp.aa_nat_nat _let_1 P3))) (let ((_let_3 (tptp.aa_nat_nat _let_1 tptp.one_one_nat))) (let ((_let_4 (tptp.groups3542108847815614940at_nat G))) (let ((_let_5 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_3)) (= (tptp.aa_set_nat_nat _let_4 (tptp.aa_nat_set_nat _let_5 _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_set_nat_nat _let_4 (tptp.aa_nat_set_nat _let_5 N2))) (tptp.aa_set_nat_nat _let_4 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (F tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger (tptp.aTP_Lamm_kn F)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (and (=> _let_2 (= _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_nat_Code_integer F M)) (tptp.aa_nat_Code_integer F (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= _let_1 tptp.zero_z3403309356797280102nteger)))))) (forall ((M tptp.nat) (N2 tptp.nat) (F tptp.fun_nat_rat)) (let ((_let_1 (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_ko F)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (and (=> _let_2 (= _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_nat_rat F M)) (tptp.aa_nat_rat F (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))) (forall ((M tptp.nat) (N2 tptp.nat) (F tptp.fun_nat_int)) (let ((_let_1 (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_kp F)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (and (=> _let_2 (= _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int F M)) (tptp.aa_nat_int F (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((M tptp.nat) (N2 tptp.nat) (F tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_kq F)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M)) N2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_nat_rat F N2)) (tptp.aa_nat_rat F M))))) (forall ((M tptp.nat) (N2 tptp.nat) (F tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_kr F)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M)) N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int F N2)) (tptp.aa_nat_int F M))))) (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.code_integer)) (let ((_let_1 (tptp.power_8256067586552552935nteger X))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) X)) (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger _let_1) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2))) (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_nat_Code_integer _let_1 M)) (tptp.aa_nat_Code_integer _let_1 (tptp.aa_nat_nat tptp.suc N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.rat)) (let ((_let_1 (tptp.power_power_rat X))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat tptp.one_one_rat) X)) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat _let_1) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_nat_rat _let_1 M)) (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat tptp.suc N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.int)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int X))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int tptp.one_one_int) X)) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int _let_1) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int _let_1 M)) (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat tptp.suc N2))))))) (forall ((K tptp.nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_ks K)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2)) tptp.one_one_rat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) tptp.one_one_nat)))) (forall ((X tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (tptp.power_power_rat X))) (let ((_let_3 (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat _let_2) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2))))) (let ((_let_4 (= X tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2)) tptp.one_one_rat))) (=> (not _let_4) (= _let_3 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_2 M)) (tptp.aa_rat_rat _let_1 (tptp.aa_nat_rat _let_2 (tptp.aa_nat_nat tptp.suc N2))))) (tptp.aa_rat_rat _let_1 X)))))))))) (forall ((A tptp.rat) (S2 tptp.set_rat) (T5 tptp.set_rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A))) (= (tptp.image_rat_rat _let_1 (tptp.inf_inf_set_rat S2 T5)) (tptp.inf_inf_set_rat (tptp.image_rat_rat _let_1 S2) (tptp.image_rat_rat _let_1 T5))))) (forall ((A tptp.int) (S2 tptp.set_int) (T5 tptp.set_int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int A))) (= (tptp.image_int_int _let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int S2) T5)) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int (tptp.image_int_int _let_1 S2)) (tptp.image_int_int _let_1 T5))))) (forall ((F tptp.fun_int_int) (A3 tptp.set_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.groups4538972089207619220nt_int (tptp.aTP_Lamm_kt F) A3)))) (forall ((F tptp.fun_int_int) (A3 tptp.set_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.groups4538972089207619220nt_int F A3))) (tptp.groups4538972089207619220nt_int (tptp.aTP_Lamm_kt F) A3)))) (forall ((G tptp.fun_bo7282069421189217543nteger)) (= (tptp.groups1682264926906508858nteger G tptp.bot_bot_set_bool) tptp.zero_z3403309356797280102nteger)) (forall ((G tptp.fun_bool_rat)) (= (tptp.groups5133371213642249141ol_rat G tptp.bot_bot_set_bool) tptp.zero_zero_rat)) (forall ((G tptp.fun_bool_nat)) (= (tptp.groups5768501273728744877ol_nat G tptp.bot_bot_set_bool) tptp.zero_zero_nat)) (forall ((G tptp.fun_bool_int)) (= (tptp.groups5766010803219694601ol_int G tptp.bot_bot_set_bool) tptp.zero_zero_int)) (forall ((G tptp.fun_nat_Code_integer)) (= (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger G) tptp.bot_bot_set_nat) tptp.zero_z3403309356797280102nteger)) (forall ((G tptp.fun_nat_rat)) (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat G) tptp.bot_bot_set_nat) tptp.zero_zero_rat)) (forall ((G tptp.fun_nat_int)) (= (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int G) tptp.bot_bot_set_nat) tptp.zero_zero_int)) (forall ((G tptp.fun_int_Code_integer)) (= (tptp.groups7873554091576472773nteger G tptp.bot_bot_set_int) tptp.zero_z3403309356797280102nteger)) (forall ((G tptp.fun_int_rat)) (= (tptp.groups3906332499630173760nt_rat G tptp.bot_bot_set_int) tptp.zero_zero_rat)) (forall ((G tptp.fun_int_nat)) (= (tptp.groups4541462559716669496nt_nat G tptp.bot_bot_set_int) tptp.zero_zero_nat)) (forall ((I5 tptp.set_bool) (X tptp.fun_bo7282069421189217543nteger) (A tptp.fun_bo7282069421189217543nteger) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 I5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_bool_Code_integer X I3))))) (=> (= (tptp.groups1682264926906508858nteger X I5) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 I5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_bool_Code_integer A I3)) B))) Delta)))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.groups1682264926906508858nteger (tptp.aa_fun1377107737837666940nteger (tptp.aTP_Lamm_ku X) A) I5)) B))) Delta)))))) (forall ((I5 tptp.set_nat) (X tptp.fun_nat_Code_integer) (A tptp.fun_nat_Code_integer) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer X I3))))) (=> (= (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger X) I5) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_nat_Code_integer A I3)) B))) Delta)))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger (tptp.aa_fun589076786913273746nteger (tptp.aTP_Lamm_kv X) A)) I5)) B))) Delta)))))) (forall ((I5 tptp.set_int) (X tptp.fun_int_Code_integer) (A tptp.fun_int_Code_integer) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_int_Code_integer X I3))))) (=> (= (tptp.groups7873554091576472773nteger X I5) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_int_Code_integer A I3)) B))) Delta)))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.groups7873554091576472773nteger (tptp.aa_fun5304498221708291146nteger (tptp.aTP_Lamm_kw X) A) I5)) B))) Delta)))))) (forall ((I5 tptp.set_bool) (X tptp.fun_bool_rat) (A tptp.fun_bool_rat) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_bool_rat X I3))))) (=> (= (tptp.groups5133371213642249141ol_rat X I5) tptp.one_one_rat) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_bool_rat A I3)) B))) Delta)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.groups5133371213642249141ol_rat (tptp.aa_fun224000846028461884ol_rat (tptp.aTP_Lamm_kx X) A) I5)) B))) Delta)))))) (forall ((I5 tptp.set_nat) (X tptp.fun_nat_rat) (A tptp.fun_nat_rat) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat X I3))))) (=> (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat X) I5) tptp.one_one_rat) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_nat_rat A I3)) B))) Delta)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_ky X) A)) I5)) B))) Delta)))))) (forall ((I5 tptp.set_int) (X tptp.fun_int_rat) (A tptp.fun_int_rat) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_int_rat X I3))))) (=> (= (tptp.groups3906332499630173760nt_rat X I5) tptp.one_one_rat) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_int_rat A I3)) B))) Delta)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.groups3906332499630173760nt_rat (tptp.aa_fun1481061427733998144nt_rat (tptp.aTP_Lamm_kz X) A) I5)) B))) Delta)))))) (forall ((I5 tptp.set_bool) (X tptp.fun_bool_int) (A tptp.fun_bool_int) (B tptp.int) (Delta tptp.int)) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 I5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_bool_int X I3))))) (=> (= (tptp.groups5766010803219694601ol_int X I5) tptp.one_one_int) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 I5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_bool_int A I3)) B))) Delta)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.groups5766010803219694601ol_int (tptp.aa_fun2092349043547419708ol_int (tptp.aTP_Lamm_la X) A) I5)) B))) Delta)))))) (forall ((I5 tptp.set_nat) (X tptp.fun_nat_int) (A tptp.fun_nat_int) (B tptp.int) (Delta tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int X I3))))) (=> (= (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int X) I5) tptp.one_one_int) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int A I3)) B))) Delta)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aa_fun5565043122120104496at_int (tptp.aTP_Lamm_lb X) A)) I5)) B))) Delta)))))) (forall ((I5 tptp.set_int) (X tptp.fun_int_int) (A tptp.fun_int_int) (B tptp.int) (Delta tptp.int)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int X I3))))) (=> (= (tptp.groups4538972089207619220nt_int X I5) tptp.one_one_int) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int A I3)) B))) Delta)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.groups4538972089207619220nt_int (tptp.aa_fun6280345759651049192nt_int (tptp.aTP_Lamm_lc X) A) I5)) B))) Delta)))))) (forall ((I5 tptp.set_set_nat) (X tptp.fun_se7586849273513198688nteger) (A tptp.fun_se7586849273513198688nteger) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat I3) I5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_set871585252387937313nteger X I3))))) (=> (= (tptp.groups9190459664516455967nteger X I5) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat I3) I5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_set871585252387937313nteger A I3)) B))) Delta)))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.groups9190459664516455967nteger (tptp.aa_fun4587287018503165694nteger (tptp.aTP_Lamm_ld X) A) I5)) B))) Delta)))))) (forall ((F tptp.fun_int_int) (A3 tptp.set_int)) (let ((_let_1 (tptp.groups4538972089207619220nt_int (tptp.aTP_Lamm_kt F) A3))) (= (tptp.aa_int_int tptp.abs_abs_int _let_1) _let_1))) (forall ((A3 tptp.set_nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat tptp.aTP_Lamm_fy) A3) tptp.zero_zero_nat)) (forall ((A3 tptp.set_int)) (= (tptp.groups4538972089207619220nt_int tptp.aTP_Lamm_fz A3) tptp.zero_zero_int)) (forall ((F tptp.fun_int_nat) (A3 tptp.set_int)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.groups4541462559716669496nt_nat F A3)) (tptp.groups4538972089207619220nt_int (tptp.aTP_Lamm_jp F) A3))) (forall ((F tptp.fun_nat_nat) (A3 tptp.set_nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A3)) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_jq F)) A3))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (G tptp.fun_Pr2602117396471556196at_nat) (F tptp.fun_Pr2602117396471556196at_nat)) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat X3) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_Pro4243173770044397973at_nat G X3)) (tptp.aa_Pro4243173770044397973at_nat F X3))))) (= (tptp.groups977919841031483927at_nat (tptp.aa_fun2351638177499875132at_nat (tptp.aTP_Lamm_le G) F) A3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.groups977919841031483927at_nat F A3)) (tptp.groups977919841031483927at_nat G A3))))) (forall ((A3 tptp.set_bool) (G tptp.fun_bool_nat) (F tptp.fun_bool_nat)) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_bool_nat G X3)) (tptp.aa_bool_nat F X3))))) (= (tptp.groups5768501273728744877ol_nat (tptp.aa_fun9101744387563128124ol_nat (tptp.aTP_Lamm_lf G) F) A3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.groups5768501273728744877ol_nat F A3)) (tptp.groups5768501273728744877ol_nat G A3))))) (forall ((A3 tptp.set_set_nat) (G tptp.fun_set_nat_nat) (F tptp.fun_set_nat_nat)) (=> (forall ((X3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat X3) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat G X3)) (tptp.aa_set_nat_nat F X3))))) (= (tptp.groups8294997508430121362at_nat (tptp.aa_fun3386010016858254564at_nat (tptp.aTP_Lamm_lg G) F) A3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.groups8294997508430121362at_nat F A3)) (tptp.groups8294997508430121362at_nat G A3))))) (forall ((A3 tptp.set_int) (G tptp.fun_int_nat) (F tptp.fun_int_nat)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat G X3)) (tptp.aa_int_nat F X3))))) (= (tptp.groups4541462559716669496nt_nat (tptp.aa_fun6506752150744536624nt_nat (tptp.aTP_Lamm_lh G) F) A3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.groups4541462559716669496nt_nat F A3)) (tptp.groups4541462559716669496nt_nat G A3))))) (forall ((A3 tptp.set_nat) (G tptp.fun_nat_nat) (F tptp.fun_nat_nat)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat G X3)) (tptp.aa_nat_nat F X3))))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_li G) F)) A3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A3)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) A3))))) (forall ((F tptp.fun_nat_nat) (A3 tptp.set_nat) (N2 tptp.nat)) (=> (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A3) (tptp.aa_nat_nat tptp.suc N2)) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat F X3))))))) (forall ((G tptp.fun_nat_fun_nat_nat) (B3 tptp.set_nat) (A3 tptp.set_nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_set6537093552120046177at_nat (tptp.aTP_Lamm_lj G) B3)) A3) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_set6537093552120046177at_nat (tptp.aTP_Lamm_ll G) A3)) B3))) (forall ((G tptp.fun_int_fun_int_int) (B3 tptp.set_int) (A3 tptp.set_int)) (= (tptp.groups4538972089207619220nt_int (tptp.aa_set7310040872927613301nt_int (tptp.aTP_Lamm_lm G) B3) A3) (tptp.groups4538972089207619220nt_int (tptp.aa_set7310040872927613301nt_int (tptp.aTP_Lamm_lo G) A3) B3))) (forall ((K5 tptp.set_bool) (F tptp.fun_bool_rat) (G tptp.fun_bool_rat)) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 K5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_bool_rat F I3)) (tptp.aa_bool_rat G I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups5133371213642249141ol_rat F K5)) (tptp.groups5133371213642249141ol_rat G K5))))) (forall ((K5 tptp.set_nat) (F tptp.fun_nat_rat) (G tptp.fun_nat_rat)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) K5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F I3)) (tptp.aa_nat_rat G I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat F) K5)) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat G) K5))))) (forall ((K5 tptp.set_int) (F tptp.fun_int_rat) (G tptp.fun_int_rat)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) K5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat F I3)) (tptp.aa_int_rat G I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups3906332499630173760nt_rat F K5)) (tptp.groups3906332499630173760nt_rat G K5))))) (forall ((K5 tptp.set_bool) (F tptp.fun_bool_nat) (G tptp.fun_bool_nat)) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 K5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_bool_nat F I3)) (tptp.aa_bool_nat G I3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.groups5768501273728744877ol_nat F K5)) (tptp.groups5768501273728744877ol_nat G K5))))) (forall ((K5 tptp.set_int) (F tptp.fun_int_nat) (G tptp.fun_int_nat)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) K5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat F I3)) (tptp.aa_int_nat G I3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.groups4541462559716669496nt_nat F K5)) (tptp.groups4541462559716669496nt_nat G K5))))) (forall ((K5 tptp.set_bool) (F tptp.fun_bool_int) (G tptp.fun_bool_int)) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 K5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_bool_int F I3)) (tptp.aa_bool_int G I3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.groups5766010803219694601ol_int F K5)) (tptp.groups5766010803219694601ol_int G K5))))) (forall ((K5 tptp.set_nat) (F tptp.fun_nat_int) (G tptp.fun_nat_int)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) K5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int F I3)) (tptp.aa_nat_int G I3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int F) K5)) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int G) K5))))) (forall ((K5 tptp.set_nat) (F tptp.fun_nat_nat) (G tptp.fun_nat_nat)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) K5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat F I3)) (tptp.aa_nat_nat G I3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) K5)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) K5))))) (forall ((K5 tptp.set_int) (F tptp.fun_int_int) (G tptp.fun_int_int)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) K5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int F I3)) (tptp.aa_int_int G I3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.groups4538972089207619220nt_int F K5)) (tptp.groups4538972089207619220nt_int G K5))))) (forall ((K5 tptp.set_set_nat) (F tptp.fun_set_nat_rat) (G tptp.fun_set_nat_rat)) (=> (forall ((I3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat I3) K5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_set_nat_rat F I3)) (tptp.aa_set_nat_rat G I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups7659867448343625626at_rat F K5)) (tptp.groups7659867448343625626at_rat G K5))))) (forall ((G tptp.fun_nat_nat) (H tptp.fun_nat_nat) (A3 tptp.set_nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_lp G) H)) A3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) A3)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat H) A3)))) (forall ((G tptp.fun_int_int) (H tptp.fun_int_int) (A3 tptp.set_int)) (= (tptp.groups4538972089207619220nt_int (tptp.aa_fun6280345759651049192nt_int (tptp.aTP_Lamm_lq G) H) A3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups4538972089207619220nt_int G A3)) (tptp.groups4538972089207619220nt_int H A3)))) (forall ((F tptp.fun_nat_nat) (A3 tptp.set_nat) (G tptp.fun_nat_nat) (B3 tptp.set_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A3)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) B3)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_set6537093552120046177at_nat (tptp.aa_fun4561837934398617467at_nat (tptp.aTP_Lamm_ls F) G) B3)) A3))) (forall ((F tptp.fun_int_int) (A3 tptp.set_int) (G tptp.fun_int_int) (B3 tptp.set_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.groups4538972089207619220nt_int F A3)) (tptp.groups4538972089207619220nt_int G B3)) (tptp.groups4538972089207619220nt_int (tptp.aa_set7310040872927613301nt_int (tptp.aa_fun8076508010538293575nt_int (tptp.aTP_Lamm_lu F) G) B3) A3))) (forall ((F tptp.fun_nat_nat) (A3 tptp.set_nat) (R3 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A3)) R3) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_lv F) R3)) A3))) (forall ((F tptp.fun_int_int) (A3 tptp.set_int) (R3 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.groups4538972089207619220nt_int F A3)) R3) (tptp.groups4538972089207619220nt_int (tptp.aa_int_fun_int_int (tptp.aTP_Lamm_lw F) R3) A3))) (forall ((R3 tptp.nat) (F tptp.fun_nat_nat) (A3 tptp.set_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat R3) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A3)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_lx R3) F)) A3))) (forall ((R3 tptp.int) (F tptp.fun_int_int) (A3 tptp.set_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int R3) (tptp.groups4538972089207619220nt_int F A3)) (tptp.groups4538972089207619220nt_int (tptp.aa_fun6280345759651049192nt_int (tptp.aTP_Lamm_ly R3) F) A3))) (forall ((F tptp.fun_int_int) (G tptp.fun_int_int) (A3 tptp.set_int)) (= (tptp.groups4538972089207619220nt_int (tptp.aa_fun6280345759651049192nt_int (tptp.aTP_Lamm_lz F) G) A3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.groups4538972089207619220nt_int F A3)) (tptp.groups4538972089207619220nt_int G A3)))) (forall ((F tptp.fun_int_int) (A3 tptp.set_int)) (= (tptp.groups4538972089207619220nt_int (tptp.aTP_Lamm_ma F) A3) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.groups4538972089207619220nt_int F A3)))) (forall ((A3 tptp.set_bool) (F tptp.fun_bo7282069421189217543nteger)) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 A3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_bool_Code_integer F X3))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.groups1682264926906508858nteger F A3))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_Code_integer)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer F X3))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger F) A3))))) (forall ((A3 tptp.set_int) (F tptp.fun_int_Code_integer)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_int_Code_integer F X3))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.groups7873554091576472773nteger F A3))))) (forall ((A3 tptp.set_bool) (F tptp.fun_bool_rat)) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_bool_rat F X3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.groups5133371213642249141ol_rat F A3))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_rat)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat F X3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat F) A3))))) (forall ((A3 tptp.set_int) (F tptp.fun_int_rat)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_int_rat F X3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.groups3906332499630173760nt_rat F A3))))) (forall ((A3 tptp.set_bool) (F tptp.fun_bool_nat)) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_bool_nat F X3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.groups5768501273728744877ol_nat F A3))))) (forall ((A3 tptp.set_int) (F tptp.fun_int_nat)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_int_nat F X3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.groups4541462559716669496nt_nat F A3))))) (forall ((A3 tptp.set_bool) (F tptp.fun_bool_int)) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 A3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_bool_int F X3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.groups5766010803219694601ol_int F A3))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_int)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int F X3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int F) A3))))) (forall ((A3 tptp.set_bool) (F tptp.fun_bo7282069421189217543nteger)) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 A3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_bool_Code_integer F X3)) tptp.zero_z3403309356797280102nteger)))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.groups1682264926906508858nteger F A3)) tptp.zero_z3403309356797280102nteger)))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_Code_integer)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer F X3)) tptp.zero_z3403309356797280102nteger)))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger F) A3)) tptp.zero_z3403309356797280102nteger)))) (forall ((A3 tptp.set_int) (F tptp.fun_int_Code_integer)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_int_Code_integer F X3)) tptp.zero_z3403309356797280102nteger)))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.groups7873554091576472773nteger F A3)) tptp.zero_z3403309356797280102nteger)))) (forall ((A3 tptp.set_bool) (F tptp.fun_bool_rat)) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_bool_rat F X3)) tptp.zero_zero_rat)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups5133371213642249141ol_rat F A3)) tptp.zero_zero_rat)))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_rat)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F X3)) tptp.zero_zero_rat)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat F) A3)) tptp.zero_zero_rat)))) (forall ((A3 tptp.set_int) (F tptp.fun_int_rat)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat F X3)) tptp.zero_zero_rat)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups3906332499630173760nt_rat F A3)) tptp.zero_zero_rat)))) (forall ((A3 tptp.set_bool) (F tptp.fun_bool_nat)) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_bool_nat F X3)) tptp.zero_zero_nat)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.groups5768501273728744877ol_nat F A3)) tptp.zero_zero_nat)))) (forall ((A3 tptp.set_int) (F tptp.fun_int_nat)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat F X3)) tptp.zero_zero_nat)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.groups4541462559716669496nt_nat F A3)) tptp.zero_zero_nat)))) (forall ((A3 tptp.set_bool) (F tptp.fun_bool_int)) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 A3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_bool_int F X3)) tptp.zero_zero_int)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.groups5766010803219694601ol_int F A3)) tptp.zero_zero_int)))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_int)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int F X3)) tptp.zero_zero_int)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int F) A3)) tptp.zero_zero_int)))) (forall ((M tptp.nat) (A tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M))) (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_rat3146053865535587600at_rat (tptp.aa_rat7467449789483521253at_rat (tptp.aTP_Lamm_mb M) A) X) Y)) _let_1) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_rat3146053865535587600at_rat (tptp.aa_rat7467449789483521253at_rat (tptp.aTP_Lamm_mc M) A) X) Y)) _let_1)))) (forall ((X tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (tptp.power_power_rat X))) (let ((_let_3 (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat _let_2) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (let ((_let_4 (= X tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat _let_1 (tptp.aa_nat_rat _let_2 (tptp.aa_nat_nat tptp.suc N2)))) (tptp.aa_rat_rat _let_1 X)))))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.divmod_nat M) N2) (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N2)))) (forall ((I2 tptp.nat) (J tptp.nat) (L tptp.list_bool) (X tptp.bool)) (let ((_let_1 (tptp.nth_bool L))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) I2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) J)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J) (tptp.size_size_list_bool L))) (=> (tptp.pp (tptp.aa_list_bool_bool (tptp.sorted_wrt_bool tptp.ord_less_eq_bool) L)) (=> (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.ord_less_eq_bool (tptp.aa_nat_bool _let_1 I2)) X)) (=> (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.ord_less_bool X) (tptp.aa_nat_bool _let_1 J))) (not (forall ((K2 tptp.nat)) (let ((_let_1 (tptp.nth_bool L))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) K2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K2) J)) (=> (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.ord_less_eq_bool (tptp.aa_nat_bool _let_1 K2)) X)) (not (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.ord_less_bool X) (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K2) tptp.one_one_nat))))))))))))))))))) (forall ((I2 tptp.nat) (J tptp.nat) (L tptp.list_rat) (X tptp.rat)) (let ((_let_1 (tptp.nth_rat L))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) I2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) J)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J) (tptp.size_size_list_rat L))) (=> (tptp.sorted_wrt_rat tptp.ord_less_eq_rat L) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat _let_1 I2)) X)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.aa_nat_rat _let_1 J))) (not (forall ((K2 tptp.nat)) (let ((_let_1 (tptp.nth_rat L))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) K2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K2) J)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat _let_1 K2)) X)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K2) tptp.one_one_nat))))))))))))))))))) (forall ((I2 tptp.nat) (J tptp.nat) (L tptp.list_num) (X tptp.num)) (let ((_let_1 (tptp.nth_num L))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) I2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) J)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J) (tptp.size_size_list_num L))) (=> (tptp.sorted_wrt_num tptp.ord_less_eq_num L) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num _let_1 I2)) X)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) (tptp.aa_nat_num _let_1 J))) (not (forall ((K2 tptp.nat)) (let ((_let_1 (tptp.nth_num L))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) K2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K2) J)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num _let_1 K2)) X)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) (tptp.aa_nat_num _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K2) tptp.one_one_nat))))))))))))))))))) (forall ((I2 tptp.nat) (J tptp.nat) (L tptp.list_nat) (X tptp.nat)) (let ((_let_1 (tptp.nth_nat L))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) I2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) J)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J) (tptp.aa_list_nat_nat tptp.size_size_list_nat L))) (=> (tptp.pp (tptp.aa_list_nat_bool (tptp.sorted_wrt_nat tptp.ord_less_eq_nat) L)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 I2)) X)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) (tptp.aa_nat_nat _let_1 J))) (not (forall ((K2 tptp.nat)) (let ((_let_1 (tptp.nth_nat L))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) K2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K2) J)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 K2)) X)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K2) tptp.one_one_nat))))))))))))))))))) (forall ((I2 tptp.nat) (J tptp.nat) (L tptp.list_int) (X tptp.int)) (let ((_let_1 (tptp.nth_int L))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) I2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) J)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J) (tptp.size_size_list_int L))) (=> (tptp.sorted_wrt_int tptp.ord_less_eq_int L) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int _let_1 I2)) X)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) (tptp.aa_nat_int _let_1 J))) (not (forall ((K2 tptp.nat)) (let ((_let_1 (tptp.nth_int L))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) K2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K2) J)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int _let_1 K2)) X)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K2) tptp.one_one_nat))))))))))))))))))) (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_nat_rat (tptp.gbinomial_rat A) _let_1) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat (tptp.aTP_Lamm_md A)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat _let_1))))) (forall ((A tptp.code_natural) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_nat_Code_natural (tptp.gbinom7368847122466276068atural A) _let_1) (tptp.divide5121882707175180666atural (tptp.groups2279045934846249631atural (tptp.aTP_Lamm_me A) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)) (tptp.aa_nat_Code_natural tptp.semiri2447717529341329178atural _let_1))))) (forall ((A tptp.code_integer) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_nat_Code_integer (tptp.gbinom8545251970709558553nteger A) _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger (tptp.aTP_Lamm_mf A)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger _let_1))))) (forall ((A tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gbinomial_nat A) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_mg A)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat _let_1))))) (forall ((A tptp.int) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.gbinomial_int A) _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_int_fun_nat_int tptp.aTP_Lamm_mh A)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int _let_1))))) (forall ((M tptp.nat) (A tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M))) (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_rat3146053865535587600at_rat (tptp.aa_rat7467449789483521253at_rat (tptp.aTP_Lamm_mb M) A) X) Y)) _let_1) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_rat3146053865535587600at_rat (tptp.aa_rat7467449789483521253at_rat (tptp.aTP_Lamm_mi M) A) X) Y)) _let_1)))) (forall ((I2 tptp.bool) (K tptp.bool)) (= (tptp.pp (tptp.member_bool I2 (tptp.set_ord_atMost_bool K))) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.ord_less_eq_bool I2) K)))) (forall ((I2 tptp.set_nat) (K tptp.set_nat)) (= (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat I2) (tptp.set_or4236626031148496127et_nat K))) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat I2) K)))) (forall ((I2 tptp.set_int) (K tptp.set_int)) (= (tptp.member_set_int I2 (tptp.set_or58775011639299419et_int K)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int I2) K)))) (forall ((I2 tptp.rat) (K tptp.rat)) (= (tptp.member_rat I2 (tptp.set_ord_atMost_rat K)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat I2) K)))) (forall ((I2 tptp.num) (K tptp.num)) (= (tptp.member_num I2 (tptp.set_ord_atMost_num K)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num I2) K)))) (forall ((I2 tptp.nat) (K tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I2) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat K))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) K)))) (forall ((I2 tptp.int) (K tptp.int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I2) (tptp.set_ord_atMost_int K))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I2) K)))) (forall ((A3 tptp.set_nat)) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat tptp.aTP_Lamm_mj) A3) tptp.one_one_nat)) (forall ((A3 tptp.set_nat)) (= (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int tptp.aTP_Lamm_mk) A3) tptp.one_one_int)) (forall ((A3 tptp.set_int)) (= (tptp.groups1705073143266064639nt_int tptp.aTP_Lamm_ml A3) tptp.one_one_int)) (forall ((F tptp.fun_int_nat) (A3 tptp.set_int)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.groups1707563613775114915nt_nat F A3)) (tptp.groups1705073143266064639nt_int (tptp.aTP_Lamm_jp F) A3))) (forall ((F tptp.fun_nat_nat) (A3 tptp.set_nat)) (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat F) A3)) (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger (tptp.aTP_Lamm_jr F)) A3))) (forall ((F tptp.fun_nat_nat) (A3 tptp.set_nat)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat F) A3)) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aTP_Lamm_js F)) A3))) (forall ((F tptp.fun_nat_nat) (A3 tptp.set_nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat F) A3)) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aTP_Lamm_jq F)) A3))) (forall ((F tptp.fun_nat_int) (A3 tptp.set_nat)) (= (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int F) A3)) (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat (tptp.aTP_Lamm_mm F)) A3))) (forall ((F tptp.fun_nat_int) (A3 tptp.set_nat)) (= (tptp.aa_int_int tptp.ring_1_of_int_int (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int F) A3)) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aTP_Lamm_mn F)) A3))) (forall ((F tptp.fun_int_int) (A3 tptp.set_int)) (= (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.groups1705073143266064639nt_int F A3)) (tptp.groups1072433553688619179nt_rat (tptp.aTP_Lamm_jt F) A3))) (forall ((F tptp.fun_int_int) (A3 tptp.set_int)) (= (tptp.aa_int_int tptp.ring_1_of_int_int (tptp.groups1705073143266064639nt_int F A3)) (tptp.groups1705073143266064639nt_int (tptp.aTP_Lamm_ju F) A3))) (forall ((G tptp.fun_bo7282069421189217543nteger)) (= (tptp.groups7272450149305381519nteger G tptp.bot_bot_set_bool) tptp.one_one_Code_integer)) (forall ((G tptp.fun_bool_assn)) (= (tptp.groups4835110720589548378l_assn G tptp.bot_bot_set_bool) tptp.one_one_assn)) (forall ((G tptp.fun_bool_rat)) (= (tptp.groups1259819201609700362ol_rat G tptp.bot_bot_set_bool) tptp.one_one_rat)) (forall ((G tptp.fun_bool_nat)) (= (tptp.groups1894949261696196098ol_nat G tptp.bot_bot_set_bool) tptp.one_one_nat)) (forall ((G tptp.fun_bool_int)) (= (tptp.groups1892458791187145822ol_int G tptp.bot_bot_set_bool) tptp.one_one_int)) (forall ((G tptp.fun_nat_Code_integer)) (= (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger G) tptp.bot_bot_set_nat) tptp.one_one_Code_integer)) (forall ((G tptp.fun_nat_assn)) (= (tptp.groups6906906614972039071t_assn G tptp.bot_bot_set_nat) tptp.one_one_assn)) (forall ((G tptp.fun_nat_rat)) (= (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat G) tptp.bot_bot_set_nat) tptp.one_one_rat)) (forall ((G tptp.fun_int_Code_integer)) (= (tptp.groups3827104343326376752nteger G tptp.bot_bot_set_int) tptp.one_one_Code_integer)) (forall ((G tptp.fun_int_assn)) (= (tptp.groups7882442080178216443t_assn G tptp.bot_bot_set_int) tptp.one_one_assn)) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (tptp.ord_le4403425263959731960et_int (tptp.set_or58775011639299419et_int X) (tptp.set_or58775011639299419et_int Y)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.ord_less_eq_set_rat (tptp.set_ord_atMost_rat X) (tptp.set_ord_atMost_rat Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.ord_less_eq_set_num (tptp.set_ord_atMost_num X) (tptp.set_ord_atMost_num Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat X)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.set_ord_atMost_int X)) (tptp.set_ord_atMost_int Y))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)))) (forall ((L tptp.set_int) (H tptp.set_int) (H3 tptp.set_int)) (= (tptp.ord_le4403425263959731960et_int (tptp.set_or370866239135849197et_int L H) (tptp.set_or58775011639299419et_int H3)) (or (not (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int L) H))) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int H) H3))))) (forall ((L tptp.rat) (H tptp.rat) (H3 tptp.rat)) (= (tptp.ord_less_eq_set_rat (tptp.set_or633870826150836451st_rat L H) (tptp.set_ord_atMost_rat H3)) (or (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat L) H))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat H) H3))))) (forall ((L tptp.num) (H tptp.num) (H3 tptp.num)) (= (tptp.ord_less_eq_set_num (tptp.set_or7049704709247886629st_num L H) (tptp.set_ord_atMost_num H3)) (or (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num L) H))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num H) H3))))) (forall ((L tptp.int) (H tptp.int) (H3 tptp.int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.set_or1266510415728281911st_int L H)) (tptp.set_ord_atMost_int H3))) (or (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int L) H))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int H) H3))))) (forall ((L tptp.nat) (H tptp.nat) (H3 tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat L) H)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat H3))) (or (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat L) H))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat H) H3))))) (forall ((L tptp.code_integer) (H tptp.code_integer) (H3 tptp.code_integer)) (= (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger (tptp.set_or189985376899183464nteger L H)) (tptp.set_or9101266186257409494nteger H3))) (or (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger L) H))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger H) H3))))) (forall ((G tptp.fun_nat_Code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (let ((_let_2 (tptp.groups3455450783089532116nteger G))) (= (tptp.aa_set871585252387937313nteger _let_2 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat _let_1)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_set871585252387937313nteger _let_2 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_nat_Code_integer G _let_1)))))) (forall ((G tptp.fun_nat_assn) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (= (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat _let_1)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_nat_assn G _let_1))))) (forall ((G tptp.fun_nat_rat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (let ((_let_2 (tptp.groups73079841787564623at_rat G))) (= (tptp.aa_set_nat_rat _let_2 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat _let_1)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_set_nat_rat _let_2 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_nat_rat G _let_1)))))) (forall ((G tptp.fun_nat_nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (let ((_let_2 (tptp.groups708209901874060359at_nat G))) (= (tptp.aa_set_nat_nat _let_2 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_set_nat_nat _let_2 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_nat_nat G _let_1)))))) (forall ((G tptp.fun_nat_int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (let ((_let_2 (tptp.groups705719431365010083at_int G))) (= (tptp.aa_set_nat_int _let_2 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_set_nat_int _let_2 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_nat_int G _let_1)))))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (let ((_let_2 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (tptp.groups3455450783089532116nteger G))) (let ((_let_4 (tptp.aa_set871585252387937313nteger _let_3 (tptp.aa_nat_set_nat _let_2 _let_1)))) (let ((_let_5 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) M)))) (and (=> _let_5 (= _let_4 tptp.one_one_Code_integer)) (=> (not _let_5) (= _let_4 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_set871585252387937313nteger _let_3 (tptp.aa_nat_set_nat _let_2 N2))) (tptp.aa_nat_Code_integer G _let_1))))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_nat_assn)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (let ((_let_2 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat _let_2 _let_1)))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) M)))) (and (=> _let_4 (= _let_3 tptp.one_one_assn)) (=> (not _let_4) (= _let_3 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat _let_2 N2))) (tptp.aa_nat_assn G _let_1)))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (let ((_let_2 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (tptp.groups73079841787564623at_rat G))) (let ((_let_4 (tptp.aa_set_nat_rat _let_3 (tptp.aa_nat_set_nat _let_2 _let_1)))) (let ((_let_5 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) M)))) (and (=> _let_5 (= _let_4 tptp.one_one_rat)) (=> (not _let_5) (= _let_4 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_set_nat_rat _let_3 (tptp.aa_nat_set_nat _let_2 N2))) (tptp.aa_nat_rat G _let_1))))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (let ((_let_2 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (tptp.groups708209901874060359at_nat G))) (let ((_let_4 (tptp.aa_set_nat_nat _let_3 (tptp.aa_nat_set_nat _let_2 _let_1)))) (let ((_let_5 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) M)))) (and (=> _let_5 (= _let_4 tptp.one_one_nat)) (=> (not _let_5) (= _let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_set_nat_nat _let_3 (tptp.aa_nat_set_nat _let_2 N2))) (tptp.aa_nat_nat G _let_1))))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (let ((_let_2 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (tptp.groups705719431365010083at_int G))) (let ((_let_4 (tptp.aa_set_nat_int _let_3 (tptp.aa_nat_set_nat _let_2 _let_1)))) (let ((_let_5 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) M)))) (and (=> _let_5 (= _let_4 tptp.one_one_int)) (=> (not _let_5) (= _let_4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_set_nat_int _let_3 (tptp.aa_nat_set_nat _let_2 N2))) (tptp.aa_nat_int G _let_1))))))))))) (forall ((G tptp.fun_nat_fun_nat_nat) (B3 tptp.set_nat) (A3 tptp.set_nat)) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_set6537093552120046177at_nat (tptp.aTP_Lamm_mo G) B3)) A3) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_set6537093552120046177at_nat (tptp.aTP_Lamm_mp G) A3)) B3))) (forall ((G tptp.fun_nat_fun_nat_int) (B3 tptp.set_nat) (A3 tptp.set_nat)) (= (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_set2359242532610849469at_int (tptp.aTP_Lamm_mq G) B3)) A3) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_set2359242532610849469at_int (tptp.aTP_Lamm_ms G) A3)) B3))) (forall ((G tptp.fun_nat_fun_int_int) (B3 tptp.set_int) (A3 tptp.set_nat)) (= (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_set6310687161026558745at_int (tptp.aTP_Lamm_mt G) B3)) A3) (tptp.groups1705073143266064639nt_int (tptp.aa_set3358596244511904025nt_int (tptp.aTP_Lamm_mv G) A3) B3))) (forall ((G tptp.fun_int_fun_nat_int) (B3 tptp.set_nat) (A3 tptp.set_int)) (= (tptp.groups1705073143266064639nt_int (tptp.aa_set3358596244511904025nt_int (tptp.aTP_Lamm_mw G) B3) A3) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_set6310687161026558745at_int (tptp.aTP_Lamm_my G) A3)) B3))) (forall ((G tptp.fun_int_fun_int_int) (B3 tptp.set_int) (A3 tptp.set_int)) (= (tptp.groups1705073143266064639nt_int (tptp.aa_set7310040872927613301nt_int (tptp.aTP_Lamm_mz G) B3) A3) (tptp.groups1705073143266064639nt_int (tptp.aa_set7310040872927613301nt_int (tptp.aTP_Lamm_na G) A3) B3))) (forall ((Xs tptp.list_nat)) (tptp.pp (tptp.aa_list_nat_bool (tptp.sorted_wrt_nat tptp.aTP_Lamm_nb) Xs))) (forall ((Xs tptp.list_int)) (tptp.sorted_wrt_int tptp.aTP_Lamm_nc Xs)) (forall ((H tptp.bool)) (not (= tptp.bot_bot_set_bool (tptp.set_ord_atMost_bool H)))) (forall ((H tptp.nat)) (not (= tptp.bot_bot_set_nat (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat H)))) (forall ((H tptp.int)) (not (= tptp.bot_bot_set_int (tptp.set_ord_atMost_int H)))) (forall ((G tptp.fun_nat_nat) (H tptp.fun_nat_nat) (A3 tptp.set_nat)) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_nd G) H)) A3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat G) A3)) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat H) A3)))) (forall ((G tptp.fun_nat_int) (H tptp.fun_nat_int) (A3 tptp.set_nat)) (= (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_fun5565043122120104496at_int (tptp.aTP_Lamm_ne G) H)) A3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int G) A3)) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int H) A3)))) (forall ((G tptp.fun_int_int) (H tptp.fun_int_int) (A3 tptp.set_int)) (= (tptp.groups1705073143266064639nt_int (tptp.aa_fun6280345759651049192nt_int (tptp.aTP_Lamm_nf G) H) A3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.groups1705073143266064639nt_int G A3)) (tptp.groups1705073143266064639nt_int H A3)))) (forall ((F tptp.fun_nat_nat) (A3 tptp.set_nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat F) A3)) N2) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_ng F) N2)) A3))) (forall ((F tptp.fun_nat_int) (A3 tptp.set_nat) (N2 tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int F) A3)) N2) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_nh F) N2)) A3))) (forall ((F tptp.fun_int_int) (A3 tptp.set_int) (N2 tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.groups1705073143266064639nt_int F A3)) N2) (tptp.groups1705073143266064639nt_int (tptp.aa_nat_fun_int_int (tptp.aTP_Lamm_ni F) N2) A3))) (forall ((F tptp.fun_nat_nat) (A tptp.nat) (A3 tptp.set_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_jv F) A)) A3)) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat F) A3)) A))) (forall ((F tptp.fun_nat_int) (A tptp.int) (A3 tptp.set_nat)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_nj F) A)) A3)) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int F) A3)) A))) (forall ((F tptp.fun_int_int) (A tptp.int) (A3 tptp.set_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.groups1705073143266064639nt_int (tptp.aa_int_fun_int_int (tptp.aTP_Lamm_jw F) A) A3)) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.groups1705073143266064639nt_int F A3)) A))) (forall ((G tptp.fun_nat_Code_integer) (N2 tptp.nat)) (= (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer G tptp.zero_zero_nat)) (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger (tptp.aTP_Lamm_nk G)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))))) (forall ((G tptp.fun_nat_assn) (N2 tptp.nat)) (= (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.aa_nat_assn G tptp.zero_zero_nat)) (tptp.groups6906906614972039071t_assn (tptp.aTP_Lamm_nl G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))))) (forall ((G tptp.fun_nat_rat) (N2 tptp.nat)) (= (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat G tptp.zero_zero_nat)) (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat (tptp.aTP_Lamm_kb G)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))))) (forall ((G tptp.fun_nat_nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat G tptp.zero_zero_nat)) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aTP_Lamm_jx G)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))))) (forall ((G tptp.fun_nat_int) (N2 tptp.nat)) (= (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int G tptp.zero_zero_nat)) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aTP_Lamm_kc G)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))))) (forall ((U tptp.set_nat)) (= (tptp.set_or4236626031148496127et_nat U) (tptp.collect_set_nat (tptp.aa_set5116768664143533222t_bool tptp.aTP_Lamm_cz U)))) (forall ((U tptp.set_int)) (= (tptp.set_or58775011639299419et_int U) (tptp.collect_set_int (tptp.aa_set7694327796961020398t_bool tptp.aTP_Lamm_dd U)))) (forall ((U tptp.rat)) (= (tptp.set_ord_atMost_rat U) (tptp.collect_rat (tptp.aa_rat_fun_rat_bool tptp.aTP_Lamm_dh U)))) (forall ((U tptp.num)) (= (tptp.set_ord_atMost_num U) (tptp.collect_num (tptp.aa_num_fun_num_bool tptp.aTP_Lamm_nm U)))) (forall ((U tptp.nat)) (= (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat U) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_df U)))) (forall ((U tptp.int)) (= (tptp.set_ord_atMost_int U) (tptp.collect_int (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_dj U)))) (forall ((Xs tptp.list_rat)) (=> (tptp.sorted_wrt_rat tptp.ord_less_rat Xs) (tptp.sorted_wrt_rat tptp.ord_less_eq_rat Xs))) (forall ((Xs tptp.list_num)) (=> (tptp.sorted_wrt_num tptp.ord_less_num Xs) (tptp.sorted_wrt_num tptp.ord_less_eq_num Xs))) (forall ((Xs tptp.list_nat)) (=> (tptp.pp (tptp.aa_list_nat_bool (tptp.sorted_wrt_nat tptp.ord_less_nat) Xs)) (tptp.pp (tptp.aa_list_nat_bool (tptp.sorted_wrt_nat tptp.ord_less_eq_nat) Xs)))) (forall ((Xs tptp.list_int)) (=> (tptp.sorted_wrt_int tptp.ord_less_int Xs) (tptp.sorted_wrt_int tptp.ord_less_eq_int Xs))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_nat)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_nat_nat F X3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat F) A3))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_int)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int F X3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int F) A3))))) (forall ((A3 tptp.set_int) (F tptp.fun_int_int)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int F X3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.groups1705073143266064639nt_int F A3))))) (forall ((A3 tptp.set_bool) (F tptp.fun_bo7282069421189217543nteger) (G tptp.fun_bo7282069421189217543nteger)) (=> (forall ((I3 tptp.bool)) (let ((_let_1 (tptp.aa_bool_Code_integer F I3))) (=> (tptp.pp (tptp.member_bool I3 A3)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger _let_1) (tptp.aa_bool_Code_integer G I3))))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.groups7272450149305381519nteger F A3)) (tptp.groups7272450149305381519nteger G A3))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_Code_integer) (G tptp.fun_nat_Code_integer)) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_integer F I3))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) A3)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger _let_1) (tptp.aa_nat_Code_integer G I3))))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger F) A3)) (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger G) A3))))) (forall ((A3 tptp.set_int) (F tptp.fun_int_Code_integer) (G tptp.fun_int_Code_integer)) (=> (forall ((I3 tptp.int)) (let ((_let_1 (tptp.aa_int_Code_integer F I3))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) A3)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger _let_1) (tptp.aa_int_Code_integer G I3))))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.groups3827104343326376752nteger F A3)) (tptp.groups3827104343326376752nteger G A3))))) (forall ((A3 tptp.set_bool) (F tptp.fun_bool_rat) (G tptp.fun_bool_rat)) (=> (forall ((I3 tptp.bool)) (let ((_let_1 (tptp.aa_bool_rat F I3))) (=> (tptp.pp (tptp.member_bool I3 A3)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1) (tptp.aa_bool_rat G I3))))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups1259819201609700362ol_rat F A3)) (tptp.groups1259819201609700362ol_rat G A3))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_rat) (G tptp.fun_nat_rat)) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat F I3))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) A3)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1) (tptp.aa_nat_rat G I3))))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat F) A3)) (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat G) A3))))) (forall ((A3 tptp.set_int) (F tptp.fun_int_rat) (G tptp.fun_int_rat)) (=> (forall ((I3 tptp.int)) (let ((_let_1 (tptp.aa_int_rat F I3))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) A3)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1) (tptp.aa_int_rat G I3))))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups1072433553688619179nt_rat F A3)) (tptp.groups1072433553688619179nt_rat G A3))))) (forall ((A3 tptp.set_bool) (F tptp.fun_bool_nat) (G tptp.fun_bool_nat)) (=> (forall ((I3 tptp.bool)) (let ((_let_1 (tptp.aa_bool_nat F I3))) (=> (tptp.pp (tptp.member_bool I3 A3)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) (tptp.aa_bool_nat G I3))))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.groups1894949261696196098ol_nat F A3)) (tptp.groups1894949261696196098ol_nat G A3))))) (forall ((A3 tptp.set_int) (F tptp.fun_int_nat) (G tptp.fun_int_nat)) (=> (forall ((I3 tptp.int)) (let ((_let_1 (tptp.aa_int_nat F I3))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) A3)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) (tptp.aa_int_nat G I3))))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.groups1707563613775114915nt_nat F A3)) (tptp.groups1707563613775114915nt_nat G A3))))) (forall ((A3 tptp.set_bool) (F tptp.fun_bool_int) (G tptp.fun_bool_int)) (=> (forall ((I3 tptp.bool)) (let ((_let_1 (tptp.aa_bool_int F I3))) (=> (tptp.pp (tptp.member_bool I3 A3)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_1) (tptp.aa_bool_int G I3))))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.groups1892458791187145822ol_int F A3)) (tptp.groups1892458791187145822ol_int G A3))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_nat) (G tptp.fun_nat_nat)) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat F I3))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) A3)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) (tptp.aa_nat_nat G I3))))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat F) A3)) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat G) A3))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_nat)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat F X3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat F) A3))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_int)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_nat_int F X3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int F) A3))))) (forall ((A3 tptp.set_int) (F tptp.fun_int_int)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int F X3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.groups1705073143266064639nt_int F A3))))) (forall ((A3 tptp.set_bool) (F tptp.fun_bo7282069421189217543nteger)) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 A3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (tptp.aa_bool_Code_integer F X3))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (tptp.groups7272450149305381519nteger F A3))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_Code_integer)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (tptp.aa_nat_Code_integer F X3))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger F) A3))))) (forall ((A3 tptp.set_int) (F tptp.fun_int_Code_integer)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (tptp.aa_int_Code_integer F X3))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (tptp.groups3827104343326376752nteger F A3))))) (forall ((A3 tptp.set_bool) (F tptp.fun_bool_rat)) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_bool_rat F X3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.groups1259819201609700362ol_rat F A3))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_rat)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_nat_rat F X3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat F) A3))))) (forall ((A3 tptp.set_int) (F tptp.fun_int_rat)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_int_rat F X3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.groups1072433553688619179nt_rat F A3))))) (forall ((A3 tptp.set_bool) (F tptp.fun_bool_nat)) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) (tptp.aa_bool_nat F X3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) (tptp.groups1894949261696196098ol_nat F A3))))) (forall ((A3 tptp.set_int) (F tptp.fun_int_nat)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) (tptp.aa_int_nat F X3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) (tptp.groups1707563613775114915nt_nat F A3))))) (forall ((A3 tptp.set_bool) (F tptp.fun_bool_int)) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 A3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) (tptp.aa_bool_int F X3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) (tptp.groups1892458791187145822ol_int F A3))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_nat)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) (tptp.aa_nat_nat F X3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat F) A3))))) (forall ((Ns tptp.list_nat) (I2 tptp.nat)) (=> (tptp.pp (tptp.aa_list_nat_bool (tptp.sorted_wrt_nat tptp.ord_less_nat) Ns)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) (tptp.aa_list_nat_nat tptp.size_size_list_nat Ns))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) (tptp.aa_nat_nat (tptp.nth_nat Ns) I2)))))) (forall ((H tptp.int) (L3 tptp.int) (H3 tptp.int)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.set_ord_atMost_int H)) (tptp.set_or1266510415728281911st_int L3 H3))))) (forall ((G tptp.fun_nat_nat) (M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat G) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M)) (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aTP_Lamm_jx G)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)))) (forall ((G tptp.fun_nat_int) (M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int G) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M)) (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aTP_Lamm_kc G)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)))) (forall ((C tptp.nat) (F tptp.fun_nat_nat) (A3 tptp.set_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat C) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A3)) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_nn C) F)) A3))) (forall ((C tptp.int) (F tptp.fun_nat_nat) (A3 tptp.set_nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int C) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A3)) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_fun1613598493704395220at_int (tptp.aTP_Lamm_no C) F)) A3))) (forall ((C tptp.int) (F tptp.fun_int_nat) (A3 tptp.set_int)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int C) (tptp.groups4541462559716669496nt_nat F A3)) (tptp.groups1705073143266064639nt_int (tptp.aa_fun2328901131235339916nt_int (tptp.aTP_Lamm_np C) F) A3))) (forall ((G tptp.fun_nat_nat) (M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat G) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) K))) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_jy G) K)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)))) (forall ((G tptp.fun_nat_int) (M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int G) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) K))) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_nq G) K)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)))) (forall ((A3 tptp.set_bool) (F tptp.fun_bo7282069421189217543nteger)) (=> (forall ((X3 tptp.bool)) (let ((_let_1 (tptp.aa_bool_Code_integer F X3))) (=> (tptp.pp (tptp.member_bool X3 A3)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger _let_1) tptp.one_one_Code_integer)))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.groups7272450149305381519nteger F A3)) tptp.one_one_Code_integer)))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_Code_integer)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_integer F X3))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger _let_1) tptp.one_one_Code_integer)))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger F) A3)) tptp.one_one_Code_integer)))) (forall ((A3 tptp.set_int) (F tptp.fun_int_Code_integer)) (=> (forall ((X3 tptp.int)) (let ((_let_1 (tptp.aa_int_Code_integer F X3))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger _let_1) tptp.one_one_Code_integer)))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.groups3827104343326376752nteger F A3)) tptp.one_one_Code_integer)))) (forall ((A3 tptp.set_bool) (F tptp.fun_bool_rat)) (=> (forall ((X3 tptp.bool)) (let ((_let_1 (tptp.aa_bool_rat F X3))) (=> (tptp.pp (tptp.member_bool X3 A3)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1) tptp.one_one_rat)))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups1259819201609700362ol_rat F A3)) tptp.one_one_rat)))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_rat)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat F X3))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1) tptp.one_one_rat)))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat F) A3)) tptp.one_one_rat)))) (forall ((A3 tptp.set_int) (F tptp.fun_int_rat)) (=> (forall ((X3 tptp.int)) (let ((_let_1 (tptp.aa_int_rat F X3))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1) tptp.one_one_rat)))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups1072433553688619179nt_rat F A3)) tptp.one_one_rat)))) (forall ((A3 tptp.set_bool) (F tptp.fun_bool_nat)) (=> (forall ((X3 tptp.bool)) (let ((_let_1 (tptp.aa_bool_nat F X3))) (=> (tptp.pp (tptp.member_bool X3 A3)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) tptp.one_one_nat)))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.groups1894949261696196098ol_nat F A3)) tptp.one_one_nat)))) (forall ((A3 tptp.set_int) (F tptp.fun_int_nat)) (=> (forall ((X3 tptp.int)) (let ((_let_1 (tptp.aa_int_nat F X3))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) tptp.one_one_nat)))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.groups1707563613775114915nt_nat F A3)) tptp.one_one_nat)))) (forall ((A3 tptp.set_bool) (F tptp.fun_bool_int)) (=> (forall ((X3 tptp.bool)) (let ((_let_1 (tptp.aa_bool_int F X3))) (=> (tptp.pp (tptp.member_bool X3 A3)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_1) tptp.one_one_int)))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.groups1892458791187145822ol_int F A3)) tptp.one_one_int)))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_nat)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat F X3))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) tptp.one_one_nat)))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat F) A3)) tptp.one_one_nat)))) (forall ((P tptp.fun_int_fun_int_bool) (Xs tptp.list_int)) (= (tptp.sorted_wrt_int P Xs) (forall ((I4 tptp.nat) (J3 tptp.nat)) (let ((_let_1 (tptp.nth_int Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) J3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J3) (tptp.size_size_list_int Xs))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P (tptp.aa_nat_int _let_1 I4)) (tptp.aa_nat_int _let_1 J3))))))))) (forall ((P tptp.fun_nat_fun_nat_bool) (Xs tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool (tptp.sorted_wrt_nat P) Xs)) (forall ((I4 tptp.nat) (J3 tptp.nat)) (let ((_let_1 (tptp.nth_nat Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) J3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J3) (tptp.aa_list_nat_nat tptp.size_size_list_nat Xs))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P (tptp.aa_nat_nat _let_1 I4)) (tptp.aa_nat_nat _let_1 J3))))))))) (forall ((P tptp.fun_bo1841576699660343469l_bool) (Xs tptp.list_bool)) (= (tptp.pp (tptp.aa_list_bool_bool (tptp.sorted_wrt_bool P) Xs)) (forall ((I4 tptp.nat) (J3 tptp.nat)) (let ((_let_1 (tptp.nth_bool Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) J3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J3) (tptp.size_size_list_bool Xs))) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool P (tptp.aa_nat_bool _let_1 I4)) (tptp.aa_nat_bool _let_1 J3))))))))) (forall ((P tptp.fun_int_fun_int_bool) (Xs tptp.list_int) (I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.nth_int Xs))) (=> (tptp.sorted_wrt_int P Xs) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) J)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J) (tptp.size_size_list_int Xs))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P (tptp.aa_nat_int _let_1 I2)) (tptp.aa_nat_int _let_1 J)))))))) (forall ((P tptp.fun_nat_fun_nat_bool) (Xs tptp.list_nat) (I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.nth_nat Xs))) (=> (tptp.pp (tptp.aa_list_nat_bool (tptp.sorted_wrt_nat P) Xs)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) J)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J) (tptp.aa_list_nat_nat tptp.size_size_list_nat Xs))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P (tptp.aa_nat_nat _let_1 I2)) (tptp.aa_nat_nat _let_1 J)))))))) (forall ((P tptp.fun_bo1841576699660343469l_bool) (Xs tptp.list_bool) (I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.nth_bool Xs))) (=> (tptp.pp (tptp.aa_list_bool_bool (tptp.sorted_wrt_bool P) Xs)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) J)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J) (tptp.size_size_list_bool Xs))) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool P (tptp.aa_nat_bool _let_1 I2)) (tptp.aa_nat_bool _let_1 J)))))))) (forall ((Xs tptp.list_int) (P tptp.fun_int_fun_int_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.size_size_list_int Xs)) tptp.one_one_nat)) (tptp.sorted_wrt_int P Xs))) (forall ((Xs tptp.list_nat) (P tptp.fun_nat_fun_nat_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_list_nat_nat tptp.size_size_list_nat Xs)) tptp.one_one_nat)) (tptp.pp (tptp.aa_list_nat_bool (tptp.sorted_wrt_nat P) Xs)))) (forall ((Xs tptp.list_bool) (P tptp.fun_bo1841576699660343469l_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.size_size_list_bool Xs)) tptp.one_one_nat)) (tptp.pp (tptp.aa_list_bool_bool (tptp.sorted_wrt_bool P) Xs)))) (forall ((G tptp.fun_nat_nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat N2) M))) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat G) _let_1) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_nat3783148529270815480at_nat (tptp.aTP_Lamm_jz G) N2) M)) _let_1)))) (forall ((G tptp.fun_nat_int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat N2) M))) (= (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int G) _let_1) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_nat_fun_nat_int (tptp.aa_nat1293065384339088724at_int (tptp.aTP_Lamm_nr G) N2) M)) _let_1)))) (forall ((P3 tptp.nat) (K tptp.nat) (G tptp.fun_nat_Code_integer) (H tptp.fun_nat_Code_integer)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) P3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) P3)) (= (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger (tptp.aa_fun589076786913273746nteger (tptp.aa_fun3918145391673965625nteger (tptp.aTP_Lamm_ns K) G) H)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat P3)) (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger (tptp.aa_fun589076786913273746nteger (tptp.aa_fun3918145391673965625nteger (tptp.aTP_Lamm_nt K) G) H)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat P3) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))))))) (forall ((P3 tptp.nat) (K tptp.nat) (G tptp.fun_nat_assn) (H tptp.fun_nat_assn)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) P3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) P3)) (= (tptp.groups6906906614972039071t_assn (tptp.aa_fun785744391571715112t_assn (tptp.aa_fun6591345337174305434t_assn (tptp.aTP_Lamm_nu K) G) H) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat P3)) (tptp.groups6906906614972039071t_assn (tptp.aa_fun785744391571715112t_assn (tptp.aa_fun6591345337174305434t_assn (tptp.aTP_Lamm_nv K) G) H) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat P3) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))))))) (forall ((P3 tptp.nat) (K tptp.nat) (G tptp.fun_nat_rat) (H tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) P3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) P3)) (= (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat (tptp.aa_fun765758790203053448at_rat (tptp.aa_fun3638354034882855594at_rat (tptp.aTP_Lamm_nw K) G) H)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat P3)) (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat (tptp.aa_fun765758790203053448at_rat (tptp.aa_fun3638354034882855594at_rat (tptp.aTP_Lamm_nx K) G) H)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat P3) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))))))) (forall ((P3 tptp.nat) (K tptp.nat) (G tptp.fun_nat_nat) (H tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) P3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) P3)) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aa_fun6854695580826382482at_nat (tptp.aTP_Lamm_ny K) G) H)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat P3)) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aa_fun6854695580826382482at_nat (tptp.aTP_Lamm_nz K) G) H)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat P3) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))))))) (forall ((P3 tptp.nat) (K tptp.nat) (G tptp.fun_nat_int) (H tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) P3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) P3)) (= (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_fun5565043122120104496at_int (tptp.aa_fun5140708168904641446at_int (tptp.aTP_Lamm_oa K) G) H)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat P3)) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_fun5565043122120104496at_int (tptp.aa_fun5140708168904641446at_int (tptp.aTP_Lamm_ob K) G) H)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat P3) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))))))) (forall ((Xs tptp.list_bool)) (= (tptp.pp (tptp.aa_list_bool_bool (tptp.sorted_wrt_bool tptp.ord_less_eq_bool) Xs)) (forall ((I4 tptp.nat) (J3 tptp.nat)) (let ((_let_1 (tptp.nth_bool Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) J3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J3) (tptp.size_size_list_bool Xs))) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.ord_less_eq_bool (tptp.aa_nat_bool _let_1 I4)) (tptp.aa_nat_bool _let_1 J3))))))))) (forall ((Xs tptp.list_rat)) (= (tptp.sorted_wrt_rat tptp.ord_less_eq_rat Xs) (forall ((I4 tptp.nat) (J3 tptp.nat)) (let ((_let_1 (tptp.nth_rat Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) J3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J3) (tptp.size_size_list_rat Xs))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat _let_1 I4)) (tptp.aa_nat_rat _let_1 J3))))))))) (forall ((Xs tptp.list_num)) (= (tptp.sorted_wrt_num tptp.ord_less_eq_num Xs) (forall ((I4 tptp.nat) (J3 tptp.nat)) (let ((_let_1 (tptp.nth_num Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) J3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J3) (tptp.size_size_list_num Xs))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num _let_1 I4)) (tptp.aa_nat_num _let_1 J3))))))))) (forall ((Xs tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool (tptp.sorted_wrt_nat tptp.ord_less_eq_nat) Xs)) (forall ((I4 tptp.nat) (J3 tptp.nat)) (let ((_let_1 (tptp.nth_nat Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) J3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J3) (tptp.aa_list_nat_nat tptp.size_size_list_nat Xs))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 I4)) (tptp.aa_nat_nat _let_1 J3))))))))) (forall ((Xs tptp.list_int)) (= (tptp.sorted_wrt_int tptp.ord_less_eq_int Xs) (forall ((I4 tptp.nat) (J3 tptp.nat)) (let ((_let_1 (tptp.nth_int Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I4) J3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J3) (tptp.size_size_list_int Xs))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int _let_1 I4)) (tptp.aa_nat_int _let_1 J3))))))))) (forall ((Xs tptp.list_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.size_size_list_bool Xs)) tptp.one_one_nat)) (tptp.pp (tptp.aa_list_bool_bool (tptp.sorted_wrt_bool tptp.ord_less_eq_bool) Xs)))) (forall ((Xs tptp.list_rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.size_size_list_rat Xs)) tptp.one_one_nat)) (tptp.sorted_wrt_rat tptp.ord_less_eq_rat Xs))) (forall ((Xs tptp.list_num)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.size_size_list_num Xs)) tptp.one_one_nat)) (tptp.sorted_wrt_num tptp.ord_less_eq_num Xs))) (forall ((Xs tptp.list_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_list_nat_nat tptp.size_size_list_nat Xs)) tptp.one_one_nat)) (tptp.pp (tptp.aa_list_nat_bool (tptp.sorted_wrt_nat tptp.ord_less_eq_nat) Xs)))) (forall ((Xs tptp.list_int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.size_size_list_int Xs)) tptp.one_one_nat)) (tptp.sorted_wrt_int tptp.ord_less_eq_int Xs))) (forall ((G tptp.fun_nat_Code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (let ((_let_2 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (tptp.groups3455450783089532116nteger G))) (= (tptp.aa_set871585252387937313nteger _let_3 (tptp.aa_nat_set_nat _let_2 _let_1)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_set871585252387937313nteger _let_3 (tptp.aa_nat_set_nat _let_2 N2))) (tptp.aa_nat_Code_integer G _let_1))))))) (forall ((G tptp.fun_nat_assn) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (let ((_let_2 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (= (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat _let_2 _let_1)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat _let_2 N2))) (tptp.aa_nat_assn G _let_1)))))) (forall ((G tptp.fun_nat_rat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (let ((_let_2 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (tptp.groups73079841787564623at_rat G))) (= (tptp.aa_set_nat_rat _let_3 (tptp.aa_nat_set_nat _let_2 _let_1)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_set_nat_rat _let_3 (tptp.aa_nat_set_nat _let_2 N2))) (tptp.aa_nat_rat G _let_1))))))) (forall ((G tptp.fun_nat_nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (let ((_let_2 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (tptp.groups708209901874060359at_nat G))) (= (tptp.aa_set_nat_nat _let_3 (tptp.aa_nat_set_nat _let_2 _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_set_nat_nat _let_3 (tptp.aa_nat_set_nat _let_2 N2))) (tptp.aa_nat_nat G _let_1))))))) (forall ((G tptp.fun_nat_int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (let ((_let_2 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (tptp.groups705719431365010083at_int G))) (= (tptp.aa_set_nat_int _let_3 (tptp.aa_nat_set_nat _let_2 _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_set_nat_int _let_3 (tptp.aa_nat_set_nat _let_2 N2))) (tptp.aa_nat_int G _let_1))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (tptp.groups3455450783089532116nteger G))) (let ((_let_3 (tptp.aa_nat_nat tptp.suc N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_3)) (= (tptp.aa_set871585252387937313nteger _let_2 (tptp.aa_nat_set_nat _let_1 _let_3)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer G _let_3)) (tptp.aa_set871585252387937313nteger _let_2 (tptp.aa_nat_set_nat _let_1 N2))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_assn)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_2)) (= (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat _let_1 _let_2)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.aa_nat_assn G _let_2)) (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat _let_1 N2)))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (tptp.groups73079841787564623at_rat G))) (let ((_let_3 (tptp.aa_nat_nat tptp.suc N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_3)) (= (tptp.aa_set_nat_rat _let_2 (tptp.aa_nat_set_nat _let_1 _let_3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat G _let_3)) (tptp.aa_set_nat_rat _let_2 (tptp.aa_nat_set_nat _let_1 N2))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (tptp.groups708209901874060359at_nat G))) (let ((_let_3 (tptp.aa_nat_nat tptp.suc N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_3)) (= (tptp.aa_set_nat_nat _let_2 (tptp.aa_nat_set_nat _let_1 _let_3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat G _let_3)) (tptp.aa_set_nat_nat _let_2 (tptp.aa_nat_set_nat _let_1 N2))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (tptp.groups705719431365010083at_int G))) (let ((_let_3 (tptp.aa_nat_nat tptp.suc N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_3)) (= (tptp.aa_set_nat_int _let_2 (tptp.aa_nat_set_nat _let_1 _let_3)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int G _let_3)) (tptp.aa_set_nat_int _let_2 (tptp.aa_nat_set_nat _let_1 N2))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.groups3455450783089532116nteger G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_set871585252387937313nteger _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer G M)) (tptp.aa_set871585252387937313nteger _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M)) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_assn)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.aa_nat_assn G M)) (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M)) N2)))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups73079841787564623at_rat G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_set_nat_rat _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat G M)) (tptp.aa_set_nat_rat _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M)) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.groups708209901874060359at_nat G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_set_nat_nat _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat G M)) (tptp.aa_set_nat_nat _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M)) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.groups705719431365010083at_int G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_set_nat_int _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int G M)) (tptp.aa_set_nat_int _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M)) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger G) _let_1)) (tptp.aa_nat_Code_integer G (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer G M)) (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger (tptp.aTP_Lamm_nk G)) _let_1)))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_assn)) (let ((_let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups6906906614972039071t_assn G _let_1)) (tptp.aa_nat_assn G (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.aa_nat_assn G M)) (tptp.groups6906906614972039071t_assn (tptp.aTP_Lamm_nl G) _let_1)))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat G) _let_1)) (tptp.aa_nat_rat G (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat G M)) (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat (tptp.aTP_Lamm_kb G)) _let_1)))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat G) _let_1)) (tptp.aa_nat_nat G (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat G M)) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aTP_Lamm_jx G)) _let_1)))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int G) _let_1)) (tptp.aa_nat_int G (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int G M)) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aTP_Lamm_kc G)) _let_1)))))) (forall ((G tptp.fun_na2338080690716861136at_nat) (N2 tptp.nat)) (= (tptp.groups6857163185585827899at_nat G (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat (tptp.aa_nat2240542744625857721at_nat G tptp.zero_zero_nat)) (tptp.groups6857163185585827899at_nat (tptp.aTP_Lamm_ka G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))))) (forall ((G tptp.fun_nat_rat) (N2 tptp.nat)) (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat G tptp.zero_zero_nat)) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_kb G)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))))) (forall ((G tptp.fun_nat_int) (N2 tptp.nat)) (= (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int G tptp.zero_zero_nat)) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_kc G)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))))) (forall ((G tptp.fun_nat_nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat G tptp.zero_zero_nat)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_jx G)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))))) (forall ((F tptp.fun_nat_rat) (I2 tptp.nat)) (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_oc F)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat I2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_nat_rat F tptp.zero_zero_nat)) (tptp.aa_nat_rat F (tptp.aa_nat_nat tptp.suc I2))))) (forall ((F tptp.fun_nat_int) (I2 tptp.nat)) (= (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_od F)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat I2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int F tptp.zero_zero_nat)) (tptp.aa_nat_int F (tptp.aa_nat_nat tptp.suc I2))))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N2) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat tptp.aTP_Lamm_fu) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2))))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger N2) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat tptp.aTP_Lamm_fu) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2))))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat tptp.aTP_Lamm_fu) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2))))) (forall ((F tptp.fun_nat_Code_integer) (A tptp.nat) (B tptp.nat)) (= (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger F) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat A) B)) (tptp.aa_Cod1783974652533396728nteger (tptp.set_fo1084959871951514735nteger (tptp.aTP_Lamm_oe F) A B) tptp.one_one_Code_integer))) (forall ((F tptp.fun_nat_assn) (A tptp.nat) (B tptp.nat)) (= (tptp.groups6906906614972039071t_assn F (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat A) B)) (tptp.aa_assn_assn (tptp.set_fo1959793692361082170t_assn (tptp.aTP_Lamm_of F) A B) tptp.one_one_assn))) (forall ((F tptp.fun_nat_rat) (A tptp.nat) (B tptp.nat)) (= (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat F) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat A) B)) (tptp.aa_rat_rat (tptp.set_fo1949268297981939178at_rat (tptp.aTP_Lamm_og F) A B) tptp.one_one_rat))) (forall ((F tptp.fun_nat_nat) (A tptp.nat) (B tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat F) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat A) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat (tptp.aTP_Lamm_oh F) A) B) tptp.one_one_nat))) (forall ((F tptp.fun_nat_int) (A tptp.nat) (B tptp.nat)) (= (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int F) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat A) B)) (tptp.aa_int_int (tptp.aa_nat_fun_int_int (tptp.set_fo2581907887559384638at_int (tptp.aTP_Lamm_oi F) A) B) tptp.one_one_int))) (forall ((Xs tptp.list_bool)) (= (tptp.pp (tptp.aa_list_bool_bool (tptp.sorted_wrt_bool tptp.ord_less_eq_bool) Xs)) (forall ((I4 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc I4))) (let ((_let_2 (tptp.nth_bool Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) (tptp.size_size_list_bool Xs))) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.ord_less_eq_bool (tptp.aa_nat_bool _let_2 I4)) (tptp.aa_nat_bool _let_2 _let_1))))))))) (forall ((Xs tptp.list_rat)) (= (tptp.sorted_wrt_rat tptp.ord_less_eq_rat Xs) (forall ((I4 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc I4))) (let ((_let_2 (tptp.nth_rat Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) (tptp.size_size_list_rat Xs))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat _let_2 I4)) (tptp.aa_nat_rat _let_2 _let_1))))))))) (forall ((Xs tptp.list_num)) (= (tptp.sorted_wrt_num tptp.ord_less_eq_num Xs) (forall ((I4 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc I4))) (let ((_let_2 (tptp.nth_num Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) (tptp.size_size_list_num Xs))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num _let_2 I4)) (tptp.aa_nat_num _let_2 _let_1))))))))) (forall ((Xs tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool (tptp.sorted_wrt_nat tptp.ord_less_eq_nat) Xs)) (forall ((I4 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc I4))) (let ((_let_2 (tptp.nth_nat Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) (tptp.aa_list_nat_nat tptp.size_size_list_nat Xs))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_2 I4)) (tptp.aa_nat_nat _let_2 _let_1))))))))) (forall ((Xs tptp.list_int)) (= (tptp.sorted_wrt_int tptp.ord_less_eq_int Xs) (forall ((I4 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc I4))) (let ((_let_2 (tptp.nth_int Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) (tptp.size_size_list_int Xs))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int _let_2 I4)) (tptp.aa_nat_int _let_2 _let_1))))))))) (forall ((Xs tptp.list_bool) (I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.nth_bool Xs))) (=> (tptp.pp (tptp.aa_list_bool_bool (tptp.sorted_wrt_bool tptp.ord_less_eq_bool) Xs)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) J)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J) (tptp.size_size_list_bool Xs))) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.ord_less_eq_bool (tptp.aa_nat_bool _let_1 I2)) (tptp.aa_nat_bool _let_1 J)))))))) (forall ((Xs tptp.list_rat) (I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.nth_rat Xs))) (=> (tptp.sorted_wrt_rat tptp.ord_less_eq_rat Xs) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) J)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J) (tptp.size_size_list_rat Xs))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat _let_1 I2)) (tptp.aa_nat_rat _let_1 J)))))))) (forall ((Xs tptp.list_num) (I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.nth_num Xs))) (=> (tptp.sorted_wrt_num tptp.ord_less_eq_num Xs) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) J)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J) (tptp.size_size_list_num Xs))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num _let_1 I2)) (tptp.aa_nat_num _let_1 J)))))))) (forall ((Xs tptp.list_nat) (I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.nth_nat Xs))) (=> (tptp.pp (tptp.aa_list_nat_bool (tptp.sorted_wrt_nat tptp.ord_less_eq_nat) Xs)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) J)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J) (tptp.aa_list_nat_nat tptp.size_size_list_nat Xs))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 I2)) (tptp.aa_nat_nat _let_1 J)))))))) (forall ((Xs tptp.list_int) (I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.nth_int Xs))) (=> (tptp.sorted_wrt_int tptp.ord_less_eq_int Xs) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) J)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J) (tptp.size_size_list_int Xs))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int _let_1 I2)) (tptp.aa_nat_int _let_1 J)))))))) (forall ((Xs tptp.list_bool)) (= (tptp.pp (tptp.aa_list_bool_bool (tptp.sorted_wrt_bool tptp.ord_less_eq_bool) Xs)) (forall ((I4 tptp.nat) (J3 tptp.nat)) (let ((_let_1 (tptp.nth_bool Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I4) J3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J3) (tptp.size_size_list_bool Xs))) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.ord_less_eq_bool (tptp.aa_nat_bool _let_1 I4)) (tptp.aa_nat_bool _let_1 J3))))))))) (forall ((Xs tptp.list_rat)) (= (tptp.sorted_wrt_rat tptp.ord_less_eq_rat Xs) (forall ((I4 tptp.nat) (J3 tptp.nat)) (let ((_let_1 (tptp.nth_rat Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I4) J3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J3) (tptp.size_size_list_rat Xs))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat _let_1 I4)) (tptp.aa_nat_rat _let_1 J3))))))))) (forall ((Xs tptp.list_num)) (= (tptp.sorted_wrt_num tptp.ord_less_eq_num Xs) (forall ((I4 tptp.nat) (J3 tptp.nat)) (let ((_let_1 (tptp.nth_num Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I4) J3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J3) (tptp.size_size_list_num Xs))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num _let_1 I4)) (tptp.aa_nat_num _let_1 J3))))))))) (forall ((Xs tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool (tptp.sorted_wrt_nat tptp.ord_less_eq_nat) Xs)) (forall ((I4 tptp.nat) (J3 tptp.nat)) (let ((_let_1 (tptp.nth_nat Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I4) J3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J3) (tptp.aa_list_nat_nat tptp.size_size_list_nat Xs))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 I4)) (tptp.aa_nat_nat _let_1 J3))))))))) (forall ((Xs tptp.list_int)) (= (tptp.sorted_wrt_int tptp.ord_less_eq_int Xs) (forall ((I4 tptp.nat) (J3 tptp.nat)) (let ((_let_1 (tptp.nth_int Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I4) J3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J3) (tptp.size_size_list_int Xs))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int _let_1 I4)) (tptp.aa_nat_int _let_1 J3))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_Code_integer) (P3 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2))) (let ((_let_2 (tptp.aa_nat_nat _let_1 P3))) (let ((_let_3 (tptp.aa_nat_nat _let_1 tptp.one_one_nat))) (let ((_let_4 (tptp.groups3455450783089532116nteger G))) (let ((_let_5 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_3)) (= (tptp.aa_set871585252387937313nteger _let_4 (tptp.aa_nat_set_nat _let_5 _let_2)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_set871585252387937313nteger _let_4 (tptp.aa_nat_set_nat _let_5 N2))) (tptp.aa_set871585252387937313nteger _let_4 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_assn) (P3 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2))) (let ((_let_2 (tptp.aa_nat_nat _let_1 P3))) (let ((_let_3 (tptp.aa_nat_nat _let_1 tptp.one_one_nat))) (let ((_let_4 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_3)) (= (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat _let_4 _let_2)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat _let_4 N2))) (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat _let_3) _let_2)))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_rat) (P3 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2))) (let ((_let_2 (tptp.aa_nat_nat _let_1 P3))) (let ((_let_3 (tptp.aa_nat_nat _let_1 tptp.one_one_nat))) (let ((_let_4 (tptp.groups73079841787564623at_rat G))) (let ((_let_5 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_3)) (= (tptp.aa_set_nat_rat _let_4 (tptp.aa_nat_set_nat _let_5 _let_2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_set_nat_rat _let_4 (tptp.aa_nat_set_nat _let_5 N2))) (tptp.aa_set_nat_rat _let_4 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_nat) (P3 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2))) (let ((_let_2 (tptp.aa_nat_nat _let_1 P3))) (let ((_let_3 (tptp.aa_nat_nat _let_1 tptp.one_one_nat))) (let ((_let_4 (tptp.groups708209901874060359at_nat G))) (let ((_let_5 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_3)) (= (tptp.aa_set_nat_nat _let_4 (tptp.aa_nat_set_nat _let_5 _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_set_nat_nat _let_4 (tptp.aa_nat_set_nat _let_5 N2))) (tptp.aa_set_nat_nat _let_4 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_int) (P3 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2))) (let ((_let_2 (tptp.aa_nat_nat _let_1 P3))) (let ((_let_3 (tptp.aa_nat_nat _let_1 tptp.one_one_nat))) (let ((_let_4 (tptp.groups705719431365010083at_int G))) (let ((_let_5 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_3)) (= (tptp.aa_set_nat_int _let_4 (tptp.aa_nat_set_nat _let_5 _let_2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_set_nat_int _let_4 (tptp.aa_nat_set_nat _let_5 N2))) (tptp.aa_set_nat_int _let_4 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((A tptp.rat) (N2 tptp.nat)) (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_oj A)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))) tptp.one_one_rat)) N2))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (= (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2)) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat tptp.aTP_Lamm_fu) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc N2)) M)))))) (forall ((X tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger X))) (let ((_let_2 (tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger _let_2 X)) (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger _let_1) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_Cod1783974652533396728nteger _let_2 (tptp.aa_nat_Code_integer _let_1 (tptp.aa_nat_nat tptp.suc N2))))))) (forall ((X tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_power_rat X))) (let ((_let_2 (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat tptp.one_one_rat))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat _let_2 X)) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat _let_1) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_rat_rat _let_2 (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat tptp.suc N2))))))) (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int X))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.minus_minus_int tptp.one_one_int))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int _let_2 X)) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int _let_1) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_int_int _let_2 (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat tptp.suc N2))))))) (forall ((A tptp.rat) (N2 tptp.nat)) (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat A) (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat (tptp.aTP_Lamm_ok A)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger A) (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger (tptp.aTP_Lamm_ol A)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))) (forall ((A tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat A) (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_om A)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))) (forall ((A tptp.int) (N2 tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int A) (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_int_fun_nat_int tptp.aTP_Lamm_on A)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))) (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.code_integer)) (let ((_let_1 (tptp.power_8256067586552552935nteger X))) (let ((_let_2 (tptp.groups7501900531339628137nteger _let_1))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_set871585252387937313nteger _let_2 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer _let_1 M)) (tptp.aa_set871585252387937313nteger _let_2 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.rat)) (let ((_let_1 (tptp.power_power_rat X))) (let ((_let_2 (tptp.groups2906978787729119204at_rat _let_1))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_set_nat_rat _let_2 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat _let_1 M)) (tptp.aa_set_nat_rat _let_2 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.int)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int X))) (let ((_let_2 (tptp.groups3539618377306564664at_int _let_1))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_set_nat_int _let_2 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_1 M)) (tptp.aa_set_nat_int _let_2 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M))))))))) (forall ((A tptp.rat) (N2 tptp.nat)) (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat A) N2) (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat (tptp.aa_nat_fun_nat_rat (tptp.aTP_Lamm_oo A) N2)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger A) N2) (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger (tptp.aa_nat2010205248571845816nteger (tptp.aTP_Lamm_op A) N2)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)))) (forall ((A tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat A) N2) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_oq A) N2)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)))) (forall ((A tptp.int) (N2 tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int A) N2) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_or A) N2)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat M)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2)) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat tptp.aTP_Lamm_fu) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) tptp.one_one_nat)) M))))) (forall ((A tptp.rat) (M tptp.nat)) (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_os A)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) M)) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat A) tptp.one_one_rat)) M)))) (forall ((A tptp.rat) (N2 tptp.nat)) (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat A) (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat (tptp.aa_nat_fun_nat_rat (tptp.aTP_Lamm_oo A) N2)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger A) (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger (tptp.aa_nat2010205248571845816nteger (tptp.aTP_Lamm_op A) N2)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))) (forall ((A tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat A) (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_oq A) N2)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))) (forall ((A tptp.int) (N2 tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int A) (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_or A) N2)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))) (forall ((P3 tptp.nat) (K tptp.nat) (G tptp.fun_nat_Code_integer) (H tptp.fun_nat_Code_integer)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) P3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) P3)) (= (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger (tptp.aa_fun589076786913273746nteger (tptp.aa_fun3918145391673965625nteger (tptp.aTP_Lamm_ot K) G) H)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat P3)) (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger (tptp.aa_fun589076786913273746nteger (tptp.aa_fun3918145391673965625nteger (tptp.aTP_Lamm_nt K) G) H)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat P3) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))))))) (forall ((P3 tptp.nat) (K tptp.nat) (G tptp.fun_na2338080690716861136at_nat) (H tptp.fun_na2338080690716861136at_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) P3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) P3)) (= (tptp.groups6857163185585827899at_nat (tptp.aa_fun4141531684813184444at_nat (tptp.aa_fun8230936523094545239at_nat (tptp.aTP_Lamm_ou K) G) H) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat P3)) (tptp.groups6857163185585827899at_nat (tptp.aa_fun4141531684813184444at_nat (tptp.aa_fun8230936523094545239at_nat (tptp.aTP_Lamm_ov K) G) H) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat P3) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))))))) (forall ((P3 tptp.nat) (K tptp.nat) (G tptp.fun_nat_rat) (H tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) P3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) P3)) (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aa_fun765758790203053448at_rat (tptp.aa_fun3638354034882855594at_rat (tptp.aTP_Lamm_ow K) G) H)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat P3)) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aa_fun765758790203053448at_rat (tptp.aa_fun3638354034882855594at_rat (tptp.aTP_Lamm_nx K) G) H)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat P3) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))))))) (forall ((P3 tptp.nat) (K tptp.nat) (G tptp.fun_nat_int) (H tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) P3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) P3)) (= (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aa_fun5565043122120104496at_int (tptp.aa_fun5140708168904641446at_int (tptp.aTP_Lamm_ox K) G) H)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat P3)) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aa_fun5565043122120104496at_int (tptp.aa_fun5140708168904641446at_int (tptp.aTP_Lamm_ob K) G) H)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat P3) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))))))) (forall ((P3 tptp.nat) (K tptp.nat) (G tptp.fun_nat_nat) (H tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) P3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) P3)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aa_fun6854695580826382482at_nat (tptp.aTP_Lamm_oy K) G) H)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat P3)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aa_fun6854695580826382482at_nat (tptp.aTP_Lamm_nz K) G) H)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat P3) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))))))) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_oz N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) tptp.zero_zero_rat))) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aa_nat_fun_nat_int tptp.aTP_Lamm_pa N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) tptp.zero_zero_int))) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger (tptp.aTP_Lamm_pb N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) tptp.zero_z3403309356797280102nteger))) (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.one_one_nat)) (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_pc N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) tptp.zero_zero_rat))) (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.one_one_nat)) (= (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aa_nat_fun_nat_int tptp.aTP_Lamm_pd N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) tptp.zero_zero_int))) (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.one_one_nat)) (= (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger (tptp.aTP_Lamm_pe N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) tptp.zero_z3403309356797280102nteger))) (forall ((Z tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc N2))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat Z) _let_2)) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Z) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat tptp.one_one_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat _let_1)))) _let_2)) (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat (tptp.aTP_Lamm_pf Z)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N2)) tptp.one_one_nat))))))) (forall ((A3 tptp.set_nat) (C tptp.fun_nat_rat) (D2 tptp.fun_nat_rat)) (let ((_let_1 (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_pg C) D2)) A3))) (let ((_let_2 (and (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) A3))))) (and (=> _let_2 (= _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_nat_rat C tptp.zero_zero_nat)) (tptp.aa_nat_rat D2 tptp.zero_zero_nat)))) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))) (forall ((M tptp.nat) (Xs tptp.list_int) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.size_size_list_int Xs))) (= (tptp.nth_Pr3440142176431000676at_int (tptp.enumerate_int N2 Xs) M) (tptp.product_Pair_nat_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) M) (tptp.aa_nat_int (tptp.nth_int Xs) M))))) (forall ((M tptp.nat) (Xs tptp.list_nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_list_nat_nat tptp.size_size_list_nat Xs))) (= (tptp.aa_nat7603221163087113075at_nat (tptp.nth_Pr7617993195940197384at_nat (tptp.enumerate_nat N2 Xs)) M) (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) M)) (tptp.aa_nat_nat (tptp.nth_nat Xs) M))))) (forall ((M tptp.nat) (Xs tptp.list_bool) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.size_size_list_bool Xs))) (= (tptp.nth_Pr396318242284072693t_bool (tptp.enumerate_bool N2 Xs) M) (tptp.produc3913204875133826030t_bool (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) M) (tptp.aa_nat_bool (tptp.nth_bool Xs) M))))) (forall ((A tptp.rat) (K tptp.nat)) (= (tptp.aa_nat_rat (tptp.gbinomial_rat A) K) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat (tptp.aTP_Lamm_md A)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K))) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat K)))) (forall ((A tptp.code_natural) (K tptp.nat)) (= (tptp.aa_nat_Code_natural (tptp.gbinom7368847122466276068atural A) K) (tptp.divide5121882707175180666atural (tptp.groups2279045934846249631atural (tptp.aTP_Lamm_me A) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K)) (tptp.aa_nat_Code_natural tptp.semiri2447717529341329178atural K)))) (forall ((A tptp.code_integer) (K tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.gbinom8545251970709558553nteger A) K) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger (tptp.aTP_Lamm_mf A)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K))) (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger K)))) (forall ((A tptp.nat) (K tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gbinomial_nat A) K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_mg A)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K))) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat K)))) (forall ((A tptp.int) (K tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.gbinomial_int A) K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_int_fun_nat_int tptp.aTP_Lamm_mh A)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K))) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int K)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_num_num tptp.bit0 N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_num_num tptp.bit0 N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) N2)))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) tptp.one)))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num tptp.one) N2))) (forall ((I2 tptp.bool) (L tptp.bool) (U tptp.bool)) (= (tptp.pp (tptp.member_bool I2 (tptp.set_or8576162586734908840n_bool L U))) (and (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.ord_less_eq_bool L) I2)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.ord_less_bool I2) U))))) (forall ((I2 tptp.set_nat) (L tptp.set_nat) (U tptp.set_nat)) (= (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat I2) (tptp.set_or3540276404033026485et_nat L U))) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat L) I2)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat I2) U))))) (forall ((I2 tptp.assn) (L tptp.assn) (U tptp.assn)) (= (tptp.member_assn I2 (tptp.set_or5523502641901747543n_assn L U)) (and (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn L) I2)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn I2) U))))) (forall ((I2 tptp.set_int) (L tptp.set_int) (U tptp.set_int)) (= (tptp.member_set_int I2 (tptp.set_or8585797421378605585et_int L U)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int L) I2)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int I2) U))))) (forall ((I2 tptp.rat) (L tptp.rat) (U tptp.rat)) (= (tptp.member_rat I2 (tptp.set_or4029947393144176647an_rat L U)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat L) I2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat I2) U))))) (forall ((I2 tptp.num) (L tptp.num) (U tptp.num)) (= (tptp.member_num I2 (tptp.set_or1222409239386451017an_num L U)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num L) I2)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num I2) U))))) (forall ((I2 tptp.nat) (L tptp.nat) (U tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I2) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat L) U))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat L) I2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) U))))) (forall ((I2 tptp.int) (L tptp.int) (U tptp.int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I2) (tptp.set_or4662586982721622107an_int L U))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int L) I2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int I2) U))))) (forall ((I2 tptp.code_integer) (L tptp.code_integer) (U tptp.code_integer)) (= (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I2) (tptp.set_or8404916559141939852nteger L U))) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger L) I2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger I2) U))))) (forall ((B tptp.bool) (A tptp.bool)) (=> (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.ord_less_eq_bool B) A)) (= (tptp.set_or8576162586734908840n_bool A B) tptp.bot_bot_set_bool))) (forall ((B tptp.set_int) (A tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B) A)) (= (tptp.set_or8585797421378605585et_int A B) tptp.bot_bot_set_set_int))) (forall ((B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (= (tptp.set_or4029947393144176647an_rat A B) tptp.bot_bot_set_rat))) (forall ((B tptp.num) (A tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (= (tptp.set_or1222409239386451017an_num A B) tptp.bot_bot_set_num))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (= (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat A) B) tptp.bot_bot_set_nat))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (= (tptp.set_or4662586982721622107an_int A B) tptp.bot_bot_set_int))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) A)) (= (tptp.set_or8404916559141939852nteger A B) tptp.bot_bo3990330152332043303nteger))) (forall ((A tptp.rat) (B tptp.rat)) (= (not (tptp.finite_finite_rat (tptp.set_or633870826150836451st_rat A B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)))) (forall ((A tptp.bool) (B tptp.bool)) (= (= tptp.bot_bot_set_bool (tptp.set_or8576162586734908840n_bool A B)) (not (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.ord_less_bool A) B))))) (forall ((A tptp.assn) (B tptp.assn)) (= (= tptp.bot_bot_set_assn (tptp.set_or5523502641901747543n_assn A B)) (not (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) B))))) (forall ((A tptp.rat) (B tptp.rat)) (= (= tptp.bot_bot_set_rat (tptp.set_or4029947393144176647an_rat A B)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))))) (forall ((A tptp.num) (B tptp.num)) (= (= tptp.bot_bot_set_num (tptp.set_or1222409239386451017an_num A B)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B))))) (forall ((A tptp.nat) (B tptp.nat)) (= (= tptp.bot_bot_set_nat (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat A) B)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B))))) (forall ((A tptp.int) (B tptp.int)) (= (= tptp.bot_bot_set_int (tptp.set_or4662586982721622107an_int A B)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= tptp.bot_bo3990330152332043303nteger (tptp.set_or8404916559141939852nteger A B)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B))))) (forall ((A tptp.bool) (B tptp.bool)) (= (= (tptp.set_or8576162586734908840n_bool A B) tptp.bot_bot_set_bool) (not (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.ord_less_bool A) B))))) (forall ((A tptp.assn) (B tptp.assn)) (= (= (tptp.set_or5523502641901747543n_assn A B) tptp.bot_bot_set_assn) (not (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn A) B))))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (tptp.set_or4029947393144176647an_rat A B) tptp.bot_bot_set_rat) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))))) (forall ((A tptp.num) (B tptp.num)) (= (= (tptp.set_or1222409239386451017an_num A B) tptp.bot_bot_set_num) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B))))) (forall ((A tptp.nat) (B tptp.nat)) (= (= (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat A) B) tptp.bot_bot_set_nat) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B))))) (forall ((A tptp.int) (B tptp.int)) (= (= (tptp.set_or4662586982721622107an_int A B) tptp.bot_bot_set_int) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (tptp.set_or8404916559141939852nteger A B) tptp.bot_bo3990330152332043303nteger) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B))))) (forall ((A tptp.rat) (B tptp.rat)) (= (not (tptp.finite_finite_rat (tptp.set_or4029947393144176647an_rat A B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)))) (forall ((I2 tptp.rat) (J tptp.rat) (M tptp.rat) (N2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat J))) (= (tptp.ord_less_eq_set_rat (tptp.set_or4029947393144176647an_rat I2 J) (tptp.set_or4029947393144176647an_rat M N2)) (or (tptp.pp (tptp.aa_rat_bool _let_1 I2)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat M) I2)) (tptp.pp (tptp.aa_rat_bool _let_1 N2))))))) (forall ((I2 tptp.num) (J tptp.num) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num J))) (= (tptp.ord_less_eq_set_num (tptp.set_or1222409239386451017an_num I2 J) (tptp.set_or1222409239386451017an_num M N2)) (or (tptp.pp (tptp.aa_num_bool _let_1 I2)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) I2)) (tptp.pp (tptp.aa_num_bool _let_1 N2))))))) (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat J))) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat I2) J)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2))) (or (tptp.pp (tptp.aa_nat_bool _let_1 I2)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) I2)) (tptp.pp (tptp.aa_nat_bool _let_1 N2))))))) (forall ((I2 tptp.int) (J tptp.int) (M tptp.int) (N2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int J))) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.set_or4662586982721622107an_int I2 J)) (tptp.set_or4662586982721622107an_int M N2))) (or (tptp.pp (tptp.aa_int_bool _let_1 I2)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int M) I2)) (tptp.pp (tptp.aa_int_bool _let_1 N2))))))) (forall ((I2 tptp.code_integer) (J tptp.code_integer) (M tptp.code_integer) (N2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger J))) (= (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger (tptp.set_or8404916559141939852nteger I2 J)) (tptp.set_or8404916559141939852nteger M N2))) (or (tptp.pp (tptp.aa_Code_integer_bool _let_1 I2)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger M) I2)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 N2))))))) (forall ((I2 tptp.rat) (N2 tptp.rat) (M tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat I2) N2)) (= (tptp.minus_minus_set_rat (tptp.set_or4029947393144176647an_rat I2 M) (tptp.set_or4029947393144176647an_rat I2 N2)) (tptp.set_or4029947393144176647an_rat N2 M)))) (forall ((I2 tptp.num) (N2 tptp.num) (M tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num I2) N2)) (= (tptp.minus_minus_set_num (tptp.set_or1222409239386451017an_num I2 M) (tptp.set_or1222409239386451017an_num I2 N2)) (tptp.set_or1222409239386451017an_num N2 M)))) (forall ((I2 tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat I2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) N2)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat (tptp.aa_nat_set_nat _let_1 M)) (tptp.aa_nat_set_nat _let_1 N2)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat N2) M))))) (forall ((I2 tptp.int) (N2 tptp.int) (M tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I2) N2)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int (tptp.set_or4662586982721622107an_int I2 M)) (tptp.set_or4662586982721622107an_int I2 N2)) (tptp.set_or4662586982721622107an_int N2 M)))) (forall ((I2 tptp.code_integer) (N2 tptp.code_integer) (M tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger I2) N2)) (= (tptp.minus_2355218937544613996nteger (tptp.set_or8404916559141939852nteger I2 M) (tptp.set_or8404916559141939852nteger I2 N2)) (tptp.set_or8404916559141939852nteger N2 M)))) (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N2) K) tptp.zero_zero_nat) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) K)))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num tptp.bit0 M)) tptp.one)))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num tptp.one) (tptp.aa_num_num tptp.bit0 N2)))) (forall ((S tptp.set_bool) (A tptp.bool) (B tptp.fun_bo7282069421189217543nteger)) (let ((_let_1 (tptp.groups1682264926906508858nteger (tptp.aa_fun1377107737837666940nteger (tptp.aTP_Lamm_ph A) B) S))) (let ((_let_2 (tptp.pp (tptp.member_bool A S)))) (=> (tptp.finite_finite_bool S) (and (=> _let_2 (= _let_1 (tptp.aa_bool_Code_integer B A))) (=> (not _let_2) (= _let_1 tptp.zero_z3403309356797280102nteger))))))) (forall ((S tptp.set_nat) (A tptp.nat) (B tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger (tptp.aa_fun589076786913273746nteger (tptp.aTP_Lamm_pi A) B)) S))) (let ((_let_2 (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A) S)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (and (=> _let_2 (= _let_1 (tptp.aa_nat_Code_integer B A))) (=> (not _let_2) (= _let_1 tptp.zero_z3403309356797280102nteger))))))) (forall ((S tptp.set_int) (A tptp.int) (B tptp.fun_int_Code_integer)) (let ((_let_1 (tptp.groups7873554091576472773nteger (tptp.aa_fun5304498221708291146nteger (tptp.aTP_Lamm_pj A) B) S))) (let ((_let_2 (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A) S)))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (and (=> _let_2 (= _let_1 (tptp.aa_int_Code_integer B A))) (=> (not _let_2) (= _let_1 tptp.zero_z3403309356797280102nteger))))))) (forall ((S tptp.set_Code_integer) (A tptp.code_integer) (B tptp.fun_Co8499238673658658103nteger)) (let ((_let_1 (tptp.groups879477027807139574nteger (tptp.aa_fun4435975922079263404nteger (tptp.aTP_Lamm_pk A) B) S))) (let ((_let_2 (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A) S)))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S)) (and (=> _let_2 (= _let_1 (tptp.aa_Cod1783974652533396728nteger B A))) (=> (not _let_2) (= _let_1 tptp.zero_z3403309356797280102nteger))))))) (forall ((S tptp.set_bool) (A tptp.bool) (B tptp.fun_bool_rat)) (let ((_let_1 (tptp.groups5133371213642249141ol_rat (tptp.aa_fun224000846028461884ol_rat (tptp.aTP_Lamm_pl A) B) S))) (let ((_let_2 (tptp.pp (tptp.member_bool A S)))) (=> (tptp.finite_finite_bool S) (and (=> _let_2 (= _let_1 (tptp.aa_bool_rat B A))) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat))))))) (forall ((S tptp.set_nat) (A tptp.nat) (B tptp.fun_nat_rat)) (let ((_let_1 (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_pm A) B)) S))) (let ((_let_2 (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A) S)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (and (=> _let_2 (= _let_1 (tptp.aa_nat_rat B A))) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat))))))) (forall ((S tptp.set_int) (A tptp.int) (B tptp.fun_int_rat)) (let ((_let_1 (tptp.groups3906332499630173760nt_rat (tptp.aa_fun1481061427733998144nt_rat (tptp.aTP_Lamm_pn A) B) S))) (let ((_let_2 (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A) S)))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (and (=> _let_2 (= _let_1 (tptp.aa_int_rat B A))) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat))))))) (forall ((S tptp.set_Code_integer) (A tptp.code_integer) (B tptp.fun_Code_integer_rat)) (let ((_let_1 (tptp.groups6602215022474089585er_rat (tptp.aa_fun8169474305930283170er_rat (tptp.aTP_Lamm_po A) B) S))) (let ((_let_2 (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A) S)))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S)) (and (=> _let_2 (= _let_1 (tptp.aa_Code_integer_rat B A))) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat))))))) (forall ((S tptp.set_bool) (A tptp.bool) (B tptp.fun_bool_nat)) (let ((_let_1 (tptp.groups5768501273728744877ol_nat (tptp.aa_fun9101744387563128124ol_nat (tptp.aTP_Lamm_pp A) B) S))) (let ((_let_2 (tptp.pp (tptp.member_bool A S)))) (=> (tptp.finite_finite_bool S) (and (=> _let_2 (= _let_1 (tptp.aa_bool_nat B A))) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat))))))) (forall ((S tptp.set_int) (A tptp.int) (B tptp.fun_int_nat)) (let ((_let_1 (tptp.groups4541462559716669496nt_nat (tptp.aa_fun6506752150744536624nt_nat (tptp.aTP_Lamm_pq A) B) S))) (let ((_let_2 (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A) S)))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (and (=> _let_2 (= _let_1 (tptp.aa_int_nat B A))) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat))))))) (forall ((S tptp.set_bool) (A tptp.bool) (B tptp.fun_bo7282069421189217543nteger)) (let ((_let_1 (tptp.groups1682264926906508858nteger (tptp.aa_fun1377107737837666940nteger (tptp.aTP_Lamm_pr A) B) S))) (let ((_let_2 (tptp.pp (tptp.member_bool A S)))) (=> (tptp.finite_finite_bool S) (and (=> _let_2 (= _let_1 (tptp.aa_bool_Code_integer B A))) (=> (not _let_2) (= _let_1 tptp.zero_z3403309356797280102nteger))))))) (forall ((S tptp.set_nat) (A tptp.nat) (B tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger (tptp.aa_fun589076786913273746nteger (tptp.aTP_Lamm_ps A) B)) S))) (let ((_let_2 (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A) S)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (and (=> _let_2 (= _let_1 (tptp.aa_nat_Code_integer B A))) (=> (not _let_2) (= _let_1 tptp.zero_z3403309356797280102nteger))))))) (forall ((S tptp.set_int) (A tptp.int) (B tptp.fun_int_Code_integer)) (let ((_let_1 (tptp.groups7873554091576472773nteger (tptp.aa_fun5304498221708291146nteger (tptp.aTP_Lamm_pt A) B) S))) (let ((_let_2 (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A) S)))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (and (=> _let_2 (= _let_1 (tptp.aa_int_Code_integer B A))) (=> (not _let_2) (= _let_1 tptp.zero_z3403309356797280102nteger))))))) (forall ((S tptp.set_Code_integer) (A tptp.code_integer) (B tptp.fun_Co8499238673658658103nteger)) (let ((_let_1 (tptp.groups879477027807139574nteger (tptp.aa_fun4435975922079263404nteger (tptp.aTP_Lamm_pu A) B) S))) (let ((_let_2 (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A) S)))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S)) (and (=> _let_2 (= _let_1 (tptp.aa_Cod1783974652533396728nteger B A))) (=> (not _let_2) (= _let_1 tptp.zero_z3403309356797280102nteger))))))) (forall ((S tptp.set_bool) (A tptp.bool) (B tptp.fun_bool_rat)) (let ((_let_1 (tptp.groups5133371213642249141ol_rat (tptp.aa_fun224000846028461884ol_rat (tptp.aTP_Lamm_pv A) B) S))) (let ((_let_2 (tptp.pp (tptp.member_bool A S)))) (=> (tptp.finite_finite_bool S) (and (=> _let_2 (= _let_1 (tptp.aa_bool_rat B A))) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat))))))) (forall ((S tptp.set_nat) (A tptp.nat) (B tptp.fun_nat_rat)) (let ((_let_1 (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_pw A) B)) S))) (let ((_let_2 (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A) S)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (and (=> _let_2 (= _let_1 (tptp.aa_nat_rat B A))) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat))))))) (forall ((S tptp.set_int) (A tptp.int) (B tptp.fun_int_rat)) (let ((_let_1 (tptp.groups3906332499630173760nt_rat (tptp.aa_fun1481061427733998144nt_rat (tptp.aTP_Lamm_px A) B) S))) (let ((_let_2 (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A) S)))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (and (=> _let_2 (= _let_1 (tptp.aa_int_rat B A))) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat))))))) (forall ((S tptp.set_Code_integer) (A tptp.code_integer) (B tptp.fun_Code_integer_rat)) (let ((_let_1 (tptp.groups6602215022474089585er_rat (tptp.aa_fun8169474305930283170er_rat (tptp.aTP_Lamm_py A) B) S))) (let ((_let_2 (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A) S)))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S)) (and (=> _let_2 (= _let_1 (tptp.aa_Code_integer_rat B A))) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat))))))) (forall ((S tptp.set_bool) (A tptp.bool) (B tptp.fun_bool_nat)) (let ((_let_1 (tptp.groups5768501273728744877ol_nat (tptp.aa_fun9101744387563128124ol_nat (tptp.aTP_Lamm_pz A) B) S))) (let ((_let_2 (tptp.pp (tptp.member_bool A S)))) (=> (tptp.finite_finite_bool S) (and (=> _let_2 (= _let_1 (tptp.aa_bool_nat B A))) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat))))))) (forall ((S tptp.set_int) (A tptp.int) (B tptp.fun_int_nat)) (let ((_let_1 (tptp.groups4541462559716669496nt_nat (tptp.aa_fun6506752150744536624nt_nat (tptp.aTP_Lamm_qa A) B) S))) (let ((_let_2 (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A) S)))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (and (=> _let_2 (= _let_1 (tptp.aa_int_nat B A))) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat))))))) (forall ((K tptp.rat) (I2 tptp.rat) (J tptp.rat)) (= (tptp.image_rat_rat (tptp.aa_rat_fun_rat_rat tptp.aTP_Lamm_hs K) (tptp.set_or4029947393144176647an_rat I2 J)) (tptp.set_or4029947393144176647an_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat I2) K) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat J) K)))) (forall ((K tptp.nat) (I2 tptp.nat) (J tptp.nat)) (= (tptp.image_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_hu K) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat I2) J)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) K)))) (forall ((K tptp.int) (I2 tptp.int) (J tptp.int)) (= (tptp.image_int_int (tptp.aa_int_fun_int_int tptp.aTP_Lamm_ht K) (tptp.set_or4662586982721622107an_int I2 J)) (tptp.set_or4662586982721622107an_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I2) K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) K)))) (forall ((K tptp.code_integer) (I2 tptp.code_integer) (J tptp.code_integer)) (= (tptp.image_4470545334726330049nteger (tptp.aTP_Lamm_hv K) (tptp.set_or8404916559141939852nteger I2 J)) (tptp.set_or8404916559141939852nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger I2) K) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger J) K)))) (forall ((S tptp.set_bool) (A tptp.bool) (B tptp.fun_bo7282069421189217543nteger)) (let ((_let_1 (tptp.groups7272450149305381519nteger (tptp.aa_fun1377107737837666940nteger (tptp.aTP_Lamm_qb A) B) S))) (let ((_let_2 (tptp.pp (tptp.member_bool A S)))) (=> (tptp.finite_finite_bool S) (and (=> _let_2 (= _let_1 (tptp.aa_bool_Code_integer B A))) (=> (not _let_2) (= _let_1 tptp.one_one_Code_integer))))))) (forall ((S tptp.set_nat) (A tptp.nat) (B tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger (tptp.aa_fun589076786913273746nteger (tptp.aTP_Lamm_qc A) B)) S))) (let ((_let_2 (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A) S)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (and (=> _let_2 (= _let_1 (tptp.aa_nat_Code_integer B A))) (=> (not _let_2) (= _let_1 tptp.one_one_Code_integer))))))) (forall ((S tptp.set_int) (A tptp.int) (B tptp.fun_int_Code_integer)) (let ((_let_1 (tptp.groups3827104343326376752nteger (tptp.aa_fun5304498221708291146nteger (tptp.aTP_Lamm_qd A) B) S))) (let ((_let_2 (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A) S)))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (and (=> _let_2 (= _let_1 (tptp.aa_int_Code_integer B A))) (=> (not _let_2) (= _let_1 tptp.one_one_Code_integer))))))) (forall ((S tptp.set_Code_integer) (A tptp.code_integer) (B tptp.fun_Co8499238673658658103nteger)) (let ((_let_1 (tptp.groups3674199335183972705nteger (tptp.aa_fun4435975922079263404nteger (tptp.aTP_Lamm_qe A) B) S))) (let ((_let_2 (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A) S)))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S)) (and (=> _let_2 (= _let_1 (tptp.aa_Cod1783974652533396728nteger B A))) (=> (not _let_2) (= _let_1 tptp.one_one_Code_integer))))))) (forall ((S tptp.set_bool) (A tptp.bool) (B tptp.fun_bool_assn)) (let ((_let_1 (tptp.groups4835110720589548378l_assn (tptp.aa_fun923664478788943164l_assn (tptp.aTP_Lamm_qf A) B) S))) (let ((_let_2 (tptp.pp (tptp.member_bool A S)))) (=> (tptp.finite_finite_bool S) (and (=> _let_2 (= _let_1 (tptp.aa_bool_assn B A))) (=> (not _let_2) (= _let_1 tptp.one_one_assn))))))) (forall ((S tptp.set_nat) (A tptp.nat) (B tptp.fun_nat_assn)) (let ((_let_1 (tptp.groups6906906614972039071t_assn (tptp.aa_fun785744391571715112t_assn (tptp.aTP_Lamm_qg A) B) S))) (let ((_let_2 (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A) S)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (and (=> _let_2 (= _let_1 (tptp.aa_nat_assn B A))) (=> (not _let_2) (= _let_1 tptp.one_one_assn))))))) (forall ((S tptp.set_int) (A tptp.int) (B tptp.fun_int_assn)) (let ((_let_1 (tptp.groups7882442080178216443t_assn (tptp.aa_fun919007281442365664t_assn (tptp.aTP_Lamm_qh A) B) S))) (let ((_let_2 (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A) S)))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (and (=> _let_2 (= _let_1 (tptp.aa_int_assn B A))) (=> (not _let_2) (= _let_1 tptp.one_one_assn))))))) (forall ((S tptp.set_Code_integer) (A tptp.code_integer) (B tptp.fun_Co4490034186337852034r_assn)) (let ((_let_1 (tptp.groups1304777262505850412r_assn (tptp.aa_fun4119713415300323650r_assn (tptp.aTP_Lamm_qi A) B) S))) (let ((_let_2 (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A) S)))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S)) (and (=> _let_2 (= _let_1 (tptp.aa_Code_integer_assn B A))) (=> (not _let_2) (= _let_1 tptp.one_one_assn))))))) (forall ((S tptp.set_bool) (A tptp.bool) (B tptp.fun_bool_rat)) (let ((_let_1 (tptp.groups1259819201609700362ol_rat (tptp.aa_fun224000846028461884ol_rat (tptp.aTP_Lamm_qj A) B) S))) (let ((_let_2 (tptp.pp (tptp.member_bool A S)))) (=> (tptp.finite_finite_bool S) (and (=> _let_2 (= _let_1 (tptp.aa_bool_rat B A))) (=> (not _let_2) (= _let_1 tptp.one_one_rat))))))) (forall ((S tptp.set_nat) (A tptp.nat) (B tptp.fun_nat_rat)) (let ((_let_1 (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_qk A) B)) S))) (let ((_let_2 (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A) S)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (and (=> _let_2 (= _let_1 (tptp.aa_nat_rat B A))) (=> (not _let_2) (= _let_1 tptp.one_one_rat))))))) (forall ((S tptp.set_bool) (A tptp.bool) (B tptp.fun_bo7282069421189217543nteger)) (let ((_let_1 (tptp.groups7272450149305381519nteger (tptp.aa_fun1377107737837666940nteger (tptp.aTP_Lamm_ql A) B) S))) (let ((_let_2 (tptp.pp (tptp.member_bool A S)))) (=> (tptp.finite_finite_bool S) (and (=> _let_2 (= _let_1 (tptp.aa_bool_Code_integer B A))) (=> (not _let_2) (= _let_1 tptp.one_one_Code_integer))))))) (forall ((S tptp.set_nat) (A tptp.nat) (B tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger (tptp.aa_fun589076786913273746nteger (tptp.aTP_Lamm_qm A) B)) S))) (let ((_let_2 (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A) S)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (and (=> _let_2 (= _let_1 (tptp.aa_nat_Code_integer B A))) (=> (not _let_2) (= _let_1 tptp.one_one_Code_integer))))))) (forall ((S tptp.set_int) (A tptp.int) (B tptp.fun_int_Code_integer)) (let ((_let_1 (tptp.groups3827104343326376752nteger (tptp.aa_fun5304498221708291146nteger (tptp.aTP_Lamm_qn A) B) S))) (let ((_let_2 (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A) S)))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (and (=> _let_2 (= _let_1 (tptp.aa_int_Code_integer B A))) (=> (not _let_2) (= _let_1 tptp.one_one_Code_integer))))))) (forall ((S tptp.set_Code_integer) (A tptp.code_integer) (B tptp.fun_Co8499238673658658103nteger)) (let ((_let_1 (tptp.groups3674199335183972705nteger (tptp.aa_fun4435975922079263404nteger (tptp.aTP_Lamm_qo A) B) S))) (let ((_let_2 (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A) S)))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S)) (and (=> _let_2 (= _let_1 (tptp.aa_Cod1783974652533396728nteger B A))) (=> (not _let_2) (= _let_1 tptp.one_one_Code_integer))))))) (forall ((S tptp.set_bool) (A tptp.bool) (B tptp.fun_bool_assn)) (let ((_let_1 (tptp.groups4835110720589548378l_assn (tptp.aa_fun923664478788943164l_assn (tptp.aTP_Lamm_qp A) B) S))) (let ((_let_2 (tptp.pp (tptp.member_bool A S)))) (=> (tptp.finite_finite_bool S) (and (=> _let_2 (= _let_1 (tptp.aa_bool_assn B A))) (=> (not _let_2) (= _let_1 tptp.one_one_assn))))))) (forall ((S tptp.set_nat) (A tptp.nat) (B tptp.fun_nat_assn)) (let ((_let_1 (tptp.groups6906906614972039071t_assn (tptp.aa_fun785744391571715112t_assn (tptp.aTP_Lamm_qq A) B) S))) (let ((_let_2 (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A) S)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (and (=> _let_2 (= _let_1 (tptp.aa_nat_assn B A))) (=> (not _let_2) (= _let_1 tptp.one_one_assn))))))) (forall ((S tptp.set_int) (A tptp.int) (B tptp.fun_int_assn)) (let ((_let_1 (tptp.groups7882442080178216443t_assn (tptp.aa_fun919007281442365664t_assn (tptp.aTP_Lamm_qr A) B) S))) (let ((_let_2 (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A) S)))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (and (=> _let_2 (= _let_1 (tptp.aa_int_assn B A))) (=> (not _let_2) (= _let_1 tptp.one_one_assn))))))) (forall ((S tptp.set_Code_integer) (A tptp.code_integer) (B tptp.fun_Co4490034186337852034r_assn)) (let ((_let_1 (tptp.groups1304777262505850412r_assn (tptp.aa_fun4119713415300323650r_assn (tptp.aTP_Lamm_qs A) B) S))) (let ((_let_2 (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A) S)))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S)) (and (=> _let_2 (= _let_1 (tptp.aa_Code_integer_assn B A))) (=> (not _let_2) (= _let_1 tptp.one_one_assn))))))) (forall ((S tptp.set_bool) (A tptp.bool) (B tptp.fun_bool_rat)) (let ((_let_1 (tptp.groups1259819201609700362ol_rat (tptp.aa_fun224000846028461884ol_rat (tptp.aTP_Lamm_qt A) B) S))) (let ((_let_2 (tptp.pp (tptp.member_bool A S)))) (=> (tptp.finite_finite_bool S) (and (=> _let_2 (= _let_1 (tptp.aa_bool_rat B A))) (=> (not _let_2) (= _let_1 tptp.one_one_rat))))))) (forall ((S tptp.set_nat) (A tptp.nat) (B tptp.fun_nat_rat)) (let ((_let_1 (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_qu A) B)) S))) (let ((_let_2 (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A) S)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (and (=> _let_2 (= _let_1 (tptp.aa_nat_rat B A))) (=> (not _let_2) (= _let_1 tptp.one_one_rat))))))) (forall ((N2 tptp.nat) (K tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N2) K))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)))) (forall ((A3 tptp.set_int) (F tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.groups1707563613775114915nt_nat F A3))) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_int_nat F X4)))))))) (forall ((A3 tptp.set_Code_integer) (F tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.groups3190895334310489300er_nat F A3))) (forall ((X4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X4) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_Code_integer_nat F X4)))))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (F tptp.fun_Pr2602117396471556196at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat A3)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.groups4077766827762148844at_nat F A3))) (forall ((X4 tptp.product_prod_nat_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat X4) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_Pro4243173770044397973at_nat F X4)))))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat F) A3))) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat F X4)))))))) (forall ((M tptp.num)) (= (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))))) (not (= M tptp.one)))) (forall ((M tptp.num)) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))))) (not (= M tptp.one)))) (forall ((M tptp.num)) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))))) (not (= M tptp.one)))) (forall ((M tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))) (not (= M tptp.one)))) (forall ((M tptp.num)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (not (= M tptp.one)))) (forall ((M tptp.num)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))) (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat))) (not (= M tptp.one)))) (forall ((N2 tptp.num)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2)) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num N2) tptp.one)))) (forall ((N2 tptp.num)) (= (tptp.pp (tptp.aa_Code_natural_bool (tptp.aa_Cod6910080592713026658l_bool tptp.ord_le1926595141338095240atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural N2)) tptp.one_one_Code_natural)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num N2) tptp.one)))) (forall ((N2 tptp.num)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2)) tptp.one_one_rat)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num N2) tptp.one)))) (forall ((N2 tptp.num)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat N2)) tptp.one_one_nat)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num N2) tptp.one)))) (forall ((N2 tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int tptp.numeral_numeral_int N2)) tptp.one_one_int)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num N2) tptp.one)))) (forall ((N2 tptp.num)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num tptp.one) N2)))) (forall ((N2 tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) (tptp.aa_num_int tptp.numeral_numeral_int N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num tptp.one) N2)))) (forall ((N2 tptp.num)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num tptp.one) N2)))) (forall ((N2 tptp.num)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num tptp.one) N2)))) (forall ((N2 tptp.num)) (= (tptp.pp (tptp.aa_Code_natural_bool (tptp.aa_Cod6910080592713026658l_bool tptp.ord_le5570908160329646204atural tptp.one_one_Code_natural) (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num tptp.one) N2)))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.zero_z3403309356797280102nteger)) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.zero_zero_rat)) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.zero_zero_int)) (= A tptp.zero_zero_int))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_2 X)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_2 Y)) (= (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) _let_1) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Y) _let_1)) (= X Y))))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_2 X)) (=> (tptp.pp (tptp.aa_rat_bool _let_2 Y)) (= (= (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1)) (= X Y))))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_2 X)) (=> (tptp.pp (tptp.aa_nat_bool _let_2 Y)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Y) _let_1)) (= X Y))))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_2 X)) (=> (tptp.pp (tptp.aa_int_bool _let_2 Y)) (= (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int X) _let_1) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Y) _let_1)) (= X Y))))))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (not (= A tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (not (= A tptp.zero_zero_rat)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (not (= A tptp.zero_zero_int)))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (tptp.groups7501900531339628137nteger G))) (let ((_let_3 (tptp.aa_set871585252387937313nteger _let_2 (tptp.aa_nat_set_nat _let_1 (tptp.aa_nat_nat tptp.suc N2))))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)))) (and (=> _let_4 (= _let_3 tptp.zero_z3403309356797280102nteger)) (=> (not _let_4) (= _let_3 (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_set871585252387937313nteger _let_2 (tptp.aa_nat_set_nat _let_1 N2))) (tptp.aa_nat_Code_integer G N2)))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_na2338080690716861136at_nat)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (tptp.groups6857163185585827899at_nat G (tptp.aa_nat_set_nat _let_1 (tptp.aa_nat_nat tptp.suc N2))))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)))) (and (=> _let_3 (= _let_2 tptp.zero_z1048942125864253310at_nat)) (=> (not _let_3) (= _let_2 (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat (tptp.groups6857163185585827899at_nat G (tptp.aa_nat_set_nat _let_1 N2))) (tptp.aa_nat2240542744625857721at_nat G N2))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (tptp.groups2906978787729119204at_rat G))) (let ((_let_3 (tptp.aa_set_nat_rat _let_2 (tptp.aa_nat_set_nat _let_1 (tptp.aa_nat_nat tptp.suc N2))))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)))) (and (=> _let_4 (= _let_3 tptp.zero_zero_rat)) (=> (not _let_4) (= _let_3 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_set_nat_rat _let_2 (tptp.aa_nat_set_nat _let_1 N2))) (tptp.aa_nat_rat G N2)))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (tptp.groups3539618377306564664at_int G))) (let ((_let_3 (tptp.aa_set_nat_int _let_2 (tptp.aa_nat_set_nat _let_1 (tptp.aa_nat_nat tptp.suc N2))))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)))) (and (=> _let_4 (= _let_3 tptp.zero_zero_int)) (=> (not _let_4) (= _let_3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_set_nat_int _let_2 (tptp.aa_nat_set_nat _let_1 N2))) (tptp.aa_nat_int G N2)))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (tptp.groups3542108847815614940at_nat G))) (let ((_let_3 (tptp.aa_set_nat_nat _let_2 (tptp.aa_nat_set_nat _let_1 (tptp.aa_nat_nat tptp.suc N2))))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)))) (and (=> _let_4 (= _let_3 tptp.zero_zero_nat)) (=> (not _let_4) (= _let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_set_nat_nat _let_2 (tptp.aa_nat_set_nat _let_1 N2))) (tptp.aa_nat_nat G N2)))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (tptp.groups3455450783089532116nteger G))) (let ((_let_3 (tptp.aa_set871585252387937313nteger _let_2 (tptp.aa_nat_set_nat _let_1 (tptp.aa_nat_nat tptp.suc N2))))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)))) (and (=> _let_4 (= _let_3 tptp.one_one_Code_integer)) (=> (not _let_4) (= _let_3 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_set871585252387937313nteger _let_2 (tptp.aa_nat_set_nat _let_1 N2))) (tptp.aa_nat_Code_integer G N2)))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_nat_assn)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat _let_1 (tptp.aa_nat_nat tptp.suc N2))))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)))) (and (=> _let_3 (= _let_2 tptp.one_one_assn)) (=> (not _let_3) (= _let_2 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat _let_1 N2))) (tptp.aa_nat_assn G N2))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (tptp.groups73079841787564623at_rat G))) (let ((_let_3 (tptp.aa_set_nat_rat _let_2 (tptp.aa_nat_set_nat _let_1 (tptp.aa_nat_nat tptp.suc N2))))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)))) (and (=> _let_4 (= _let_3 tptp.one_one_rat)) (=> (not _let_4) (= _let_3 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_set_nat_rat _let_2 (tptp.aa_nat_set_nat _let_1 N2))) (tptp.aa_nat_rat G N2)))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (tptp.groups708209901874060359at_nat G))) (let ((_let_3 (tptp.aa_set_nat_nat _let_2 (tptp.aa_nat_set_nat _let_1 (tptp.aa_nat_nat tptp.suc N2))))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)))) (and (=> _let_4 (= _let_3 tptp.one_one_nat)) (=> (not _let_4) (= _let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_set_nat_nat _let_2 (tptp.aa_nat_set_nat _let_1 N2))) (tptp.aa_nat_nat G N2)))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (tptp.groups705719431365010083at_int G))) (let ((_let_3 (tptp.aa_set_nat_int _let_2 (tptp.aa_nat_set_nat _let_1 (tptp.aa_nat_nat tptp.suc N2))))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)))) (and (=> _let_4 (= _let_3 tptp.one_one_int)) (=> (not _let_4) (= _let_3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_set_nat_int _let_2 (tptp.aa_nat_set_nat _let_1 N2))) (tptp.aa_nat_int G N2)))))))))) (forall ((A3 tptp.set_nat) (C tptp.fun_nat_rat)) (let ((_let_1 (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_qv C)) A3))) (let ((_let_2 (and (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) A3))))) (and (=> _let_2 (= _let_1 (tptp.aa_nat_rat C tptp.zero_zero_nat))) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))) X)))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X)) tptp.one_one_int)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) _let_1)) (= _let_1 tptp.one_one_nat)))) (forall ((F tptp.fun_int_nat) (A3 tptp.set_int)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.groups1707563613775114915nt_nat F A3)) (tptp.groups1705073143266064639nt_int (tptp.aTP_Lamm_jp F) A3))) (forall ((F tptp.fun_nat_nat) (A3 tptp.set_nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat F) A3)) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aTP_Lamm_jq F)) A3))) (forall ((S tptp.set_int) (S4 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (tptp.finite6197958912794628473et_int (tptp.collect_set_int (tptp.aa_set7694327796961020398t_bool (tptp.aTP_Lamm_qw S) S4))))) (forall ((S tptp.set_Code_integer) (S4 tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S)) (tptp.finite6931041176100689706nteger (tptp.collec574505750873337192nteger (tptp.aa_set8732061614394825996r_bool (tptp.aTP_Lamm_qx S) S4))))) (forall ((S tptp.set_Pr1261947904930325089at_nat) (S4 tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat S)) (tptp.finite9047747110432174090at_nat (tptp.collec5514110066124741708at_nat (tptp.aa_set7594618562247239262t_bool (tptp.aTP_Lamm_qy S) S4))))) (forall ((S tptp.set_nat) (S4 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat (tptp.collect_set_nat (tptp.aa_set5116768664143533222t_bool (tptp.aTP_Lamm_qz S) S4)))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (not (tptp.finite_finite_rat (tptp.set_or4029947393144176647an_rat A B))))) (forall ((N2 tptp.nat) (K tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) D2)) (= (= (tptp.set_or4029947393144176647an_rat A B) (tptp.set_or4029947393144176647an_rat C D2)) (and (= A C) (= B D2)))))) (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D2 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num C) D2)) (= (= (tptp.set_or1222409239386451017an_num A B) (tptp.set_or1222409239386451017an_num C D2)) (and (= A C) (= B D2)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C) D2)) (= (= (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat A) B) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat C) D2)) (and (= A C) (= B D2)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) D2)) (= (= (tptp.set_or4662586982721622107an_int A B) (tptp.set_or4662586982721622107an_int C D2)) (and (= A C) (= B D2)))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger C) D2)) (= (= (tptp.set_or8404916559141939852nteger A B) (tptp.set_or8404916559141939852nteger C D2)) (and (= A C) (= B D2)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (= (tptp.set_or4029947393144176647an_rat A B) (tptp.set_or4029947393144176647an_rat C D2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) D2)) (= A C))))) (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D2 tptp.num)) (=> (= (tptp.set_or1222409239386451017an_num A B) (tptp.set_or1222409239386451017an_num C D2)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num C) D2)) (= A C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (= (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat A) B) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat C) D2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C) D2)) (= A C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= (tptp.set_or4662586982721622107an_int A B) (tptp.set_or4662586982721622107an_int C D2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) D2)) (= A C))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (= (tptp.set_or8404916559141939852nteger A B) (tptp.set_or8404916559141939852nteger C D2)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger C) D2)) (= A C))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (= (tptp.set_or4029947393144176647an_rat A B) (tptp.set_or4029947393144176647an_rat C D2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) D2)) (= B D2))))) (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D2 tptp.num)) (=> (= (tptp.set_or1222409239386451017an_num A B) (tptp.set_or1222409239386451017an_num C D2)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num C) D2)) (= B D2))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (= (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat A) B) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat C) D2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C) D2)) (= B D2))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= (tptp.set_or4662586982721622107an_int A B) (tptp.set_or4662586982721622107an_int C D2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) D2)) (= B D2))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (= (tptp.set_or8404916559141939852nteger A B) (tptp.set_or8404916559141939852nteger C D2)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger C) D2)) (= B D2))))) (forall ((N7 tptp.set_nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat N7) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat N7)))) (forall ((N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (forall ((N7 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat N7)) (exists ((M3 tptp.nat)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) N7)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X4) M3))))))) (forall ((N7 tptp.set_nat) (N2 tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) N7)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) N2)))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat N7)))) (forall ((N7 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat N7)) (exists ((M3 tptp.nat)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) N7)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X4) M3))))))) (forall ((N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_ra N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) N2))) (forall ((Z tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Z) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Z) Z))) (forall ((Z tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) Z) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Z) Z))) (forall ((Z tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) Z) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger Z) Z))) (forall ((Z tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))) Z) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Z) Z))) (forall ((Z tptp.code_natural)) (= (tptp.times_2397367101498566445atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)) Z) (tptp.plus_p4538020629002901425atural Z Z))) (forall ((Z tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Z) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Z) Z))) (forall ((Z tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Z) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Z) Z))) (forall ((Z tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger Z) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger Z) Z))) (forall ((Z tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Z) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Z) Z))) (forall ((Z tptp.code_natural)) (= (tptp.times_2397367101498566445atural Z (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.plus_p4538020629002901425atural Z Z))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat _let_1 B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) A)) B)))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int A))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int _let_1 B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) A)) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.plus_p5714425477246183910nteger A))) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger _let_1 B)) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) A)) B)))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat _let_1 B)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))) A)) B)))) (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (tptp.plus_p4538020629002901425atural A (tptp.plus_p4538020629002901425atural A B)) (tptp.plus_p4538020629002901425atural (tptp.times_2397367101498566445atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)) A) B))) (forall ((X tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) tptp.one)) (= X tptp.one))) (forall ((X tptp.code_integer)) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger X) X)) X)) X))) (forall ((X tptp.assn)) (= (tptp.aa_nat_assn (tptp.power_power_assn X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn X) X)) X)) X))) (forall ((X tptp.rat)) (= (tptp.aa_nat_rat (tptp.power_power_rat X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X) X)) X)) X))) (forall ((X tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat X) X)) X)) X))) (forall ((X tptp.int)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) X)) X)) X))) (forall ((A tptp.code_integer)) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) A))) (forall ((A tptp.assn)) (= (tptp.aa_nat_assn (tptp.power_power_assn A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn A) A))) (forall ((A tptp.rat)) (= (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) A))) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) A))) (forall ((A tptp.int)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) A))) (forall ((P tptp.fun_nat_bool) (I2 tptp.nat)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_rb P) I2))))) (forall ((F tptp.fun_nat_nat) (U tptp.nat)) (=> (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N5) (tptp.aa_nat_nat F N5)))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_rc F) U)))))) (forall ((A3 tptp.set_bool) (B3 tptp.set_nat) (G tptp.fun_bool_fun_nat_nat) (R tptp.fun_bo3288154511880838028t_bool)) (=> (tptp.finite_finite_bool A3) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (= (tptp.groups5768501273728744877ol_nat (tptp.aa_fun7928520491197679664ol_nat (tptp.aa_fun5318524179215677308ol_nat (tptp.aTP_Lamm_re B3) G) R) A3) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun4984880352635657191at_nat (tptp.aa_fun8028557108643889at_nat (tptp.aTP_Lamm_rh A3) G) R)) B3))))) (forall ((A3 tptp.set_int) (B3 tptp.set_nat) (G tptp.fun_int_fun_nat_nat) (R tptp.fun_int_fun_nat_bool)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (= (tptp.groups4541462559716669496nt_nat (tptp.aa_fun5132377469993263754nt_nat (tptp.aa_fun348247319442030677nt_nat (tptp.aTP_Lamm_rj B3) G) R) A3) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun4133023758092209198at_nat (tptp.aa_fun7384697781603784697at_nat (tptp.aTP_Lamm_rm A3) G) R)) B3))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_nat) (G tptp.fun_Co3312552843764780407at_nat) (R tptp.fun_Co8657364630979331932t_bool)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (= (tptp.groups7237345082560585321er_nat (tptp.aa_fun2949368542467568330er_nat (tptp.aa_fun8366171557965857828er_nat (tptp.aTP_Lamm_ro B3) G) R) A3) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun7549014261834767933at_nat (tptp.aa_fun5721305349739569687at_nat (tptp.aTP_Lamm_rr A3) G) R)) B3))))) (forall ((A3 tptp.set_bool) (B3 tptp.set_int) (G tptp.fun_bool_fun_int_int) (R tptp.fun_bo2827871560234191408t_bool)) (=> (tptp.finite_finite_bool A3) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (= (tptp.groups5766010803219694601ol_int (tptp.aa_fun2977339950115259112ol_int (tptp.aa_fun6505924867870464892ol_int (tptp.aTP_Lamm_rt B3) G) R) A3) (tptp.groups4538972089207619220nt_int (tptp.aa_fun4844225129491648835nt_int (tptp.aa_fun4909036969399236677nt_int (tptp.aTP_Lamm_rw A3) G) R) B3))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_int) (G tptp.fun_nat_fun_int_int) (R tptp.fun_nat_fun_int_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (= (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aa_fun3504929462025808522at_int (tptp.aa_fun3325927984641084153at_int (tptp.aTP_Lamm_ry B3) G) R)) A3) (tptp.groups4538972089207619220nt_int (tptp.aa_fun4504283173926863078nt_int (tptp.aa_fun5512849559334105941nt_int (tptp.aTP_Lamm_sa A3) G) R) B3))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_int) (G tptp.fun_Co3009391273526075439nt_int) (R tptp.fun_Co8197081679332685312t_bool)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (= (tptp.groups7234854612051535045er_int (tptp.aa_fun531554186711482826er_int (tptp.aa_fun2196751070425669740er_int (tptp.aTP_Lamm_sc B3) G) R) A3) (tptp.groups4538972089207619220nt_int (tptp.aa_fun7408359038690759577nt_int (tptp.aa_fun3657818423959754427nt_int (tptp.aTP_Lamm_sf A3) G) R) B3))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_bool) (G tptp.fun_nat_fun_bool_nat) (R tptp.fun_na9137082442855928016l_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.finite_finite_bool B3) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun4035688661005363499at_nat (tptp.aa_fun2816605880368898353at_nat (tptp.aTP_Lamm_sh B3) G) R)) A3) (tptp.groups5768501273728744877ol_nat (tptp.aa_fun8887362042153257964ol_nat (tptp.aa_fun8325916554501496444ol_nat (tptp.aTP_Lamm_sk A3) G) R) B3))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_int) (G tptp.fun_nat_fun_int_nat) (R tptp.fun_nat_fun_int_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun7682780481535005230at_nat (tptp.aa_fun503657754853467129at_nat (tptp.aTP_Lamm_sl B3) G) R)) A3) (tptp.groups4541462559716669496nt_nat (tptp.aa_fun8682134193436059786nt_nat (tptp.aa_fun2690579329546488917nt_nat (tptp.aTP_Lamm_sn A3) G) R) B3))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_Code_integer) (G tptp.fun_na5492297256294505719er_nat) (R tptp.fun_na7774394808840722396r_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun8701945955350064829at_nat (tptp.aa_fun5063706727594296087at_nat (tptp.aTP_Lamm_sp B3) G) R)) A3) (tptp.groups7237345082560585321er_nat (tptp.aa_fun490956603642643274er_nat (tptp.aa_fun3698671732857677092er_nat (tptp.aTP_Lamm_ss A3) G) R) B3))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G tptp.fun_nat_fun_nat_nat) (R tptp.fun_nat_fun_nat_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun4644938397070871434at_nat (tptp.aa_fun7390876557192650417at_nat (tptp.aTP_Lamm_su B3) G) R)) A3) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun4644938397070871434at_nat (tptp.aa_fun7390876557192650417at_nat (tptp.aTP_Lamm_sw A3) G) R)) B3))))) (forall ((A3 tptp.set_bool) (B3 tptp.set_nat) (G tptp.fun_bool_fun_nat_nat) (R tptp.fun_bo3288154511880838028t_bool)) (=> (tptp.finite_finite_bool A3) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (= (tptp.groups1894949261696196098ol_nat (tptp.aa_fun7928520491197679664ol_nat (tptp.aa_fun5318524179215677308ol_nat (tptp.aTP_Lamm_sx B3) G) R) A3) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_fun4984880352635657191at_nat (tptp.aa_fun8028557108643889at_nat (tptp.aTP_Lamm_sy A3) G) R)) B3))))) (forall ((A3 tptp.set_int) (B3 tptp.set_nat) (G tptp.fun_int_fun_nat_nat) (R tptp.fun_int_fun_nat_bool)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (= (tptp.groups1707563613775114915nt_nat (tptp.aa_fun5132377469993263754nt_nat (tptp.aa_fun348247319442030677nt_nat (tptp.aTP_Lamm_sz B3) G) R) A3) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_fun4133023758092209198at_nat (tptp.aa_fun7384697781603784697at_nat (tptp.aTP_Lamm_ta A3) G) R)) B3))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_nat) (G tptp.fun_Co3312552843764780407at_nat) (R tptp.fun_Co8657364630979331932t_bool)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (= (tptp.groups3190895334310489300er_nat (tptp.aa_fun2949368542467568330er_nat (tptp.aa_fun8366171557965857828er_nat (tptp.aTP_Lamm_tb B3) G) R) A3) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_fun7549014261834767933at_nat (tptp.aa_fun5721305349739569687at_nat (tptp.aTP_Lamm_tc A3) G) R)) B3))))) (forall ((A3 tptp.set_bool) (B3 tptp.set_nat) (G tptp.fun_bool_fun_nat_int) (R tptp.fun_bo3288154511880838028t_bool)) (=> (tptp.finite_finite_bool A3) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (= (tptp.groups1892458791187145822ol_int (tptp.aa_fun3750669471688482956ol_int (tptp.aa_fun5436235457428229244ol_int (tptp.aTP_Lamm_td B3) G) R) A3) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_fun807029333126460483at_int (tptp.aa_fun5144677179269963497at_int (tptp.aTP_Lamm_tf A3) G) R)) B3))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_nat) (G tptp.fun_Co822469698833053651at_int) (R tptp.fun_Co8657364630979331932t_bool)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (= (tptp.groups3188404863801439024er_int (tptp.aa_fun7994889559813147430er_int (tptp.aa_fun6206124202175859492er_int (tptp.aTP_Lamm_tg B3) G) R) A3) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_fun3371163242325571225at_int (tptp.aa_fun5074241136823302423at_int (tptp.aTP_Lamm_ti A3) G) R)) B3))))) (forall ((A3 tptp.set_bool) (B3 tptp.set_int) (G tptp.fun_bool_fun_int_int) (R tptp.fun_bo2827871560234191408t_bool)) (=> (tptp.finite_finite_bool A3) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (= (tptp.groups1892458791187145822ol_int (tptp.aa_fun2977339950115259112ol_int (tptp.aa_fun6505924867870464892ol_int (tptp.aTP_Lamm_tj B3) G) R) A3) (tptp.groups1705073143266064639nt_int (tptp.aa_fun4844225129491648835nt_int (tptp.aa_fun4909036969399236677nt_int (tptp.aTP_Lamm_tk A3) G) R) B3))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_int) (G tptp.fun_Co3009391273526075439nt_int) (R tptp.fun_Co8197081679332685312t_bool)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (= (tptp.groups3188404863801439024er_int (tptp.aa_fun531554186711482826er_int (tptp.aa_fun2196751070425669740er_int (tptp.aTP_Lamm_tl B3) G) R) A3) (tptp.groups1705073143266064639nt_int (tptp.aa_fun7408359038690759577nt_int (tptp.aa_fun3657818423959754427nt_int (tptp.aTP_Lamm_tm A3) G) R) B3))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_bool) (G tptp.fun_nat_fun_bool_nat) (R tptp.fun_na9137082442855928016l_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.finite_finite_bool B3) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_fun4035688661005363499at_nat (tptp.aa_fun2816605880368898353at_nat (tptp.aTP_Lamm_tn B3) G) R)) A3) (tptp.groups1894949261696196098ol_nat (tptp.aa_fun8887362042153257964ol_nat (tptp.aa_fun8325916554501496444ol_nat (tptp.aTP_Lamm_to A3) G) R) B3))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_int) (G tptp.fun_nat_fun_int_nat) (R tptp.fun_nat_fun_int_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_fun7682780481535005230at_nat (tptp.aa_fun503657754853467129at_nat (tptp.aTP_Lamm_tp B3) G) R)) A3) (tptp.groups1707563613775114915nt_nat (tptp.aa_fun8682134193436059786nt_nat (tptp.aa_fun2690579329546488917nt_nat (tptp.aTP_Lamm_tq A3) G) R) B3))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_Code_integer) (G tptp.fun_na5492297256294505719er_nat) (R tptp.fun_na7774394808840722396r_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_fun8701945955350064829at_nat (tptp.aa_fun5063706727594296087at_nat (tptp.aTP_Lamm_tr B3) G) R)) A3) (tptp.groups3190895334310489300er_nat (tptp.aa_fun490956603642643274er_nat (tptp.aa_fun3698671732857677092er_nat (tptp.aTP_Lamm_ts A3) G) R) B3))))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (forall ((K tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat K) M))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat M) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat N2) _let_1))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat M) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (forall ((K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat _let_1) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 K)) tptp.one_one_nat)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat tptp.aTP_Lamm_fu) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat)))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((N2 tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) K)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N2) K) tptp.zero_zero_nat))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.pp (tptp.aa_rat_bool _let_1 A))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat A) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B))) (=> (tptp.ord_less_eq_set_rat (tptp.set_or4029947393144176647an_rat A B) (tptp.set_or4029947393144176647an_rat C D2)) (or (tptp.pp (tptp.aa_rat_bool _let_1 A)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) A)) (tptp.pp (tptp.aa_rat_bool _let_1 D2))))))) (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D2 tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B))) (=> (tptp.ord_less_eq_set_num (tptp.set_or1222409239386451017an_num A B) (tptp.set_or1222409239386451017an_num C D2)) (or (tptp.pp (tptp.aa_num_bool _let_1 A)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num C) A)) (tptp.pp (tptp.aa_num_bool _let_1 D2))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat A) B)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat C) D2))) (or (tptp.pp (tptp.aa_nat_bool _let_1 A)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) A)) (tptp.pp (tptp.aa_nat_bool _let_1 D2))))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.set_or4662586982721622107an_int A B)) (tptp.set_or4662586982721622107an_int C D2))) (or (tptp.pp (tptp.aa_int_bool _let_1 A)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) A)) (tptp.pp (tptp.aa_int_bool _let_1 D2))))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger (tptp.set_or8404916559141939852nteger A B)) (tptp.set_or8404916559141939852nteger C D2))) (or (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger C) A)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 D2))))))) (forall ((A tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) _let_2) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Y) _let_2)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 X)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 Y)) (= X Y))))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (= (tptp.aa_nat_rat (tptp.power_power_rat X) _let_2) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_2)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (= X Y))))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Y) _let_2)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 Y)) (= X Y))))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int X) _let_2) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Y) _let_2)) (=> (tptp.pp (tptp.aa_int_bool _let_1 X)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (= X Y))))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) _let_1)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Y) _let_1))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) Y)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger X) Y)))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Y) _let_1))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Y) _let_1))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)))))) (forall ((A tptp.code_integer)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.rat)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.zero_zero_rat)))) (forall ((A tptp.int)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.zero_zero_int)))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.binomial N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (= (tptp.aa_nat_nat _let_1 K) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K)))))) (forall ((L tptp.rat) (M tptp.rat) (U tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat L) M)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat M) U)) (= (tptp.sup_sup_set_rat (tptp.set_or4029947393144176647an_rat L M) (tptp.set_or4029947393144176647an_rat M U)) (tptp.set_or4029947393144176647an_rat L U))))) (forall ((L tptp.num) (M tptp.num) (U tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num L) M)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) U)) (= (tptp.sup_sup_set_num (tptp.set_or1222409239386451017an_num L M) (tptp.set_or1222409239386451017an_num M U)) (tptp.set_or1222409239386451017an_num L U))))) (forall ((L tptp.nat) (M tptp.nat) (U tptp.nat)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat L))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat L) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) U)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.aa_nat_set_nat _let_1 M)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) U)) (tptp.aa_nat_set_nat _let_1 U)))))) (forall ((L tptp.int) (M tptp.int) (U tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int L) M)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int M) U)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int (tptp.set_or4662586982721622107an_int L M)) (tptp.set_or4662586982721622107an_int M U)) (tptp.set_or4662586982721622107an_int L U))))) (forall ((L tptp.code_integer) (M tptp.code_integer) (U tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger L) M)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger M) U)) (= (tptp.sup_su848401254843788991nteger (tptp.set_or8404916559141939852nteger L M) (tptp.set_or8404916559141939852nteger M U)) (tptp.set_or8404916559141939852nteger L U))))) (forall ((N2 tptp.nat) (P tptp.fun_nat_bool)) (= (exists ((M3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M3) N2)) (tptp.pp (tptp.aa_nat_bool P M3)))) (exists ((X4 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2))) (tptp.pp (tptp.aa_nat_bool P X4)))))) (forall ((N2 tptp.nat) (P tptp.fun_nat_bool)) (= (forall ((M3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M3) N2)) (tptp.pp (tptp.aa_nat_bool P M3)))) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2))) (tptp.pp (tptp.aa_nat_bool P X4)))))) (forall ((N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (or (= N2 tptp.zero_zero_nat) (= N2 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (or (= N2 tptp.zero_zero_nat) (= N2 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))) (forall ((L tptp.bool) (M tptp.bool) (U tptp.bool)) (= (tptp.inf_inf_set_bool (tptp.set_or8576162586734908840n_bool L M) (tptp.set_or8576162586734908840n_bool M U)) tptp.bot_bot_set_bool)) (forall ((L tptp.nat) (M tptp.nat) (U tptp.nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat L) M)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) U)) tptp.bot_bot_set_nat)) (forall ((L tptp.int) (M tptp.int) (U tptp.int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int (tptp.set_or4662586982721622107an_int L M)) (tptp.set_or4662586982721622107an_int M U)) tptp.bot_bot_set_int)) (forall ((L tptp.code_integer) (M tptp.code_integer) (U tptp.code_integer)) (= (tptp.inf_in1364745209274528805nteger (tptp.set_or8404916559141939852nteger L M) (tptp.set_or8404916559141939852nteger M U)) tptp.bot_bo3990330152332043303nteger)) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer X)) (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer Y))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) _let_1)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Y) _let_1)))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat X)) (tptp.aa_rat_rat tptp.abs_abs_rat Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int X)) (tptp.aa_int_int tptp.abs_abs_int Y))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Y) _let_1)))))) (forall ((S tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S)) (=> (not (= S tptp.bot_bo3990330152332043303nteger)) (exists ((X3 tptp.code_integer)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) S)) (not (exists ((Xa3 tptp.code_integer)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Xa3) S)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger Xa3) X3)))))))))) (forall ((S tptp.set_bool)) (=> (tptp.finite_finite_bool S) (=> (not (= S tptp.bot_bot_set_bool)) (exists ((X3 tptp.bool)) (and (tptp.pp (tptp.member_bool X3 S)) (not (exists ((Xa3 tptp.bool)) (and (tptp.pp (tptp.member_bool Xa3 S)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.ord_less_bool Xa3) X3)))))))))) (forall ((S tptp.set_assn)) (=> (tptp.finite_finite_assn S) (=> (not (= S tptp.bot_bot_set_assn)) (exists ((X3 tptp.assn)) (and (tptp.member_assn X3 S) (not (exists ((Xa3 tptp.assn)) (and (tptp.member_assn Xa3 S) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn Xa3) X3)))))))))) (forall ((S tptp.set_rat)) (=> (tptp.finite_finite_rat S) (=> (not (= S tptp.bot_bot_set_rat)) (exists ((X3 tptp.rat)) (and (tptp.member_rat X3 S) (not (exists ((Xa3 tptp.rat)) (and (tptp.member_rat Xa3 S) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Xa3) X3)))))))))) (forall ((S tptp.set_num)) (=> (tptp.finite_finite_num S) (=> (not (= S tptp.bot_bot_set_num)) (exists ((X3 tptp.num)) (and (tptp.member_num X3 S) (not (exists ((Xa3 tptp.num)) (and (tptp.member_num Xa3 S) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Xa3) X3)))))))))) (forall ((S tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (=> (not (= S tptp.bot_bot_set_nat)) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) S)) (not (exists ((Xa3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa3) S)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Xa3) X3)))))))))) (forall ((S tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (=> (not (= S tptp.bot_bot_set_int)) (exists ((X3 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) S)) (not (exists ((Xa3 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa3) S)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Xa3) X3)))))))))) (forall ((X6 tptp.set_Code_integer)) (=> (not (= X6 tptp.bot_bo3990330152332043303nteger)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) X6)) (exists ((Xa3 tptp.code_integer)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Xa3) X6)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger X3) Xa3)))))) (not (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger X6)))))) (forall ((X6 tptp.set_bool)) (=> (not (= X6 tptp.bot_bot_set_bool)) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 X6)) (exists ((Xa3 tptp.bool)) (and (tptp.pp (tptp.member_bool Xa3 X6)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.ord_less_bool X3) Xa3)))))) (not (tptp.finite_finite_bool X6))))) (forall ((X6 tptp.set_rat)) (=> (not (= X6 tptp.bot_bot_set_rat)) (=> (forall ((X3 tptp.rat)) (=> (tptp.member_rat X3 X6) (exists ((Xa3 tptp.rat)) (and (tptp.member_rat Xa3 X6) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Xa3)))))) (not (tptp.finite_finite_rat X6))))) (forall ((X6 tptp.set_num)) (=> (not (= X6 tptp.bot_bot_set_num)) (=> (forall ((X3 tptp.num)) (=> (tptp.member_num X3 X6) (exists ((Xa3 tptp.num)) (and (tptp.member_num Xa3 X6) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X3) Xa3)))))) (not (tptp.finite_finite_num X6))))) (forall ((X6 tptp.set_nat)) (=> (not (= X6 tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) X6)) (exists ((Xa3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa3) X6)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) Xa3)))))) (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat X6)))))) (forall ((X6 tptp.set_int)) (=> (not (= X6 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) X6)) (exists ((Xa3 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa3) X6)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) Xa3)))))) (not (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int X6)))))) (forall ((R3 tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat R3) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N2) R3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat N2) R3))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N2))))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) M))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_2) tptp.one_one_nat))) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) _let_2))))) (forall ((M tptp.nat)) (= (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) tptp.zero_zero_nat) tptp.bot_bot_set_nat)) (forall ((N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_tt N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat))))) (forall ((F tptp.fun_bool_rat) (I5 tptp.set_bool) (G tptp.fun_bool_rat) (I2 tptp.bool)) (=> (= (tptp.groups5133371213642249141ol_rat F I5) (tptp.groups5133371213642249141ol_rat G I5)) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_bool_rat F I3)) (tptp.aa_bool_rat G I3))))) (=> (tptp.pp (tptp.member_bool I2 I5)) (=> (tptp.finite_finite_bool I5) (= (tptp.aa_bool_rat F I2) (tptp.aa_bool_rat G I2))))))) (forall ((F tptp.fun_nat_rat) (I5 tptp.set_nat) (G tptp.fun_nat_rat) (I2 tptp.nat)) (=> (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat F) I5) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat G) I5)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F I3)) (tptp.aa_nat_rat G I3))))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I2) I5)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat I5)) (= (tptp.aa_nat_rat F I2) (tptp.aa_nat_rat G I2))))))) (forall ((F tptp.fun_int_rat) (I5 tptp.set_int) (G tptp.fun_int_rat) (I2 tptp.int)) (=> (= (tptp.groups3906332499630173760nt_rat F I5) (tptp.groups3906332499630173760nt_rat G I5)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat F I3)) (tptp.aa_int_rat G I3))))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I2) I5)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int I5)) (= (tptp.aa_int_rat F I2) (tptp.aa_int_rat G I2))))))) (forall ((F tptp.fun_Code_integer_rat) (I5 tptp.set_Code_integer) (G tptp.fun_Code_integer_rat) (I2 tptp.code_integer)) (=> (= (tptp.groups6602215022474089585er_rat F I5) (tptp.groups6602215022474089585er_rat G I5)) (=> (forall ((I3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_Code_integer_rat F I3)) (tptp.aa_Code_integer_rat G I3))))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I2) I5)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger I5)) (= (tptp.aa_Code_integer_rat F I2) (tptp.aa_Code_integer_rat G I2))))))) (forall ((F tptp.fun_bool_nat) (I5 tptp.set_bool) (G tptp.fun_bool_nat) (I2 tptp.bool)) (=> (= (tptp.groups5768501273728744877ol_nat F I5) (tptp.groups5768501273728744877ol_nat G I5)) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 I5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_bool_nat F I3)) (tptp.aa_bool_nat G I3))))) (=> (tptp.pp (tptp.member_bool I2 I5)) (=> (tptp.finite_finite_bool I5) (= (tptp.aa_bool_nat F I2) (tptp.aa_bool_nat G I2))))))) (forall ((F tptp.fun_int_nat) (I5 tptp.set_int) (G tptp.fun_int_nat) (I2 tptp.int)) (=> (= (tptp.groups4541462559716669496nt_nat F I5) (tptp.groups4541462559716669496nt_nat G I5)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat F I3)) (tptp.aa_int_nat G I3))))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I2) I5)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int I5)) (= (tptp.aa_int_nat F I2) (tptp.aa_int_nat G I2))))))) (forall ((F tptp.fun_Code_integer_nat) (I5 tptp.set_Code_integer) (G tptp.fun_Code_integer_nat) (I2 tptp.code_integer)) (=> (= (tptp.groups7237345082560585321er_nat F I5) (tptp.groups7237345082560585321er_nat G I5)) (=> (forall ((I3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I3) I5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_Code_integer_nat F I3)) (tptp.aa_Code_integer_nat G I3))))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I2) I5)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger I5)) (= (tptp.aa_Code_integer_nat F I2) (tptp.aa_Code_integer_nat G I2))))))) (forall ((F tptp.fun_bool_int) (I5 tptp.set_bool) (G tptp.fun_bool_int) (I2 tptp.bool)) (=> (= (tptp.groups5766010803219694601ol_int F I5) (tptp.groups5766010803219694601ol_int G I5)) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 I5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_bool_int F I3)) (tptp.aa_bool_int G I3))))) (=> (tptp.pp (tptp.member_bool I2 I5)) (=> (tptp.finite_finite_bool I5) (= (tptp.aa_bool_int F I2) (tptp.aa_bool_int G I2))))))) (forall ((F tptp.fun_nat_int) (I5 tptp.set_nat) (G tptp.fun_nat_int) (I2 tptp.nat)) (=> (= (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int F) I5) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int G) I5)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int F I3)) (tptp.aa_nat_int G I3))))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I2) I5)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat I5)) (= (tptp.aa_nat_int F I2) (tptp.aa_nat_int G I2))))))) (forall ((F tptp.fun_Code_integer_int) (I5 tptp.set_Code_integer) (G tptp.fun_Code_integer_int) (I2 tptp.code_integer)) (=> (= (tptp.groups7234854612051535045er_int F I5) (tptp.groups7234854612051535045er_int G I5)) (=> (forall ((I3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I3) I5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_Code_integer_int F I3)) (tptp.aa_Code_integer_int G I3))))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I2) I5)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger I5)) (= (tptp.aa_Code_integer_int F I2) (tptp.aa_Code_integer_int G I2))))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (not (tptp.finite_finite_rat (tptp.set_or633870826150836451st_rat A B))))) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one)) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) (tptp.aa_num_int tptp.numeral_numeral_int tptp.one)) A)) (forall ((A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger tptp.one)) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) (tptp.aa_num_rat tptp.numeral_numeral_rat tptp.one)) A)) (forall ((A tptp.code_natural)) (= (tptp.times_2397367101498566445atural A (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural tptp.one)) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one)) A) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int tptp.one)) A) A)) (forall ((A tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger tptp.one)) A) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat tptp.one)) A) A)) (forall ((A tptp.code_natural)) (= (tptp.times_2397367101498566445atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural tptp.one) A) A)) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_tu M)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_nat_nat tptp.suc M)))) (forall ((G tptp.fun_nat_nat) (M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat (tptp.aa_nat_nat tptp.suc M)) (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_jx G)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2)))) (forall ((G tptp.fun_nat_nat) (M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) K))) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_jy G) K)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2)))) (forall ((G tptp.fun_nat_nat) (M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat G) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat (tptp.aa_nat_nat tptp.suc M)) (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aTP_Lamm_jx G)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2)))) (forall ((G tptp.fun_nat_int) (M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int G) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat (tptp.aa_nat_nat tptp.suc M)) (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aTP_Lamm_kc G)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2)))) (forall ((I5 tptp.set_bool) (X tptp.fun_bo7282069421189217543nteger) (Y tptp.fun_bo7282069421189217543nteger)) (let ((_let_1 (tptp.aTP_Lamm_tv I5))) (=> (tptp.finite_finite_bool (tptp.collect_bool (tptp.aa_fun7063430368917475406l_bool _let_1 X))) (=> (tptp.finite_finite_bool (tptp.collect_bool (tptp.aa_fun7063430368917475406l_bool _let_1 Y))) (tptp.finite_finite_bool (tptp.collect_bool (tptp.aa_fun7063430368917475406l_bool (tptp.aa_fun8946763977956929170l_bool (tptp.aTP_Lamm_tw I5) X) Y))))))) (forall ((I5 tptp.set_nat) (X tptp.fun_nat_Code_integer) (Y tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.aTP_Lamm_tx I5))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun1752071697927428280t_bool _let_1 X)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun1752071697927428280t_bool _let_1 Y)))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun1752071697927428280t_bool (tptp.aa_fun4813323487062687079t_bool (tptp.aTP_Lamm_ty I5) X) Y)))))))) (forall ((I5 tptp.set_int) (X tptp.fun_int_Code_integer) (Y tptp.fun_int_Code_integer)) (let ((_let_1 (tptp.aTP_Lamm_tz I5))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun3610984093196804608t_bool _let_1 X)))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun3610984093196804608t_bool _let_1 Y)))) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun3610984093196804608t_bool (tptp.aa_fun2519502641837456723t_bool (tptp.aTP_Lamm_ua I5) X) Y)))))))) (forall ((I5 tptp.set_Code_integer) (X tptp.fun_Co8499238673658658103nteger) (Y tptp.fun_Co8499238673658658103nteger)) (let ((_let_1 (tptp.aTP_Lamm_ub I5))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.collect_Code_integer (tptp.aa_fun6999757421500609566r_bool _let_1 X)))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.collect_Code_integer (tptp.aa_fun6999757421500609566r_bool _let_1 Y)))) (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.collect_Code_integer (tptp.aa_fun6999757421500609566r_bool (tptp.aa_fun4344203112627146752r_bool (tptp.aTP_Lamm_uc I5) X) Y)))))))) (forall ((I5 tptp.set_bool) (X tptp.fun_bool_rat) (Y tptp.fun_bool_rat)) (let ((_let_1 (tptp.aTP_Lamm_ud I5))) (=> (tptp.finite_finite_bool (tptp.collect_bool (tptp.aa_fun4510340986217973961l_bool _let_1 X))) (=> (tptp.finite_finite_bool (tptp.collect_bool (tptp.aa_fun4510340986217973961l_bool _let_1 Y))) (tptp.finite_finite_bool (tptp.collect_bool (tptp.aa_fun4510340986217973961l_bool (tptp.aa_fun5608642267463484754l_bool (tptp.aTP_Lamm_ue I5) X) Y))))))) (forall ((I5 tptp.set_nat) (X tptp.fun_nat_rat) (Y tptp.fun_nat_rat)) (let ((_let_1 (tptp.aTP_Lamm_uf I5))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun5637262893798792573t_bool _let_1 X)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun5637262893798792573t_bool _let_1 Y)))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun5637262893798792573t_bool (tptp.aa_fun2107527232086395633t_bool (tptp.aTP_Lamm_ug I5) X) Y)))))))) (forall ((I5 tptp.set_int) (X tptp.fun_int_rat) (Y tptp.fun_int_rat)) (let ((_let_1 (tptp.aTP_Lamm_uh I5))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun258058769140594373t_bool _let_1 X)))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun258058769140594373t_bool _let_1 Y)))) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun258058769140594373t_bool (tptp.aa_fun465274253410646749t_bool (tptp.aTP_Lamm_ui I5) X) Y)))))))) (forall ((I5 tptp.set_Code_integer) (X tptp.fun_Code_integer_rat) (Y tptp.fun_Code_integer_rat)) (let ((_let_1 (tptp.aTP_Lamm_uj I5))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.collect_Code_integer (tptp.aa_fun6870034422411604195r_bool _let_1 X)))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.collect_Code_integer (tptp.aa_fun6870034422411604195r_bool _let_1 Y)))) (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.collect_Code_integer (tptp.aa_fun6870034422411604195r_bool (tptp.aa_fun5917639483493975434r_bool (tptp.aTP_Lamm_uk I5) X) Y)))))))) (forall ((I5 tptp.set_bool) (X tptp.fun_bool_nat) (Y tptp.fun_bool_nat)) (let ((_let_1 (tptp.aTP_Lamm_ul I5))) (=> (tptp.finite_finite_bool (tptp.collect_bool (tptp.aa_fun7969004623323359937l_bool _let_1 X))) (=> (tptp.finite_finite_bool (tptp.collect_bool (tptp.aa_fun7969004623323359937l_bool _let_1 Y))) (tptp.finite_finite_bool (tptp.collect_bool (tptp.aa_fun7969004623323359937l_bool (tptp.aa_fun1357226766775296850l_bool (tptp.aTP_Lamm_um I5) X) Y))))))) (forall ((I5 tptp.set_nat) (X tptp.fun_nat_nat) (Y tptp.fun_nat_nat)) (let ((_let_1 (tptp.aTP_Lamm_un I5))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun1783405840085286277t_bool _let_1 X)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun1783405840085286277t_bool _let_1 Y)))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun1783405840085286277t_bool (tptp.aa_fun5267048652646918913t_bool (tptp.aTP_Lamm_uo I5) X) Y)))))))) (forall ((G tptp.fun_nat_nat) (M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat G) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) K))) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_jy G) K)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2)))) (forall ((G tptp.fun_nat_int) (M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int G) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) K))) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_nq G) K)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2)))) (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A))) (let ((_let_2 (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) B)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_2) B)) (= _let_2 (tptp.aa_nat_nat _let_1 B))))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A))) (let ((_let_2 (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) B)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int _let_2) B)) (= _let_2 (tptp.aa_int_int _let_1 B))))))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (tptp.modulo364778990260209775nteger A))) (let ((_let_2 (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) B)))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger _let_2) B)) (= _let_2 (tptp.aa_Cod1783974652533396728nteger _let_1 B))))))) (forall ((I5 tptp.set_bool) (X tptp.fun_bo7282069421189217543nteger) (Y tptp.fun_bo7282069421189217543nteger)) (let ((_let_1 (tptp.aTP_Lamm_up I5))) (=> (tptp.finite_finite_bool (tptp.collect_bool (tptp.aa_fun7063430368917475406l_bool _let_1 X))) (=> (tptp.finite_finite_bool (tptp.collect_bool (tptp.aa_fun7063430368917475406l_bool _let_1 Y))) (tptp.finite_finite_bool (tptp.collect_bool (tptp.aa_fun7063430368917475406l_bool (tptp.aa_fun8946763977956929170l_bool (tptp.aTP_Lamm_uq I5) X) Y))))))) (forall ((I5 tptp.set_nat) (X tptp.fun_nat_Code_integer) (Y tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.aTP_Lamm_ur I5))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun1752071697927428280t_bool _let_1 X)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun1752071697927428280t_bool _let_1 Y)))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun1752071697927428280t_bool (tptp.aa_fun4813323487062687079t_bool (tptp.aTP_Lamm_us I5) X) Y)))))))) (forall ((I5 tptp.set_int) (X tptp.fun_int_Code_integer) (Y tptp.fun_int_Code_integer)) (let ((_let_1 (tptp.aTP_Lamm_ut I5))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun3610984093196804608t_bool _let_1 X)))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun3610984093196804608t_bool _let_1 Y)))) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun3610984093196804608t_bool (tptp.aa_fun2519502641837456723t_bool (tptp.aTP_Lamm_uu I5) X) Y)))))))) (forall ((I5 tptp.set_Code_integer) (X tptp.fun_Co8499238673658658103nteger) (Y tptp.fun_Co8499238673658658103nteger)) (let ((_let_1 (tptp.aTP_Lamm_uv I5))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.collect_Code_integer (tptp.aa_fun6999757421500609566r_bool _let_1 X)))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.collect_Code_integer (tptp.aa_fun6999757421500609566r_bool _let_1 Y)))) (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.collect_Code_integer (tptp.aa_fun6999757421500609566r_bool (tptp.aa_fun4344203112627146752r_bool (tptp.aTP_Lamm_uw I5) X) Y)))))))) (forall ((I5 tptp.set_bool) (X tptp.fun_bool_assn) (Y tptp.fun_bool_assn)) (let ((_let_1 (tptp.aTP_Lamm_ux I5))) (=> (tptp.finite_finite_bool (tptp.collect_bool (tptp.aa_fun4109262947370446873l_bool _let_1 X))) (=> (tptp.finite_finite_bool (tptp.collect_bool (tptp.aa_fun4109262947370446873l_bool _let_1 Y))) (tptp.finite_finite_bool (tptp.collect_bool (tptp.aa_fun4109262947370446873l_bool (tptp.aa_fun3956630383439263058l_bool (tptp.aTP_Lamm_uy I5) X) Y))))))) (forall ((I5 tptp.set_nat) (X tptp.fun_nat_assn) (Y tptp.fun_nat_assn)) (let ((_let_1 (tptp.aTP_Lamm_uz I5))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun1272683333798124589t_bool _let_1 X)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun1272683333798124589t_bool _let_1 Y)))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun1272683333798124589t_bool (tptp.aa_fun7103831392407232081t_bool (tptp.aTP_Lamm_va I5) X) Y)))))))) (forall ((I5 tptp.set_int) (X tptp.fun_int_assn) (Y tptp.fun_int_assn)) (let ((_let_1 (tptp.aTP_Lamm_vb I5))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun1414614411059211637t_bool _let_1 X)))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun1414614411059211637t_bool _let_1 Y)))) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun1414614411059211637t_bool (tptp.aa_fun5523883950577104445t_bool (tptp.aTP_Lamm_vc I5) X) Y)))))))) (forall ((I5 tptp.set_Code_integer) (X tptp.fun_Co4490034186337852034r_assn) (Y tptp.fun_Co4490034186337852034r_assn)) (let ((_let_1 (tptp.aTP_Lamm_vd I5))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.collect_Code_integer (tptp.aa_fun8795547071341169043r_bool _let_1 X)))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.collect_Code_integer (tptp.aa_fun8795547071341169043r_bool _let_1 Y)))) (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.collect_Code_integer (tptp.aa_fun8795547071341169043r_bool (tptp.aa_fun7758107644544034538r_bool (tptp.aTP_Lamm_ve I5) X) Y)))))))) (forall ((I5 tptp.set_bool) (X tptp.fun_bool_rat) (Y tptp.fun_bool_rat)) (let ((_let_1 (tptp.aTP_Lamm_vf I5))) (=> (tptp.finite_finite_bool (tptp.collect_bool (tptp.aa_fun4510340986217973961l_bool _let_1 X))) (=> (tptp.finite_finite_bool (tptp.collect_bool (tptp.aa_fun4510340986217973961l_bool _let_1 Y))) (tptp.finite_finite_bool (tptp.collect_bool (tptp.aa_fun4510340986217973961l_bool (tptp.aa_fun5608642267463484754l_bool (tptp.aTP_Lamm_vg I5) X) Y))))))) (forall ((I5 tptp.set_nat) (X tptp.fun_nat_rat) (Y tptp.fun_nat_rat)) (let ((_let_1 (tptp.aTP_Lamm_vh I5))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun5637262893798792573t_bool _let_1 X)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun5637262893798792573t_bool _let_1 Y)))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun5637262893798792573t_bool (tptp.aa_fun2107527232086395633t_bool (tptp.aTP_Lamm_vi I5) X) Y)))))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) _let_1)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Y) _let_1))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) Y)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger X) Y)))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Y) _let_1))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Y) _let_1))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) _let_1)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Y) _let_1))) tptp.zero_z3403309356797280102nteger)) (and (= X tptp.zero_z3403309356797280102nteger) (= Y tptp.zero_z3403309356797280102nteger))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1))) tptp.zero_zero_rat)) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Y) _let_1))) tptp.zero_zero_int)) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) _let_1)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Y) _let_1)))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Y) _let_1)))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) _let_1)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Y) _let_1)))) (or (not (= X tptp.zero_z3403309356797280102nteger)) (not (= Y tptp.zero_z3403309356797280102nteger)))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1)))) (or (not (= X tptp.zero_zero_rat)) (not (= Y tptp.zero_zero_rat)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Y) _let_1)))) (or (not (= X tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int)))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) _let_1)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Y) _let_1))) tptp.zero_z3403309356797280102nteger))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1))) tptp.zero_zero_rat))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Y) _let_1))) tptp.zero_zero_int))))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N2))) (= (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) _let_1)))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N2))) (= (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) _let_1)))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2))) (= (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger _let_1) _let_1)))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat N2))) (= (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat _let_1) _let_1)))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural N2))) (= (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 N2)) (tptp.plus_p4538020629002901425atural _let_1 _let_1)))) (forall ((A3 tptp.set_bool) (G tptp.fun_bo7282069421189217543nteger) (P tptp.fun_bool_bool)) (=> (tptp.finite_finite_bool A3) (= (tptp.groups1682264926906508858nteger G (tptp.collect_bool (tptp.aa_fun8098540714523660868l_bool (tptp.aTP_Lamm_am A3) P))) (tptp.groups1682264926906508858nteger (tptp.aa_fun6792447306164353798nteger (tptp.aTP_Lamm_vj G) P) A3)))) (forall ((A3 tptp.set_nat) (G tptp.fun_nat_Code_integer) (P tptp.fun_nat_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger G) (tptp.collect_nat (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_aq A3) P))) (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger (tptp.aa_fun42370497693836430nteger (tptp.aTP_Lamm_vk G) P)) A3)))) (forall ((A3 tptp.set_int) (G tptp.fun_int_Code_integer) (P tptp.fun_int_bool)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups7873554091576472773nteger G (tptp.collect_int (tptp.aa_fun5146555767781538748t_bool (tptp.aTP_Lamm_ar A3) P))) (tptp.groups7873554091576472773nteger (tptp.aa_fun5397227419668681614nteger (tptp.aTP_Lamm_vl G) P) A3)))) (forall ((A3 tptp.set_Code_integer) (G tptp.fun_Co8499238673658658103nteger) (P tptp.fun_Co8822979462182099027r_bool)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups879477027807139574nteger G (tptp.collect_Code_integer (tptp.aa_fun8875953811088571772r_bool (tptp.aTP_Lamm_vm A3) P))) (tptp.groups879477027807139574nteger (tptp.aa_fun526110101794841038nteger (tptp.aTP_Lamm_vn G) P) A3)))) (forall ((A3 tptp.set_bool) (G tptp.fun_bool_rat) (P tptp.fun_bool_bool)) (=> (tptp.finite_finite_bool A3) (= (tptp.groups5133371213642249141ol_rat G (tptp.collect_bool (tptp.aa_fun8098540714523660868l_bool (tptp.aTP_Lamm_am A3) P))) (tptp.groups5133371213642249141ol_rat (tptp.aa_fun4278745445771542273ol_rat (tptp.aTP_Lamm_vo G) P) A3)))) (forall ((A3 tptp.set_nat) (G tptp.fun_nat_rat) (P tptp.fun_nat_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat G) (tptp.collect_nat (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_aq A3) P))) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aa_fun5656162108953708681at_rat (tptp.aTP_Lamm_vp G) P)) A3)))) (forall ((A3 tptp.set_int) (G tptp.fun_int_rat) (P tptp.fun_int_bool)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups3906332499630173760nt_rat G (tptp.collect_int (tptp.aa_fun5146555767781538748t_bool (tptp.aTP_Lamm_ar A3) P))) (tptp.groups3906332499630173760nt_rat (tptp.aa_fun4400602662665189257nt_rat (tptp.aTP_Lamm_vq G) P) A3)))) (forall ((A3 tptp.set_Code_integer) (G tptp.fun_Code_integer_rat) (P tptp.fun_Co8822979462182099027r_bool)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups6602215022474089585er_rat G (tptp.collect_Code_integer (tptp.aa_fun8875953811088571772r_bool (tptp.aTP_Lamm_vm A3) P))) (tptp.groups6602215022474089585er_rat (tptp.aa_fun4600455420518417865er_rat (tptp.aTP_Lamm_vr G) P) A3)))) (forall ((A3 tptp.set_bool) (G tptp.fun_bool_nat) (P tptp.fun_bool_bool)) (=> (tptp.finite_finite_bool A3) (= (tptp.groups5768501273728744877ol_nat G (tptp.collect_bool (tptp.aa_fun8098540714523660868l_bool (tptp.aTP_Lamm_am A3) P))) (tptp.groups5768501273728744877ol_nat (tptp.aa_fun7786974004164939001ol_nat (tptp.aTP_Lamm_vs G) P) A3)))) (forall ((A3 tptp.set_int) (G tptp.fun_int_nat) (P tptp.fun_int_bool)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups4541462559716669496nt_nat G (tptp.collect_int (tptp.aa_fun5146555767781538748t_bool (tptp.aTP_Lamm_ar A3) P))) (tptp.groups4541462559716669496nt_nat (tptp.aa_fun7908831221058585985nt_nat (tptp.aTP_Lamm_vt G) P) A3)))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) Y)) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Y) _let_1))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) X)) Y))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) Y)) _let_2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int X) _let_2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Y) _let_2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int _let_1)) X)) Y)))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger X) Y)) _let_2) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) _let_2)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Y) _let_2))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger _let_1)) X)) Y)))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) Y)) _let_2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_2)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_2))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat _let_1)) X)) Y)))))) (forall ((X tptp.code_natural) (Y tptp.code_natural)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_nat_Code_natural (tptp.power_7079662738309270450atural (tptp.plus_p4538020629002901425atural X Y)) _let_2) (tptp.plus_p4538020629002901425atural (tptp.plus_p4538020629002901425atural (tptp.aa_nat_Code_natural (tptp.power_7079662738309270450atural X) _let_2) (tptp.aa_nat_Code_natural (tptp.power_7079662738309270450atural Y) _let_2)) (tptp.times_2397367101498566445atural (tptp.times_2397367101498566445atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural _let_1) X) Y)))))) (forall ((X tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger X) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_Code_integer))))) (forall ((X tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) X)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_rat))))) (forall ((X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) X)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_int))))) (forall ((M6 tptp.fun_Pr5160692531401422620nt_nat) (P tptp.fun_Pr803113274115125473t_bool)) (=> (tptp.finite2998713641127702882nt_int (tptp.collec213857154873943460nt_int (tptp.aTP_Lamm_vu M6))) (tptp.finite2998713641127702882nt_int (tptp.collec213857154873943460nt_int (tptp.aa_fun8917503761599146496t_bool (tptp.aTP_Lamm_vv M6) P))))) (forall ((M6 tptp.fun_list_nat_nat) (P tptp.fun_list_nat_bool)) (=> (tptp.finite8100373058378681591st_nat (tptp.collect_list_nat (tptp.aTP_Lamm_vw M6))) (tptp.finite8100373058378681591st_nat (tptp.collect_list_nat (tptp.aa_fun6009467934925565500t_bool (tptp.aTP_Lamm_vx M6) P))))) (forall ((M6 tptp.fun_set_nat_nat) (P tptp.fun_set_nat_bool)) (=> (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat (tptp.collect_set_nat (tptp.aTP_Lamm_vy M6)))) (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat (tptp.collect_set_nat (tptp.aa_fun3565389549526402364t_bool (tptp.aTP_Lamm_vz M6) P)))))) (forall ((M6 tptp.fun_nat_nat) (P tptp.fun_nat_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aTP_Lamm_wa M6)))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_wb M6) P)))))) (forall ((M6 tptp.fun_int_nat) (P tptp.fun_int_bool)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aTP_Lamm_wc M6)))) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun5146555767781538748t_bool (tptp.aTP_Lamm_wd M6) P)))))) (forall ((M6 tptp.fun_Code_integer_nat) (P tptp.fun_Co8822979462182099027r_bool)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.collect_Code_integer (tptp.aTP_Lamm_we M6)))) (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.collect_Code_integer (tptp.aa_fun8875953811088571772r_bool (tptp.aTP_Lamm_wf M6) P)))))) (forall ((M6 tptp.fun_Pr2602117396471556196at_nat) (P tptp.fun_Pr7757163693017731481t_bool)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat (tptp.collec3392354462482085612at_nat (tptp.aTP_Lamm_wg M6)))) (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat (tptp.collec3392354462482085612at_nat (tptp.aa_fun830836278467416944t_bool (tptp.aTP_Lamm_wh M6) P)))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2))))) (forall ((A tptp.rat) (N2 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2))))) (forall ((A tptp.int) (N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2))))) (forall ((Y tptp.code_integer) (X tptp.code_integer)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) Y)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) _let_1)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Y) _let_1))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer X)) Y)))))) (forall ((Y tptp.rat) (X tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) Y)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat X)) Y)))))) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Y) _let_1))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int X)) Y)))))) (forall ((S tptp.set_bool) (H tptp.fun_bool_nat) (G tptp.fun_bool_nat)) (=> (tptp.finite_finite_bool S) (= (tptp.groups5768501273728744877ol_nat H S) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun9158115899668126683at_nat (tptp.aa_fun3360519976762538604at_nat (tptp.aTP_Lamm_wj S) H) G)) (tptp.image_bool_nat G S))))) (forall ((S tptp.set_int) (H tptp.fun_int_nat) (G tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (= (tptp.groups4541462559716669496nt_nat H S) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun5507398438843482068at_nat (tptp.aa_fun3220669823809117514at_nat (tptp.aTP_Lamm_wl S) H) G)) (tptp.image_int_nat G S))))) (forall ((S tptp.set_Code_integer) (H tptp.fun_Code_integer_nat) (G tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S)) (= (tptp.groups7237345082560585321er_nat H S) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun1707803128846032901at_nat (tptp.aa_fun2075405564639334828at_nat (tptp.aTP_Lamm_wn S) H) G)) (tptp.image_951025933927791156er_nat G S))))) (forall ((S tptp.set_bool) (H tptp.fun_bool_int) (G tptp.fun_bool_int)) (=> (tptp.finite_finite_bool S) (= (tptp.groups5766010803219694601ol_int H S) (tptp.groups4538972089207619220nt_int (tptp.aa_fun707691183620917999nt_int (tptp.aa_fun7930693643136840740nt_int (tptp.aTP_Lamm_wp S) H) G) (tptp.image_bool_int G S))))) (forall ((S tptp.set_nat) (H tptp.fun_nat_int) (G tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (= (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int H) S) (tptp.groups4538972089207619220nt_int (tptp.aa_fun6564396834021159052nt_int (tptp.aa_fun7327629743597663234nt_int (tptp.aTP_Lamm_wr S) H) G) (tptp.image_nat_int G S))))) (forall ((S tptp.set_Code_integer) (H tptp.fun_Code_integer_int) (G tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S)) (= (tptp.groups7234854612051535045er_int H S) (tptp.groups4538972089207619220nt_int (tptp.aa_fun2480750449653600025nt_int (tptp.aa_fun6168136379806246172nt_int (tptp.aTP_Lamm_wt S) H) G) (tptp.image_948535463418740880er_int G S))))) (forall ((S tptp.set_nat) (H tptp.fun_nat_nat) (G tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat H) S) (tptp.groups4541462559716669496nt_nat (tptp.aa_fun1518875816675579952nt_nat (tptp.aa_fun3769689747080337738nt_nat (tptp.aTP_Lamm_wu S) H) G) (tptp.image_nat_int G S))))) (forall ((S tptp.set_nat) (H tptp.fun_nat_nat) (G tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat H) S) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aa_fun6854695580826382482at_nat (tptp.aTP_Lamm_ww S) H) G)) (tptp.image_nat_nat G S))))) (forall ((S tptp.set_int) (H tptp.fun_int_int) (G tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (= (tptp.groups4538972089207619220nt_int H S) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aa_fun1329547419334285360at_int (tptp.aa_fun6778609820326443010at_int (tptp.aTP_Lamm_wx S) H) G)) (tptp.image_int_nat G S))))) (forall ((S tptp.set_int) (H tptp.fun_int_int) (G tptp.fun_int_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (= (tptp.groups4538972089207619220nt_int H S) (tptp.groups4538972089207619220nt_int (tptp.aa_fun6280345759651049192nt_int (tptp.aa_fun3693603986580398266nt_int (tptp.aTP_Lamm_wz S) H) G) (tptp.image_int_int G S))))) (forall ((X tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer X)) tptp.one_one_Code_integer)))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat X)) tptp.one_one_rat)))) (forall ((X tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int X)) tptp.one_one_int)))) (forall ((X tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer X)) tptp.one_one_Code_integer)))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.abs_abs_rat X)) tptp.one_one_rat)))) (forall ((X tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.abs_abs_int X)) tptp.one_one_int)))) (forall ((A3 tptp.set_bool) (G tptp.fun_bo7282069421189217543nteger) (P tptp.fun_bool_bool)) (=> (tptp.finite_finite_bool A3) (= (tptp.groups7272450149305381519nteger G (tptp.collect_bool (tptp.aa_fun8098540714523660868l_bool (tptp.aTP_Lamm_am A3) P))) (tptp.groups7272450149305381519nteger (tptp.aa_fun6792447306164353798nteger (tptp.aTP_Lamm_xa G) P) A3)))) (forall ((A3 tptp.set_nat) (G tptp.fun_nat_Code_integer) (P tptp.fun_nat_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger G) (tptp.collect_nat (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_aq A3) P))) (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger (tptp.aa_fun42370497693836430nteger (tptp.aTP_Lamm_xb G) P)) A3)))) (forall ((A3 tptp.set_int) (G tptp.fun_int_Code_integer) (P tptp.fun_int_bool)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups3827104343326376752nteger G (tptp.collect_int (tptp.aa_fun5146555767781538748t_bool (tptp.aTP_Lamm_ar A3) P))) (tptp.groups3827104343326376752nteger (tptp.aa_fun5397227419668681614nteger (tptp.aTP_Lamm_xc G) P) A3)))) (forall ((A3 tptp.set_Code_integer) (G tptp.fun_Co8499238673658658103nteger) (P tptp.fun_Co8822979462182099027r_bool)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups3674199335183972705nteger G (tptp.collect_Code_integer (tptp.aa_fun8875953811088571772r_bool (tptp.aTP_Lamm_vm A3) P))) (tptp.groups3674199335183972705nteger (tptp.aa_fun526110101794841038nteger (tptp.aTP_Lamm_xd G) P) A3)))) (forall ((A3 tptp.set_bool) (G tptp.fun_bool_assn) (P tptp.fun_bool_bool)) (=> (tptp.finite_finite_bool A3) (= (tptp.groups4835110720589548378l_assn G (tptp.collect_bool (tptp.aa_fun8098540714523660868l_bool (tptp.aTP_Lamm_am A3) P))) (tptp.groups4835110720589548378l_assn (tptp.aa_fun5239432835080189521l_assn (tptp.aTP_Lamm_xe G) P) A3)))) (forall ((A3 tptp.set_nat) (G tptp.fun_nat_assn) (P tptp.fun_nat_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.groups6906906614972039071t_assn G (tptp.collect_nat (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_aq A3) P))) (tptp.groups6906906614972039071t_assn (tptp.aa_fun1954384836919635929t_assn (tptp.aTP_Lamm_xf G) P) A3)))) (forall ((A3 tptp.set_int) (G tptp.fun_int_assn) (P tptp.fun_int_bool)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups7882442080178216443t_assn G (tptp.collect_int (tptp.aa_fun5146555767781538748t_bool (tptp.aTP_Lamm_ar A3) P))) (tptp.groups7882442080178216443t_assn (tptp.aa_fun6196142345855524569t_assn (tptp.aTP_Lamm_xg G) P) A3)))) (forall ((A3 tptp.set_Code_integer) (G tptp.fun_Co4490034186337852034r_assn) (P tptp.fun_Co8822979462182099027r_bool)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups1304777262505850412r_assn G (tptp.collect_Code_integer (tptp.aa_fun8875953811088571772r_bool (tptp.aTP_Lamm_vm A3) P))) (tptp.groups1304777262505850412r_assn (tptp.aa_fun8033543692415806745r_assn (tptp.aTP_Lamm_xh G) P) A3)))) (forall ((A3 tptp.set_bool) (G tptp.fun_bool_rat) (P tptp.fun_bool_bool)) (=> (tptp.finite_finite_bool A3) (= (tptp.groups1259819201609700362ol_rat G (tptp.collect_bool (tptp.aa_fun8098540714523660868l_bool (tptp.aTP_Lamm_am A3) P))) (tptp.groups1259819201609700362ol_rat (tptp.aa_fun4278745445771542273ol_rat (tptp.aTP_Lamm_xi G) P) A3)))) (forall ((A3 tptp.set_nat) (G tptp.fun_nat_rat) (P tptp.fun_nat_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat G) (tptp.collect_nat (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_aq A3) P))) (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat (tptp.aa_fun5656162108953708681at_rat (tptp.aTP_Lamm_xj G) P)) A3)))) (forall ((S tptp.set_bool) (H tptp.fun_bool_nat) (G tptp.fun_bool_nat)) (=> (tptp.finite_finite_bool S) (= (tptp.groups1894949261696196098ol_nat H S) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_fun9158115899668126683at_nat (tptp.aa_fun3360519976762538604at_nat (tptp.aTP_Lamm_xk S) H) G)) (tptp.image_bool_nat G S))))) (forall ((S tptp.set_int) (H tptp.fun_int_nat) (G tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (= (tptp.groups1707563613775114915nt_nat H S) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_fun5507398438843482068at_nat (tptp.aa_fun3220669823809117514at_nat (tptp.aTP_Lamm_xl S) H) G)) (tptp.image_int_nat G S))))) (forall ((S tptp.set_Code_integer) (H tptp.fun_Code_integer_nat) (G tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S)) (= (tptp.groups3190895334310489300er_nat H S) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_fun1707803128846032901at_nat (tptp.aa_fun2075405564639334828at_nat (tptp.aTP_Lamm_xm S) H) G)) (tptp.image_951025933927791156er_nat G S))))) (forall ((S tptp.set_bool) (H tptp.fun_bool_int) (G tptp.fun_bool_nat)) (=> (tptp.finite_finite_bool S) (= (tptp.groups1892458791187145822ol_int H S) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_fun4980264880158929975at_int (tptp.aa_fun1792327440028109676at_int (tptp.aTP_Lamm_xn S) H) G)) (tptp.image_bool_nat G S))))) (forall ((S tptp.set_Code_integer) (H tptp.fun_Code_integer_int) (G tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S)) (= (tptp.groups3188404863801439024er_int H S) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_fun6753324146191612001at_int (tptp.aa_fun29770176697515108at_int (tptp.aTP_Lamm_xo S) H) G)) (tptp.image_951025933927791156er_nat G S))))) (forall ((S tptp.set_bool) (H tptp.fun_bool_int) (G tptp.fun_bool_int)) (=> (tptp.finite_finite_bool S) (= (tptp.groups1892458791187145822ol_int H S) (tptp.groups1705073143266064639nt_int (tptp.aa_fun707691183620917999nt_int (tptp.aa_fun7930693643136840740nt_int (tptp.aTP_Lamm_xp S) H) G) (tptp.image_bool_int G S))))) (forall ((S tptp.set_Code_integer) (H tptp.fun_Code_integer_int) (G tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S)) (= (tptp.groups3188404863801439024er_int H S) (tptp.groups1705073143266064639nt_int (tptp.aa_fun2480750449653600025nt_int (tptp.aa_fun6168136379806246172nt_int (tptp.aTP_Lamm_xq S) H) G) (tptp.image_948535463418740880er_int G S))))) (forall ((S tptp.set_nat) (H tptp.fun_nat_nat) (G tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat H) S) (tptp.groups1707563613775114915nt_nat (tptp.aa_fun1518875816675579952nt_nat (tptp.aa_fun3769689747080337738nt_nat (tptp.aTP_Lamm_xr S) H) G) (tptp.image_nat_int G S))))) (forall ((S tptp.set_nat) (H tptp.fun_nat_nat) (G tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat H) S) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aa_fun6854695580826382482at_nat (tptp.aTP_Lamm_xs S) H) G)) (tptp.image_nat_nat G S))))) (forall ((S tptp.set_nat) (H tptp.fun_nat_int) (G tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (= (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int H) S) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_fun1613598493704395220at_int (tptp.aa_fun1189263540488932170at_int (tptp.aTP_Lamm_xt S) H) G)) (tptp.image_nat_nat G S))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int A)) N2))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) _let_1) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) N2))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) _let_1) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2))))) (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) N2))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) _let_1) (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_8256067586552552935nteger A))) (= (tptp.aa_nat_Code_integer _let_2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) N2))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_nat_Code_integer _let_2 N2)) _let_1)))))) (forall ((A tptp.assn) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_power_assn A))) (= (tptp.aa_nat_assn _let_2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) N2))) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn A) (tptp.aa_nat_assn (tptp.power_power_assn (tptp.aa_nat_assn _let_2 N2)) _let_1)))))) (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_power_rat A))) (= (tptp.aa_nat_rat _let_2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) N2))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_nat_rat _let_2 N2)) _let_1)))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (= (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) N2))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat _let_2 N2)) _let_1)))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_fun_nat_int tptp.power_power_int A))) (= (tptp.aa_nat_int _let_2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) N2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_nat_int _let_2 N2)) _let_1)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 N2)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N2) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (forall ((A tptp.rat) (B tptp.rat)) (tptp.finite_finite_rat (tptp.collect_rat (tptp.aa_rat_fun_rat_bool (tptp.aTP_Lamm_xu A) B)))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N2) K))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D2 tptp.nat) (G tptp.fun_nat_nat) (H tptp.fun_nat_nat)) (=> (= A C) (=> (= B D2) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) X3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) D2)) (= (tptp.aa_nat_nat G X3) (tptp.aa_nat_nat H X3))))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat A) B)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat H) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat C) D2))))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int) (G tptp.fun_int_int) (H tptp.fun_int_int)) (=> (= A C) (=> (= B D2) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) X3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) D2)) (= (tptp.aa_int_int G X3) (tptp.aa_int_int H X3))))) (= (tptp.groups4538972089207619220nt_int G (tptp.set_or4662586982721622107an_int A B)) (tptp.groups4538972089207619220nt_int H (tptp.set_or4662586982721622107an_int C D2))))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D2 tptp.nat) (G tptp.fun_nat_nat) (H tptp.fun_nat_nat)) (=> (= A C) (=> (= B D2) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) X3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) D2)) (= (tptp.aa_nat_nat G X3) (tptp.aa_nat_nat H X3))))) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat G) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat A) B)) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat H) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat C) D2))))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D2 tptp.nat) (G tptp.fun_nat_int) (H tptp.fun_nat_int)) (=> (= A C) (=> (= B D2) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) X3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) D2)) (= (tptp.aa_nat_int G X3) (tptp.aa_nat_int H X3))))) (= (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int G) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat A) B)) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int H) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat C) D2))))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int) (G tptp.fun_int_int) (H tptp.fun_int_int)) (=> (= A C) (=> (= B D2) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) X3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) D2)) (= (tptp.aa_int_int G X3) (tptp.aa_int_int H X3))))) (= (tptp.groups1705073143266064639nt_int G (tptp.set_or4662586982721622107an_int A B)) (tptp.groups1705073143266064639nt_int H (tptp.set_or4662586982721622107an_int C D2))))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.binomial N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial M) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) K)))))))) (forall ((L tptp.rat) (M tptp.rat) (U tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat L) M)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat M) U)) (= (tptp.sup_sup_set_rat (tptp.set_or4029947393144176647an_rat L M) (tptp.set_or633870826150836451st_rat M U)) (tptp.set_or633870826150836451st_rat L U))))) (forall ((L tptp.num) (M tptp.num) (U tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num L) M)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) U)) (= (tptp.sup_sup_set_num (tptp.set_or1222409239386451017an_num L M) (tptp.set_or7049704709247886629st_num M U)) (tptp.set_or7049704709247886629st_num L U))))) (forall ((L tptp.nat) (M tptp.nat) (U tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat L) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) U)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat L) M)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) U)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat L) U))))) (forall ((L tptp.int) (M tptp.int) (U tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int L) M)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int M) U)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int (tptp.set_or4662586982721622107an_int L M)) (tptp.set_or1266510415728281911st_int M U)) (tptp.set_or1266510415728281911st_int L U))))) (forall ((L tptp.code_integer) (M tptp.code_integer) (U tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger L) M)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger M) U)) (= (tptp.sup_su848401254843788991nteger (tptp.set_or8404916559141939852nteger L M) (tptp.set_or189985376899183464nteger M U)) (tptp.set_or189985376899183464nteger L U))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N2) K)) (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat (tptp.aa_nat_fun_nat_rat (tptp.aTP_Lamm_xv K) N2)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K))))) (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_nat_nat _let_2 B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_3)) B)) (= (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat _let_1 _let_3)) (tptp.aa_nat_nat _let_1 B)))))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.divide_divide_int A))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_int_int _let_2 B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) _let_3)) B)) (= (tptp.aa_int_int _let_2 (tptp.aa_int_int _let_1 _let_3)) (tptp.aa_int_int _let_1 B)))))))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (tptp.divide6298287555418463151nteger A))) (let ((_let_2 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_Cod1783974652533396728nteger _let_2 B))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) _let_3)) B)) (= (tptp.aa_Cod1783974652533396728nteger _let_2 (tptp.aa_Cod1783974652533396728nteger _let_1 _let_3)) (tptp.aa_Cod1783974652533396728nteger _let_1 B)))))))) (forall ((L tptp.bool) (M tptp.bool) (U tptp.bool)) (= (tptp.inf_inf_set_bool (tptp.set_or8576162586734908840n_bool L M) (tptp.set_or1454250544011482060t_bool M U)) tptp.bot_bot_set_bool)) (forall ((L tptp.nat) (M tptp.nat) (U tptp.nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat L) M)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) U)) tptp.bot_bot_set_nat)) (forall ((L tptp.int) (M tptp.int) (U tptp.int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int (tptp.set_or4662586982721622107an_int L M)) (tptp.set_or1266510415728281911st_int M U)) tptp.bot_bot_set_int)) (forall ((L tptp.code_integer) (M tptp.code_integer) (U tptp.code_integer)) (= (tptp.inf_in1364745209274528805nteger (tptp.set_or8404916559141939852nteger L M) (tptp.set_or189985376899183464nteger M U)) tptp.bot_bo3990330152332043303nteger)) (forall ((M tptp.nat) (N2 tptp.nat) (P3 tptp.nat) (G tptp.fun_na2338080690716861136at_nat)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) P3)) (= (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat (tptp.groups6857163185585827899at_nat G (tptp.aa_nat_set_nat _let_1 N2))) (tptp.groups6857163185585827899at_nat G (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat N2) P3))) (tptp.groups6857163185585827899at_nat G (tptp.aa_nat_set_nat _let_1 P3))))))) (forall ((M tptp.nat) (N2 tptp.nat) (P3 tptp.nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (tptp.groups2906978787729119204at_rat G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) P3)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_set_nat_rat _let_2 (tptp.aa_nat_set_nat _let_1 N2))) (tptp.aa_set_nat_rat _let_2 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat N2) P3))) (tptp.aa_set_nat_rat _let_2 (tptp.aa_nat_set_nat _let_1 P3)))))))) (forall ((M tptp.nat) (N2 tptp.nat) (P3 tptp.nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (tptp.groups3539618377306564664at_int G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) P3)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_set_nat_int _let_2 (tptp.aa_nat_set_nat _let_1 N2))) (tptp.aa_set_nat_int _let_2 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat N2) P3))) (tptp.aa_set_nat_int _let_2 (tptp.aa_nat_set_nat _let_1 P3)))))))) (forall ((M tptp.nat) (N2 tptp.nat) (P3 tptp.nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (tptp.groups3542108847815614940at_nat G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) P3)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_set_nat_nat _let_2 (tptp.aa_nat_set_nat _let_1 N2))) (tptp.aa_set_nat_nat _let_2 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat N2) P3))) (tptp.aa_set_nat_nat _let_2 (tptp.aa_nat_set_nat _let_1 P3)))))))) (forall ((M tptp.nat) (N2 tptp.nat) (P3 tptp.nat) (F tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups2906978787729119204at_rat F))) (let ((_let_2 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) P3)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_set_nat_rat _let_1 (tptp.aa_nat_set_nat _let_2 P3))) (tptp.aa_set_nat_rat _let_1 (tptp.aa_nat_set_nat _let_2 N2))) (tptp.aa_set_nat_rat _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat N2) P3)))))))) (forall ((M tptp.nat) (N2 tptp.nat) (P3 tptp.nat) (F tptp.fun_nat_int)) (let ((_let_1 (tptp.groups3539618377306564664at_int F))) (let ((_let_2 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) P3)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_set_nat_int _let_1 (tptp.aa_nat_set_nat _let_2 P3))) (tptp.aa_set_nat_int _let_1 (tptp.aa_nat_set_nat _let_2 N2))) (tptp.aa_set_nat_int _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat N2) P3)))))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) Y)) _let_2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int X) _let_2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Y) _let_2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int _let_1)) X)) Y)))))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger X) Y)) _let_2) (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) _let_2)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Y) _let_2))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger _let_1)) X)) Y)))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat X) Y)) _let_2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_2)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_2))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat _let_1)) X)) Y)))))) (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.binomial N2))) (let ((_let_3 (tptp.aa_nat_nat _let_2 K))) (let ((_let_4 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2))) (let ((_let_5 (tptp.pp (tptp.aa_nat_bool _let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) K))))) (let ((_let_6 (tptp.pp (tptp.aa_nat_bool _let_4 K)))) (and (=> _let_6 (= _let_3 tptp.zero_zero_nat)) (=> (not _let_6) (and (=> _let_5 (= _let_3 (tptp.aa_nat_nat _let_2 _let_1))) (=> (not _let_5) (= _let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat)) N2) tptp.one_one_nat)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat K)))))))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (P3 tptp.nat) (G tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (tptp.groups3455450783089532116nteger G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) P3)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_set871585252387937313nteger _let_2 (tptp.aa_nat_set_nat _let_1 N2))) (tptp.aa_set871585252387937313nteger _let_2 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat N2) P3))) (tptp.aa_set871585252387937313nteger _let_2 (tptp.aa_nat_set_nat _let_1 P3)))))))) (forall ((M tptp.nat) (N2 tptp.nat) (P3 tptp.nat) (G tptp.fun_nat_assn)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) P3)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat _let_1 N2))) (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat N2) P3))) (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat _let_1 P3))))))) (forall ((M tptp.nat) (N2 tptp.nat) (P3 tptp.nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (tptp.groups73079841787564623at_rat G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) P3)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_set_nat_rat _let_2 (tptp.aa_nat_set_nat _let_1 N2))) (tptp.aa_set_nat_rat _let_2 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat N2) P3))) (tptp.aa_set_nat_rat _let_2 (tptp.aa_nat_set_nat _let_1 P3)))))))) (forall ((M tptp.nat) (N2 tptp.nat) (P3 tptp.nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (tptp.groups708209901874060359at_nat G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) P3)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_set_nat_nat _let_2 (tptp.aa_nat_set_nat _let_1 N2))) (tptp.aa_set_nat_nat _let_2 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat N2) P3))) (tptp.aa_set_nat_nat _let_2 (tptp.aa_nat_set_nat _let_1 P3)))))))) (forall ((M tptp.nat) (N2 tptp.nat) (P3 tptp.nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (tptp.groups705719431365010083at_int G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) P3)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_set_nat_int _let_2 (tptp.aa_nat_set_nat _let_1 N2))) (tptp.aa_set_nat_int _let_2 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat N2) P3))) (tptp.aa_set_nat_int _let_2 (tptp.aa_nat_set_nat _let_1 P3)))))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2))))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 A))))) (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2))))) (tptp.pp (tptp.aa_rat_bool _let_1 A))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2))))) (tptp.pp (tptp.aa_int_bool _let_1 A))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.rat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) tptp.zero_zero_rat)))) (forall ((A tptp.int) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) tptp.zero_zero_int)))) (forall ((A3 tptp.set_bool) (F tptp.fun_bo7282069421189217543nteger)) (=> (tptp.finite_finite_bool A3) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 A3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_bool_Code_integer F X3))))) (= (= (tptp.groups1682264926906508858nteger F A3) tptp.zero_z3403309356797280102nteger) (forall ((X4 tptp.bool)) (=> (tptp.pp (tptp.member_bool X4 A3)) (= (tptp.aa_bool_Code_integer F X4) tptp.zero_z3403309356797280102nteger))))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_Code_integer)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer F X3))))) (= (= (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger F) A3) tptp.zero_z3403309356797280102nteger) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A3)) (= (tptp.aa_nat_Code_integer F X4) tptp.zero_z3403309356797280102nteger))))))) (forall ((A3 tptp.set_int) (F tptp.fun_int_Code_integer)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_int_Code_integer F X3))))) (= (= (tptp.groups7873554091576472773nteger F A3) tptp.zero_z3403309356797280102nteger) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A3)) (= (tptp.aa_int_Code_integer F X4) tptp.zero_z3403309356797280102nteger))))))) (forall ((A3 tptp.set_Code_integer) (F tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) A3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger F X3))))) (= (= (tptp.groups879477027807139574nteger F A3) tptp.zero_z3403309356797280102nteger) (forall ((X4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X4) A3)) (= (tptp.aa_Cod1783974652533396728nteger F X4) tptp.zero_z3403309356797280102nteger))))))) (forall ((A3 tptp.set_bool) (F tptp.fun_bool_rat)) (=> (tptp.finite_finite_bool A3) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_bool_rat F X3))))) (= (= (tptp.groups5133371213642249141ol_rat F A3) tptp.zero_zero_rat) (forall ((X4 tptp.bool)) (=> (tptp.pp (tptp.member_bool X4 A3)) (= (tptp.aa_bool_rat F X4) tptp.zero_zero_rat))))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat F X3))))) (= (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat F) A3) tptp.zero_zero_rat) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A3)) (= (tptp.aa_nat_rat F X4) tptp.zero_zero_rat))))))) (forall ((A3 tptp.set_int) (F tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_int_rat F X3))))) (= (= (tptp.groups3906332499630173760nt_rat F A3) tptp.zero_zero_rat) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A3)) (= (tptp.aa_int_rat F X4) tptp.zero_zero_rat))))))) (forall ((A3 tptp.set_Code_integer) (F tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_Code_integer_rat F X3))))) (= (= (tptp.groups6602215022474089585er_rat F A3) tptp.zero_zero_rat) (forall ((X4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X4) A3)) (= (tptp.aa_Code_integer_rat F X4) tptp.zero_zero_rat))))))) (forall ((A3 tptp.set_bool) (F tptp.fun_bool_nat)) (=> (tptp.finite_finite_bool A3) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_bool_nat F X3))))) (= (= (tptp.groups5768501273728744877ol_nat F A3) tptp.zero_zero_nat) (forall ((X4 tptp.bool)) (=> (tptp.pp (tptp.member_bool X4 A3)) (= (tptp.aa_bool_nat F X4) tptp.zero_zero_nat))))))) (forall ((A3 tptp.set_int) (F tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_int_nat F X3))))) (= (= (tptp.groups4541462559716669496nt_nat F A3) tptp.zero_zero_nat) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) A3)) (= (tptp.aa_int_nat F X4) tptp.zero_zero_nat))))))) (forall ((S2 tptp.set_nat) (T5 tptp.set_nat) (G tptp.fun_nat_Code_integer) (I2 tptp.fun_nat_nat) (F tptp.fun_nat_Code_integer)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S2)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T5)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) T5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer G X3))))) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) S2)) (exists ((Xa3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa3) T5)) (= (tptp.aa_nat_nat I2 Xa3) X3) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer F X3)) (tptp.aa_nat_Code_integer G Xa3))))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger F) S2)) (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger G) T5)))))))) (forall ((S2 tptp.set_nat) (T5 tptp.set_int) (G tptp.fun_int_Code_integer) (I2 tptp.fun_int_nat) (F tptp.fun_nat_Code_integer)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S2)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T5)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) T5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_int_Code_integer G X3))))) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) S2)) (exists ((Xa3 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa3) T5)) (= (tptp.aa_int_nat I2 Xa3) X3) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer F X3)) (tptp.aa_int_Code_integer G Xa3))))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger F) S2)) (tptp.groups7873554091576472773nteger G T5)))))))) (forall ((S2 tptp.set_nat) (T5 tptp.set_Code_integer) (G tptp.fun_Co8499238673658658103nteger) (I2 tptp.fun_Code_integer_nat) (F tptp.fun_nat_Code_integer)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S2)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T5)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) T5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger G X3))))) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) S2)) (exists ((Xa3 tptp.code_integer)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Xa3) T5)) (= (tptp.aa_Code_integer_nat I2 Xa3) X3) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer F X3)) (tptp.aa_Cod1783974652533396728nteger G Xa3))))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger F) S2)) (tptp.groups879477027807139574nteger G T5)))))))) (forall ((S2 tptp.set_int) (T5 tptp.set_nat) (G tptp.fun_nat_Code_integer) (I2 tptp.fun_nat_int) (F tptp.fun_int_Code_integer)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S2)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T5)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) T5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer G X3))))) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) S2)) (exists ((Xa3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa3) T5)) (= (tptp.aa_nat_int I2 Xa3) X3) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_int_Code_integer F X3)) (tptp.aa_nat_Code_integer G Xa3))))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.groups7873554091576472773nteger F S2)) (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger G) T5)))))))) (forall ((S2 tptp.set_int) (T5 tptp.set_int) (G tptp.fun_int_Code_integer) (I2 tptp.fun_int_int) (F tptp.fun_int_Code_integer)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S2)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T5)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) T5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_int_Code_integer G X3))))) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) S2)) (exists ((Xa3 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa3) T5)) (= (tptp.aa_int_int I2 Xa3) X3) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_int_Code_integer F X3)) (tptp.aa_int_Code_integer G Xa3))))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.groups7873554091576472773nteger F S2)) (tptp.groups7873554091576472773nteger G T5)))))))) (forall ((S2 tptp.set_int) (T5 tptp.set_Code_integer) (G tptp.fun_Co8499238673658658103nteger) (I2 tptp.fun_Code_integer_int) (F tptp.fun_int_Code_integer)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S2)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T5)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) T5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger G X3))))) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) S2)) (exists ((Xa3 tptp.code_integer)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Xa3) T5)) (= (tptp.aa_Code_integer_int I2 Xa3) X3) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_int_Code_integer F X3)) (tptp.aa_Cod1783974652533396728nteger G Xa3))))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.groups7873554091576472773nteger F S2)) (tptp.groups879477027807139574nteger G T5)))))))) (forall ((S2 tptp.set_Code_integer) (T5 tptp.set_nat) (G tptp.fun_nat_Code_integer) (I2 tptp.fun_nat_Code_integer) (F tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S2)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T5)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) T5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer G X3))))) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) S2)) (exists ((Xa3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa3) T5)) (= (tptp.aa_nat_Code_integer I2 Xa3) X3) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger F X3)) (tptp.aa_nat_Code_integer G Xa3))))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.groups879477027807139574nteger F S2)) (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger G) T5)))))))) (forall ((S2 tptp.set_Code_integer) (T5 tptp.set_int) (G tptp.fun_int_Code_integer) (I2 tptp.fun_int_Code_integer) (F tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S2)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T5)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) T5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_int_Code_integer G X3))))) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) S2)) (exists ((Xa3 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa3) T5)) (= (tptp.aa_int_Code_integer I2 Xa3) X3) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger F X3)) (tptp.aa_int_Code_integer G Xa3))))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.groups879477027807139574nteger F S2)) (tptp.groups7873554091576472773nteger G T5)))))))) (forall ((S2 tptp.set_Code_integer) (T5 tptp.set_Code_integer) (G tptp.fun_Co8499238673658658103nteger) (I2 tptp.fun_Co8499238673658658103nteger) (F tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S2)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T5)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) T5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger G X3))))) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) S2)) (exists ((Xa3 tptp.code_integer)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Xa3) T5)) (= (tptp.aa_Cod1783974652533396728nteger I2 Xa3) X3) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger F X3)) (tptp.aa_Cod1783974652533396728nteger G Xa3))))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.groups879477027807139574nteger F S2)) (tptp.groups879477027807139574nteger G T5)))))))) (forall ((S2 tptp.set_nat) (T5 tptp.set_nat) (G tptp.fun_nat_rat) (I2 tptp.fun_nat_nat) (F tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S2)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T5)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) T5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat G X3))))) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) S2)) (exists ((Xa3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa3) T5)) (= (tptp.aa_nat_nat I2 Xa3) X3) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F X3)) (tptp.aa_nat_rat G Xa3))))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat F) S2)) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat G) T5)))))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_rat) (G tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F X3)) (tptp.aa_nat_rat G X3))))) (=> (exists ((X5 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X5) A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat F X5)) (tptp.aa_nat_rat G X5))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat F) A3)) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat G) A3))))))) (forall ((A3 tptp.set_int) (F tptp.fun_int_rat) (G tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat F X3)) (tptp.aa_int_rat G X3))))) (=> (exists ((X5 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X5) A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat F X5)) (tptp.aa_int_rat G X5))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups3906332499630173760nt_rat F A3)) (tptp.groups3906332499630173760nt_rat G A3))))))) (forall ((A3 tptp.set_Code_integer) (F tptp.fun_Code_integer_rat) (G tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_Code_integer_rat F X3)) (tptp.aa_Code_integer_rat G X3))))) (=> (exists ((X5 tptp.code_integer)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X5) A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_Code_integer_rat F X5)) (tptp.aa_Code_integer_rat G X5))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups6602215022474089585er_rat F A3)) (tptp.groups6602215022474089585er_rat G A3))))))) (forall ((A3 tptp.set_int) (F tptp.fun_int_nat) (G tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat F X3)) (tptp.aa_int_nat G X3))))) (=> (exists ((X5 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X5) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_int_nat F X5)) (tptp.aa_int_nat G X5))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.groups4541462559716669496nt_nat F A3)) (tptp.groups4541462559716669496nt_nat G A3))))))) (forall ((A3 tptp.set_Code_integer) (F tptp.fun_Code_integer_nat) (G tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_Code_integer_nat F X3)) (tptp.aa_Code_integer_nat G X3))))) (=> (exists ((X5 tptp.code_integer)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X5) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_Code_integer_nat F X5)) (tptp.aa_Code_integer_nat G X5))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.groups7237345082560585321er_nat F A3)) (tptp.groups7237345082560585321er_nat G A3))))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_int) (G tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int F X3)) (tptp.aa_nat_int G X3))))) (=> (exists ((X5 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X5) A3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int F X5)) (tptp.aa_nat_int G X5))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int F) A3)) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int G) A3))))))) (forall ((A3 tptp.set_Code_integer) (F tptp.fun_Code_integer_int) (G tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) A3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_Code_integer_int F X3)) (tptp.aa_Code_integer_int G X3))))) (=> (exists ((X5 tptp.code_integer)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X5) A3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_Code_integer_int F X5)) (tptp.aa_Code_integer_int G X5))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.groups7234854612051535045er_int F A3)) (tptp.groups7234854612051535045er_int G A3))))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_nat) (G tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat F X3)) (tptp.aa_nat_nat G X3))))) (=> (exists ((X5 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X5) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat F X5)) (tptp.aa_nat_nat G X5))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A3)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) A3))))))) (forall ((A3 tptp.set_int) (F tptp.fun_int_int) (G tptp.fun_int_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int F X3)) (tptp.aa_int_int G X3))))) (=> (exists ((X5 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X5) A3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int F X5)) (tptp.aa_int_int G X5))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.groups4538972089207619220nt_int F A3)) (tptp.groups4538972089207619220nt_int G A3))))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (F tptp.fun_Pr8317260874932935276at_rat) (G tptp.fun_Pr8317260874932935276at_rat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat A3)) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat X3) A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_Pro3608043709957902237at_rat F X3)) (tptp.aa_Pro3608043709957902237at_rat G X3))))) (=> (exists ((X5 tptp.product_prod_nat_nat)) (and (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat X5) A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_Pro3608043709957902237at_rat F X5)) (tptp.aa_Pro3608043709957902237at_rat G X5))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups342789780944988191at_rat F A3)) (tptp.groups342789780944988191at_rat G A3))))))) (forall ((A3 tptp.set_Code_integer) (F tptp.fun_Code_integer_rat) (G tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (not (= A3 tptp.bot_bo3990330152332043303nteger)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_Code_integer_rat F X3)) (tptp.aa_Code_integer_rat G X3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups6602215022474089585er_rat F A3)) (tptp.groups6602215022474089585er_rat G A3))))))) (forall ((A3 tptp.set_bool) (F tptp.fun_bool_rat) (G tptp.fun_bool_rat)) (=> (tptp.finite_finite_bool A3) (=> (not (= A3 tptp.bot_bot_set_bool)) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_bool_rat F X3)) (tptp.aa_bool_rat G X3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups5133371213642249141ol_rat F A3)) (tptp.groups5133371213642249141ol_rat G A3))))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_rat) (G tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (not (= A3 tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat F X3)) (tptp.aa_nat_rat G X3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat F) A3)) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat G) A3))))))) (forall ((A3 tptp.set_int) (F tptp.fun_int_rat) (G tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (not (= A3 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat F X3)) (tptp.aa_int_rat G X3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups3906332499630173760nt_rat F A3)) (tptp.groups3906332499630173760nt_rat G A3))))))) (forall ((A3 tptp.set_Code_integer) (F tptp.fun_Code_integer_nat) (G tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (not (= A3 tptp.bot_bo3990330152332043303nteger)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_Code_integer_nat F X3)) (tptp.aa_Code_integer_nat G X3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.groups7237345082560585321er_nat F A3)) (tptp.groups7237345082560585321er_nat G A3))))))) (forall ((A3 tptp.set_bool) (F tptp.fun_bool_nat) (G tptp.fun_bool_nat)) (=> (tptp.finite_finite_bool A3) (=> (not (= A3 tptp.bot_bot_set_bool)) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_bool_nat F X3)) (tptp.aa_bool_nat G X3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.groups5768501273728744877ol_nat F A3)) (tptp.groups5768501273728744877ol_nat G A3))))))) (forall ((A3 tptp.set_int) (F tptp.fun_int_nat) (G tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (not (= A3 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_int_nat F X3)) (tptp.aa_int_nat G X3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.groups4541462559716669496nt_nat F A3)) (tptp.groups4541462559716669496nt_nat G A3))))))) (forall ((A3 tptp.set_Code_integer) (F tptp.fun_Code_integer_int) (G tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (not (= A3 tptp.bot_bo3990330152332043303nteger)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) A3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_Code_integer_int F X3)) (tptp.aa_Code_integer_int G X3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.groups7234854612051535045er_int F A3)) (tptp.groups7234854612051535045er_int G A3))))))) (forall ((A3 tptp.set_bool) (F tptp.fun_bool_int) (G tptp.fun_bool_int)) (=> (tptp.finite_finite_bool A3) (=> (not (= A3 tptp.bot_bot_set_bool)) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 A3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_bool_int F X3)) (tptp.aa_bool_int G X3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.groups5766010803219694601ol_int F A3)) (tptp.groups5766010803219694601ol_int G A3))))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_int) (G tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (not (= A3 tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int F X3)) (tptp.aa_nat_int G X3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int F) A3)) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int G) A3))))))) (forall ((R tptp.fun_Co8310303586393106575r_bool) (S tptp.set_nat) (H tptp.fun_nat_Code_integer) (G tptp.fun_nat_Code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool R tptp.one_one_Code_integer) tptp.one_one_Code_integer)) (=> (forall ((X12 tptp.code_integer) (Y12 tptp.code_integer) (X22 tptp.code_integer) (Y22 tptp.code_integer)) (=> (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool R X12) X22)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool R Y12) Y22))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool R (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger X12) Y12)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger X22) Y22))))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) S)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool R (tptp.aa_nat_Code_integer H X3)) (tptp.aa_nat_Code_integer G X3))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool R (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger H) S)) (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger G) S)))))))) (forall ((R tptp.fun_Co8310303586393106575r_bool) (S tptp.set_int) (H tptp.fun_int_Code_integer) (G tptp.fun_int_Code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool R tptp.one_one_Code_integer) tptp.one_one_Code_integer)) (=> (forall ((X12 tptp.code_integer) (Y12 tptp.code_integer) (X22 tptp.code_integer) (Y22 tptp.code_integer)) (=> (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool R X12) X22)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool R Y12) Y22))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool R (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger X12) Y12)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger X22) Y22))))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) S)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool R (tptp.aa_int_Code_integer H X3)) (tptp.aa_int_Code_integer G X3))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool R (tptp.groups3827104343326376752nteger H S)) (tptp.groups3827104343326376752nteger G S)))))))) (forall ((R tptp.fun_Co8310303586393106575r_bool) (S tptp.set_Code_integer) (H tptp.fun_Co8499238673658658103nteger) (G tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool R tptp.one_one_Code_integer) tptp.one_one_Code_integer)) (=> (forall ((X12 tptp.code_integer) (Y12 tptp.code_integer) (X22 tptp.code_integer) (Y22 tptp.code_integer)) (=> (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool R X12) X22)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool R Y12) Y22))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool R (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger X12) Y12)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger X22) Y22))))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) S)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool R (tptp.aa_Cod1783974652533396728nteger H X3)) (tptp.aa_Cod1783974652533396728nteger G X3))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool R (tptp.groups3674199335183972705nteger H S)) (tptp.groups3674199335183972705nteger G S)))))))) (forall ((R tptp.fun_as7903617535776176121n_bool) (S tptp.set_nat) (H tptp.fun_nat_assn) (G tptp.fun_nat_assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool R tptp.one_one_assn) tptp.one_one_assn)) (=> (forall ((X12 tptp.assn) (Y12 tptp.assn) (X22 tptp.assn) (Y22 tptp.assn)) (=> (and (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool R X12) X22)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool R Y12) Y22))) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool R (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn X12) Y12)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn X22) Y22))))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) S)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool R (tptp.aa_nat_assn H X3)) (tptp.aa_nat_assn G X3))))) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool R (tptp.groups6906906614972039071t_assn H S)) (tptp.groups6906906614972039071t_assn G S)))))))) (forall ((R tptp.fun_as7903617535776176121n_bool) (S tptp.set_int) (H tptp.fun_int_assn) (G tptp.fun_int_assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool R tptp.one_one_assn) tptp.one_one_assn)) (=> (forall ((X12 tptp.assn) (Y12 tptp.assn) (X22 tptp.assn) (Y22 tptp.assn)) (=> (and (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool R X12) X22)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool R Y12) Y22))) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool R (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn X12) Y12)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn X22) Y22))))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) S)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool R (tptp.aa_int_assn H X3)) (tptp.aa_int_assn G X3))))) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool R (tptp.groups7882442080178216443t_assn H S)) (tptp.groups7882442080178216443t_assn G S)))))))) (forall ((R tptp.fun_as7903617535776176121n_bool) (S tptp.set_Code_integer) (H tptp.fun_Co4490034186337852034r_assn) (G tptp.fun_Co4490034186337852034r_assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool R tptp.one_one_assn) tptp.one_one_assn)) (=> (forall ((X12 tptp.assn) (Y12 tptp.assn) (X22 tptp.assn) (Y22 tptp.assn)) (=> (and (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool R X12) X22)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool R Y12) Y22))) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool R (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn X12) Y12)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn X22) Y22))))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) S)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool R (tptp.aa_Code_integer_assn H X3)) (tptp.aa_Code_integer_assn G X3))))) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool R (tptp.groups1304777262505850412r_assn H S)) (tptp.groups1304777262505850412r_assn G S)))))))) (forall ((R tptp.fun_rat_fun_rat_bool) (S tptp.set_nat) (H tptp.fun_nat_rat) (G tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R tptp.one_one_rat) tptp.one_one_rat)) (=> (forall ((X12 tptp.rat) (Y12 tptp.rat) (X22 tptp.rat) (Y22 tptp.rat)) (=> (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R X12) X22)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R Y12) Y22))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X12) Y12)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X22) Y22))))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) S)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R (tptp.aa_nat_rat H X3)) (tptp.aa_nat_rat G X3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat H) S)) (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat G) S)))))))) (forall ((R tptp.fun_rat_fun_rat_bool) (S tptp.set_int) (H tptp.fun_int_rat) (G tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R tptp.one_one_rat) tptp.one_one_rat)) (=> (forall ((X12 tptp.rat) (Y12 tptp.rat) (X22 tptp.rat) (Y22 tptp.rat)) (=> (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R X12) X22)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R Y12) Y22))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X12) Y12)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X22) Y22))))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) S)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R (tptp.aa_int_rat H X3)) (tptp.aa_int_rat G X3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R (tptp.groups1072433553688619179nt_rat H S)) (tptp.groups1072433553688619179nt_rat G S)))))))) (forall ((R tptp.fun_rat_fun_rat_bool) (S tptp.set_Code_integer) (H tptp.fun_Code_integer_rat) (G tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R tptp.one_one_rat) tptp.one_one_rat)) (=> (forall ((X12 tptp.rat) (Y12 tptp.rat) (X22 tptp.rat) (Y22 tptp.rat)) (=> (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R X12) X22)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R Y12) Y22))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X12) Y12)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat X22) Y22))))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) S)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R (tptp.aa_Code_integer_rat H X3)) (tptp.aa_Code_integer_rat G X3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R (tptp.groups2555765274223993564er_rat H S)) (tptp.groups2555765274223993564er_rat G S)))))))) (forall ((R tptp.fun_nat_fun_nat_bool) (S tptp.set_int) (H tptp.fun_int_nat) (G tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R tptp.one_one_nat) tptp.one_one_nat)) (=> (forall ((X12 tptp.nat) (Y12 tptp.nat) (X22 tptp.nat) (Y22 tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R X12) X22)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R Y12) Y22))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat X12) Y12)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat X22) Y22))))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) S)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R (tptp.aa_int_nat H X3)) (tptp.aa_int_nat G X3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R (tptp.groups1707563613775114915nt_nat H S)) (tptp.groups1707563613775114915nt_nat G S)))))))) (forall ((B tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) K)) (exists ((N5 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 N5)) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N5) tptp.one_one_nat)))))))))) (forall ((B tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 K)) (exists ((N5 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 N5)) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N5) tptp.one_one_nat))))))))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) K))) (let ((_let_2 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat I2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) J)) (= (tptp.aa_nat_set_nat _let_2 _let_1) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.aa_nat_set_nat _let_2 J)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat J) _let_1))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int _let_1 N2)) tptp.one_one_int) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int _let_1) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_dg N2)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_nat_Code_integer _let_1 N2)) tptp.one_one_Code_integer) (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger _let_1) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_dg N2)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.power_7079662738309270450atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.minus_7197305767214868737atural (tptp.aa_nat_Code_natural _let_1 N2) tptp.one_one_Code_natural) (tptp.groups6325495683096345652atural _let_1 (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_dg N2)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 N2)) tptp.one_one_nat) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat _let_1) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_dg N2)))))) (forall ((B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int tptp.one))) B) (tptp.aa_int_int tptp.uminus_uminus_int B))) (forall ((B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger tptp.one))) B) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B))) (forall ((B tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat tptp.one))) B) (tptp.aa_rat_rat tptp.uminus_uminus_rat B))) (forall ((B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int tptp.one))) (tptp.aa_int_int tptp.uminus_uminus_int B))) (forall ((B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger tptp.one))) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B))) (forall ((B tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat tptp.one))) (tptp.aa_rat_rat tptp.uminus_uminus_rat B))) (forall ((G tptp.fun_na2338080690716861136at_nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.groups6857163185585827899at_nat G (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat _let_1 N2)))) (tptp.groups6857163185585827899at_nat (tptp.aTP_Lamm_xw G) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2))))) (forall ((G tptp.fun_nat_rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat G) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat _let_1 N2)))) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_xx G)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2))))) (forall ((G tptp.fun_nat_int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int G) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat _let_1 N2)))) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_xy G)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2))))) (forall ((G tptp.fun_nat_nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat _let_1 N2)))) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_xz G)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 N2)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat _let_1) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_dg N2)))))) (forall ((G tptp.fun_nat_Code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger G) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat _let_1 N2)))) (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger (tptp.aTP_Lamm_ya G)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2))))) (forall ((G tptp.fun_nat_assn) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat _let_1 N2)))) (tptp.groups6906906614972039071t_assn (tptp.aTP_Lamm_yb G) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2))))) (forall ((G tptp.fun_nat_rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat G) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat _let_1 N2)))) (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat (tptp.aTP_Lamm_yc G)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2))))) (forall ((G tptp.fun_nat_nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat G) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat _let_1 N2)))) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aTP_Lamm_yd G)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2))))) (forall ((G tptp.fun_nat_int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int G) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat _let_1 N2)))) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aTP_Lamm_ye G)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2))))) (forall ((N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat tptp.aTP_Lamm_fu) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((I2 tptp.nat) (J tptp.nat)) (= (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat I2) J)) (tptp.groups1705073143266064639nt_int tptp.aTP_Lamm_fv (tptp.set_or1266510415728281911st_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int I2) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int J))))) (forall ((G tptp.fun_na2338080690716861136at_nat) (N2 tptp.nat)) (= (tptp.groups6857163185585827899at_nat G (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (tptp.groups6857163185585827899at_nat (tptp.aTP_Lamm_xw G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((G tptp.fun_nat_rat) (N2 tptp.nat)) (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_xx G)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((G tptp.fun_nat_int) (N2 tptp.nat)) (= (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_xy G)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((G tptp.fun_nat_nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_xz G)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((G tptp.fun_nat_Code_integer) (N2 tptp.nat)) (= (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger (tptp.aTP_Lamm_ya G)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((G tptp.fun_nat_assn) (N2 tptp.nat)) (= (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (tptp.groups6906906614972039071t_assn (tptp.aTP_Lamm_yb G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((G tptp.fun_nat_rat) (N2 tptp.nat)) (= (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat (tptp.aTP_Lamm_yc G)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((G tptp.fun_nat_nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aTP_Lamm_yd G)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((G tptp.fun_nat_int) (N2 tptp.nat)) (= (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aTP_Lamm_ye G)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((R3 tptp.nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_yf R3)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat R3) N2))) N2))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_yg N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) M)) tptp.one_one_nat)) M))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_yg N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_1 M)) tptp.one_one_nat)) (tptp.aa_nat_nat _let_1 tptp.one_one_nat))))) (forall ((S2 tptp.set_bool) (F tptp.fun_bo7282069421189217543nteger) (I2 tptp.bool)) (=> (tptp.finite_finite_bool S2) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 S2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_bool_Code_integer F I3))))) (=> (= (tptp.groups1682264926906508858nteger F S2) tptp.zero_z3403309356797280102nteger) (=> (tptp.pp (tptp.member_bool I2 S2)) (= (tptp.aa_bool_Code_integer F I2) tptp.zero_z3403309356797280102nteger)))))) (forall ((S2 tptp.set_nat) (F tptp.fun_nat_Code_integer) (I2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S2)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) S2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer F I3))))) (=> (= (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger F) S2) tptp.zero_z3403309356797280102nteger) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I2) S2)) (= (tptp.aa_nat_Code_integer F I2) tptp.zero_z3403309356797280102nteger)))))) (forall ((S2 tptp.set_int) (F tptp.fun_int_Code_integer) (I2 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S2)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) S2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_int_Code_integer F I3))))) (=> (= (tptp.groups7873554091576472773nteger F S2) tptp.zero_z3403309356797280102nteger) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I2) S2)) (= (tptp.aa_int_Code_integer F I2) tptp.zero_z3403309356797280102nteger)))))) (forall ((S2 tptp.set_Code_integer) (F tptp.fun_Co8499238673658658103nteger) (I2 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S2)) (=> (forall ((I3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I3) S2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger F I3))))) (=> (= (tptp.groups879477027807139574nteger F S2) tptp.zero_z3403309356797280102nteger) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I2) S2)) (= (tptp.aa_Cod1783974652533396728nteger F I2) tptp.zero_z3403309356797280102nteger)))))) (forall ((S2 tptp.set_bool) (F tptp.fun_bool_rat) (I2 tptp.bool)) (=> (tptp.finite_finite_bool S2) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 S2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_bool_rat F I3))))) (=> (= (tptp.groups5133371213642249141ol_rat F S2) tptp.zero_zero_rat) (=> (tptp.pp (tptp.member_bool I2 S2)) (= (tptp.aa_bool_rat F I2) tptp.zero_zero_rat)))))) (forall ((S2 tptp.set_nat) (F tptp.fun_nat_rat) (I2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S2)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) S2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat F I3))))) (=> (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat F) S2) tptp.zero_zero_rat) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I2) S2)) (= (tptp.aa_nat_rat F I2) tptp.zero_zero_rat)))))) (forall ((S2 tptp.set_int) (F tptp.fun_int_rat) (I2 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S2)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) S2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_int_rat F I3))))) (=> (= (tptp.groups3906332499630173760nt_rat F S2) tptp.zero_zero_rat) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I2) S2)) (= (tptp.aa_int_rat F I2) tptp.zero_zero_rat)))))) (forall ((S2 tptp.set_Code_integer) (F tptp.fun_Code_integer_rat) (I2 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S2)) (=> (forall ((I3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I3) S2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_Code_integer_rat F I3))))) (=> (= (tptp.groups6602215022474089585er_rat F S2) tptp.zero_zero_rat) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I2) S2)) (= (tptp.aa_Code_integer_rat F I2) tptp.zero_zero_rat)))))) (forall ((S2 tptp.set_bool) (F tptp.fun_bool_nat) (I2 tptp.bool)) (=> (tptp.finite_finite_bool S2) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 S2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_bool_nat F I3))))) (=> (= (tptp.groups5768501273728744877ol_nat F S2) tptp.zero_zero_nat) (=> (tptp.pp (tptp.member_bool I2 S2)) (= (tptp.aa_bool_nat F I2) tptp.zero_zero_nat)))))) (forall ((S2 tptp.set_int) (F tptp.fun_int_nat) (I2 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S2)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) S2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_int_nat F I3))))) (=> (= (tptp.groups4541462559716669496nt_nat F S2) tptp.zero_zero_nat) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I2) S2)) (= (tptp.aa_int_nat F I2) tptp.zero_zero_nat)))))) (forall ((S2 tptp.set_bool) (F tptp.fun_bo7282069421189217543nteger) (B3 tptp.code_integer) (I2 tptp.bool)) (=> (tptp.finite_finite_bool S2) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 S2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_bool_Code_integer F I3))))) (=> (= (tptp.groups1682264926906508858nteger F S2) B3) (=> (tptp.pp (tptp.member_bool I2 S2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_bool_Code_integer F I2)) B3))))))) (forall ((S2 tptp.set_nat) (F tptp.fun_nat_Code_integer) (B3 tptp.code_integer) (I2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S2)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) S2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer F I3))))) (=> (= (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger F) S2) B3) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I2) S2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer F I2)) B3))))))) (forall ((S2 tptp.set_int) (F tptp.fun_int_Code_integer) (B3 tptp.code_integer) (I2 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S2)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) S2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_int_Code_integer F I3))))) (=> (= (tptp.groups7873554091576472773nteger F S2) B3) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I2) S2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_int_Code_integer F I2)) B3))))))) (forall ((S2 tptp.set_Code_integer) (F tptp.fun_Co8499238673658658103nteger) (B3 tptp.code_integer) (I2 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S2)) (=> (forall ((I3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I3) S2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger F I3))))) (=> (= (tptp.groups879477027807139574nteger F S2) B3) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I2) S2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger F I2)) B3))))))) (forall ((S2 tptp.set_bool) (F tptp.fun_bool_rat) (B3 tptp.rat) (I2 tptp.bool)) (=> (tptp.finite_finite_bool S2) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 S2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_bool_rat F I3))))) (=> (= (tptp.groups5133371213642249141ol_rat F S2) B3) (=> (tptp.pp (tptp.member_bool I2 S2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_bool_rat F I2)) B3))))))) (forall ((S2 tptp.set_nat) (F tptp.fun_nat_rat) (B3 tptp.rat) (I2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S2)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) S2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat F I3))))) (=> (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat F) S2) B3) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I2) S2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F I2)) B3))))))) (forall ((S2 tptp.set_int) (F tptp.fun_int_rat) (B3 tptp.rat) (I2 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S2)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) S2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_int_rat F I3))))) (=> (= (tptp.groups3906332499630173760nt_rat F S2) B3) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I2) S2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat F I2)) B3))))))) (forall ((S2 tptp.set_Code_integer) (F tptp.fun_Code_integer_rat) (B3 tptp.rat) (I2 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S2)) (=> (forall ((I3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I3) S2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_Code_integer_rat F I3))))) (=> (= (tptp.groups6602215022474089585er_rat F S2) B3) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I2) S2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_Code_integer_rat F I2)) B3))))))) (forall ((S2 tptp.set_bool) (F tptp.fun_bool_nat) (B3 tptp.nat) (I2 tptp.bool)) (=> (tptp.finite_finite_bool S2) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 S2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_bool_nat F I3))))) (=> (= (tptp.groups5768501273728744877ol_nat F S2) B3) (=> (tptp.pp (tptp.member_bool I2 S2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_bool_nat F I2)) B3))))))) (forall ((S2 tptp.set_int) (F tptp.fun_int_nat) (B3 tptp.nat) (I2 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S2)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) S2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_int_nat F I3))))) (=> (= (tptp.groups4541462559716669496nt_nat F S2) B3) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I2) S2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat F I2)) B3))))))) (forall ((M tptp.code_integer) (X tptp.code_integer)) (let ((_let_1 (tptp.modulo364778990260209775nteger X))) (let ((_let_2 (tptp.aa_Cod1783974652533396728nteger _let_1 M))) (let ((_let_3 (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) M)))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) M)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X)) (or (= _let_3 _let_2) (= _let_3 (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger _let_2) M))))))))) (forall ((M tptp.nat) (X tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X))) (let ((_let_2 (tptp.aa_nat_nat _let_1 M))) (let ((_let_3 (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) X)) (or (= _let_3 _let_2) (= _let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_2) M))))))))) (forall ((M tptp.int) (X tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.modulo_modulo_int X))) (let ((_let_2 (tptp.aa_int_int _let_1 M))) (let ((_let_3 (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) M)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) M)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) X)) (or (= _let_3 _let_2) (= _let_3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_2) M))))))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.modulo364778990260209775nteger A))) (let ((_let_2 (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) B)))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) _let_2)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger _let_2) B) (tptp.aa_Cod1783974652533396728nteger _let_1 B)))))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A))) (let ((_let_2 (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) B)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) _let_2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat _let_2) B) (tptp.aa_nat_nat _let_1 B)))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A))) (let ((_let_2 (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) B)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) _let_2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int _let_2) B) (tptp.aa_int_int _let_1 B)))))))) (forall ((M6 tptp.fun_Pr5160692531401422620nt_nat) (A tptp.product_prod_int_int)) (=> (tptp.finite2998713641127702882nt_int (tptp.collec213857154873943460nt_int (tptp.aTP_Lamm_vu M6))) (tptp.finite2998713641127702882nt_int (tptp.collec213857154873943460nt_int (tptp.aa_Pro1534211998248933470t_bool (tptp.aTP_Lamm_yh M6) A))))) (forall ((M6 tptp.fun_list_nat_nat) (A tptp.list_nat)) (=> (tptp.finite8100373058378681591st_nat (tptp.collect_list_nat (tptp.aTP_Lamm_vw M6))) (tptp.finite8100373058378681591st_nat (tptp.collect_list_nat (tptp.aa_lis4768068104879709938t_bool (tptp.aTP_Lamm_yi M6) A))))) (forall ((M6 tptp.fun_set_nat_nat) (A tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat (tptp.collect_set_nat (tptp.aTP_Lamm_vy M6)))) (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat (tptp.collect_set_nat (tptp.aa_set5116768664143533222t_bool (tptp.aTP_Lamm_yj M6) A)))))) (forall ((M6 tptp.fun_nat_nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aTP_Lamm_wa M6)))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_yk M6) A)))))) (forall ((M6 tptp.fun_int_nat) (A tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aTP_Lamm_wc M6)))) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_yl M6) A)))))) (forall ((M6 tptp.fun_Code_integer_nat) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.collect_Code_integer (tptp.aTP_Lamm_we M6)))) (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.collect_Code_integer (tptp.aa_Cod7250484176784686200r_bool (tptp.aTP_Lamm_ym M6) A)))))) (forall ((M6 tptp.fun_Pr2602117396471556196at_nat) (A tptp.product_prod_nat_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat (tptp.collec3392354462482085612at_nat (tptp.aTP_Lamm_wg M6)))) (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat (tptp.collec3392354462482085612at_nat (tptp.aa_Pro595088089689268830t_bool (tptp.aTP_Lamm_yn M6) A)))))) (forall ((A3 tptp.set_bool) (G tptp.fun_bo7282069421189217543nteger) (B3 tptp.set_bool)) (=> (tptp.finite_finite_bool A3) (= (tptp.groups1682264926906508858nteger G (tptp.inf_inf_set_bool A3 B3)) (tptp.groups1682264926906508858nteger (tptp.aa_set2829807854720747148nteger (tptp.aTP_Lamm_yo G) B3) A3)))) (forall ((A3 tptp.set_int) (G tptp.fun_int_Code_integer) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups7873554091576472773nteger G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3)) (tptp.groups7873554091576472773nteger (tptp.aa_set5517701783735052070nteger (tptp.aTP_Lamm_yp G) B3) A3)))) (forall ((A3 tptp.set_Code_integer) (G tptp.fun_Co8499238673658658103nteger) (B3 tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups879477027807139574nteger G (tptp.inf_in1364745209274528805nteger A3 B3)) (tptp.groups879477027807139574nteger (tptp.aa_set4294055438810586376nteger (tptp.aTP_Lamm_yq G) B3) A3)))) (forall ((A3 tptp.set_bool) (G tptp.fun_bool_rat) (B3 tptp.set_bool)) (=> (tptp.finite_finite_bool A3) (= (tptp.groups5133371213642249141ol_rat G (tptp.inf_inf_set_bool A3 B3)) (tptp.groups5133371213642249141ol_rat (tptp.aa_set1787953457065026183ol_rat (tptp.aTP_Lamm_yr G) B3) A3)))) (forall ((A3 tptp.set_int) (G tptp.fun_int_rat) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups3906332499630173760nt_rat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3)) (tptp.groups3906332499630173760nt_rat (tptp.aa_set7979663334043413281nt_rat (tptp.aTP_Lamm_ys G) B3) A3)))) (forall ((A3 tptp.set_Code_integer) (G tptp.fun_Code_integer_rat) (B3 tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups6602215022474089585er_rat G (tptp.inf_in1364745209274528805nteger A3 B3)) (tptp.groups6602215022474089585er_rat (tptp.aa_set7344733238996822275er_rat (tptp.aTP_Lamm_yt G) B3) A3)))) (forall ((A3 tptp.set_bool) (G tptp.fun_bool_nat) (B3 tptp.set_bool)) (=> (tptp.finite_finite_bool A3) (= (tptp.groups5768501273728744877ol_nat G (tptp.inf_inf_set_bool A3 B3)) (tptp.groups5768501273728744877ol_nat (tptp.aa_set5296182015458422911ol_nat (tptp.aTP_Lamm_yu G) B3) A3)))) (forall ((A3 tptp.set_int) (G tptp.fun_int_nat) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups4541462559716669496nt_nat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3)) (tptp.groups4541462559716669496nt_nat (tptp.aa_set2264519855582034201nt_nat (tptp.aTP_Lamm_yv G) B3) A3)))) (forall ((A3 tptp.set_Code_integer) (G tptp.fun_Code_integer_nat) (B3 tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups7237345082560585321er_nat G (tptp.inf_in1364745209274528805nteger A3 B3)) (tptp.groups7237345082560585321er_nat (tptp.aa_set1629589760535443195er_nat (tptp.aTP_Lamm_yw G) B3) A3)))) (forall ((A3 tptp.set_bool) (G tptp.fun_bool_int) (B3 tptp.set_bool)) (=> (tptp.finite_finite_bool A3) (= (tptp.groups5766010803219694601ol_int G (tptp.inf_inf_set_bool A3 B3)) (tptp.groups5766010803219694601ol_int (tptp.aa_set1118330995949226203ol_int (tptp.aTP_Lamm_yx G) B3) A3)))) (forall ((S tptp.set_nat) (T tptp.set_Code_integer) (G tptp.fun_nat_Code_integer) (H tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger (tptp.image_1215581382706833972nteger G S)) T)) (= (tptp.groups7237345082560585321er_nat (tptp.aa_fun2720235278490593797er_nat (tptp.aa_fun676797813428960940er_nat (tptp.aTP_Lamm_yz S) G) H) T) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat H) S)))))) (forall ((S tptp.set_nat) (T tptp.set_int) (G tptp.fun_nat_int) (H tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.image_nat_int G S)) T)) (= (tptp.groups4541462559716669496nt_nat (tptp.aa_fun6790803225114646484nt_nat (tptp.aa_fun5866268260113680714nt_nat (tptp.aTP_Lamm_za S) G) H) T) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat H) S)))))) (forall ((S tptp.set_int) (T tptp.set_nat) (G tptp.fun_int_nat) (H tptp.fun_int_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.image_int_nat G S)) T)) (= (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aa_fun5280992047749994636at_int (tptp.aa_fun4682031307293100034at_int (tptp.aTP_Lamm_zb S) G) H)) T) (tptp.groups4538972089207619220nt_int H S)))))) (forall ((S tptp.set_int) (T tptp.set_Code_integer) (G tptp.fun_int_Code_integer) (H tptp.fun_int_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger (tptp.image_1587234942943678608nteger G S)) T)) (= (tptp.groups7234854612051535045er_int (tptp.aa_fun2092574682676764953er_int (tptp.aa_fun9146121993134396956er_int (tptp.aTP_Lamm_zd S) G) H) T) (tptp.groups4538972089207619220nt_int H S)))))) (forall ((S tptp.set_bool) (T tptp.set_nat) (G tptp.fun_bool_nat) (H tptp.fun_bool_nat)) (=> (tptp.finite_finite_bool S) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.image_bool_nat G S)) T)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun9158115899668126683at_nat (tptp.aa_fun3360519976762538604at_nat (tptp.aTP_Lamm_ze S) G) H)) T) (tptp.groups5768501273728744877ol_nat H S)))))) (forall ((S tptp.set_int) (T tptp.set_nat) (G tptp.fun_int_nat) (H tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.image_int_nat G S)) T)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun5507398438843482068at_nat (tptp.aa_fun3220669823809117514at_nat (tptp.aTP_Lamm_zf S) G) H)) T) (tptp.groups4541462559716669496nt_nat H S)))))) (forall ((S tptp.set_Code_integer) (T tptp.set_nat) (G tptp.fun_Code_integer_nat) (H tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.image_951025933927791156er_nat G S)) T)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun1707803128846032901at_nat (tptp.aa_fun2075405564639334828at_nat (tptp.aTP_Lamm_zg S) G) H)) T) (tptp.groups7237345082560585321er_nat H S)))))) (forall ((S tptp.set_nat) (T tptp.set_nat) (G tptp.fun_nat_nat) (H tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.image_nat_nat G S)) T)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aa_fun6854695580826382482at_nat (tptp.aTP_Lamm_zh S) G) H)) T) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat H) S)))))) (forall ((S tptp.set_bool) (T tptp.set_int) (G tptp.fun_bool_int) (H tptp.fun_bool_int)) (=> (tptp.finite_finite_bool S) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.image_bool_int G S)) T)) (= (tptp.groups4538972089207619220nt_int (tptp.aa_fun707691183620917999nt_int (tptp.aa_fun7930693643136840740nt_int (tptp.aTP_Lamm_zi S) G) H) T) (tptp.groups5766010803219694601ol_int H S)))))) (forall ((S tptp.set_nat) (T tptp.set_int) (G tptp.fun_nat_int) (H tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.image_nat_int G S)) T)) (= (tptp.groups4538972089207619220nt_int (tptp.aa_fun6564396834021159052nt_int (tptp.aa_fun7327629743597663234nt_int (tptp.aTP_Lamm_zj S) G) H) T) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int H) S)))))) (forall ((A3 tptp.set_int) (G tptp.fun_int_Code_integer)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups7873554091576472773nteger G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) (tptp.collect_int (tptp.aTP_Lamm_zk G)))) (tptp.groups7873554091576472773nteger G A3)))) (forall ((A3 tptp.set_Code_integer) (G tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups879477027807139574nteger G (tptp.minus_2355218937544613996nteger A3 (tptp.collect_Code_integer (tptp.aTP_Lamm_zl G)))) (tptp.groups879477027807139574nteger G A3)))) (forall ((A3 tptp.set_int) (G tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups3906332499630173760nt_rat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) (tptp.collect_int (tptp.aTP_Lamm_zm G)))) (tptp.groups3906332499630173760nt_rat G A3)))) (forall ((A3 tptp.set_Code_integer) (G tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups6602215022474089585er_rat G (tptp.minus_2355218937544613996nteger A3 (tptp.collect_Code_integer (tptp.aTP_Lamm_zn G)))) (tptp.groups6602215022474089585er_rat G A3)))) (forall ((A3 tptp.set_int) (G tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups4541462559716669496nt_nat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) (tptp.collect_int (tptp.aTP_Lamm_zo G)))) (tptp.groups4541462559716669496nt_nat G A3)))) (forall ((A3 tptp.set_Code_integer) (G tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups7237345082560585321er_nat G (tptp.minus_2355218937544613996nteger A3 (tptp.collect_Code_integer (tptp.aTP_Lamm_zp G)))) (tptp.groups7237345082560585321er_nat G A3)))) (forall ((A3 tptp.set_Code_integer) (G tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups7234854612051535045er_int G (tptp.minus_2355218937544613996nteger A3 (tptp.collect_Code_integer (tptp.aTP_Lamm_zq G)))) (tptp.groups7234854612051535045er_int G A3)))) (forall ((A3 tptp.set_nat) (G tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.groups7501900531339628137nteger G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.aa_set871585252387937313nteger _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) (tptp.collect_nat (tptp.aTP_Lamm_zr G)))) (tptp.aa_set871585252387937313nteger _let_1 A3))))) (forall ((A3 tptp.set_nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups2906978787729119204at_rat G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.aa_set_nat_rat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) (tptp.collect_nat (tptp.aTP_Lamm_zs G)))) (tptp.aa_set_nat_rat _let_1 A3))))) (forall ((A3 tptp.set_nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.groups3539618377306564664at_int G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.aa_set_nat_int _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) (tptp.collect_nat (tptp.aTP_Lamm_zt G)))) (tptp.aa_set_nat_int _let_1 A3))))) (forall ((M6 tptp.fun_Pr5160692531401422620nt_nat) (N7 tptp.fun_Pr5160692531401422620nt_nat)) (=> (tptp.finite2998713641127702882nt_int (tptp.collec213857154873943460nt_int (tptp.aTP_Lamm_vu M6))) (tptp.finite2998713641127702882nt_int (tptp.collec213857154873943460nt_int (tptp.aa_fun5604724294258851521t_bool (tptp.aTP_Lamm_zu M6) N7))))) (forall ((M6 tptp.fun_list_nat_nat) (N7 tptp.fun_list_nat_nat)) (=> (tptp.finite8100373058378681591st_nat (tptp.collect_list_nat (tptp.aTP_Lamm_vw M6))) (tptp.finite8100373058378681591st_nat (tptp.collect_list_nat (tptp.aa_fun2581403542315806821t_bool (tptp.aTP_Lamm_zv M6) N7))))) (forall ((M6 tptp.fun_set_nat_nat) (N7 tptp.fun_set_nat_nat)) (=> (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat (tptp.collect_set_nat (tptp.aTP_Lamm_vy M6)))) (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat (tptp.collect_set_nat (tptp.aa_fun806690937814068505t_bool (tptp.aTP_Lamm_zw M6) N7)))))) (forall ((M6 tptp.fun_nat_nat) (N7 tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aTP_Lamm_wa M6)))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun1783405840085286277t_bool (tptp.aTP_Lamm_zx M6) N7)))))) (forall ((M6 tptp.fun_int_nat) (N7 tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aTP_Lamm_wc M6)))) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun5627573752281863885t_bool (tptp.aTP_Lamm_zy M6) N7)))))) (forall ((M6 tptp.fun_Code_integer_nat) (N7 tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.collect_Code_integer (tptp.aTP_Lamm_we M6)))) (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.collect_Code_integer (tptp.aa_fun3540204951715082475r_bool (tptp.aTP_Lamm_zz M6) N7)))))) (forall ((M6 tptp.fun_Pr2602117396471556196at_nat) (N7 tptp.fun_Pr2602117396471556196at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat (tptp.collec3392354462482085612at_nat (tptp.aTP_Lamm_wg M6)))) (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat (tptp.collec3392354462482085612at_nat (tptp.aa_fun3396476008067328193t_bool (tptp.aTP_Lamm_aaa M6) N7)))))) (forall ((S tptp.set_nat) (T tptp.set_Code_integer) (G tptp.fun_nat_Code_integer) (H tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger (tptp.image_1215581382706833972nteger G S)) T)) (= (tptp.groups3190895334310489300er_nat (tptp.aa_fun2720235278490593797er_nat (tptp.aa_fun676797813428960940er_nat (tptp.aTP_Lamm_aab S) G) H) T) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat H) S)))))) (forall ((S tptp.set_nat) (T tptp.set_int) (G tptp.fun_nat_int) (H tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.image_nat_int G S)) T)) (= (tptp.groups1707563613775114915nt_nat (tptp.aa_fun6790803225114646484nt_nat (tptp.aa_fun5866268260113680714nt_nat (tptp.aTP_Lamm_aac S) G) H) T) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat H) S)))))) (forall ((S tptp.set_nat) (T tptp.set_Code_integer) (G tptp.fun_nat_Code_integer) (H tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger (tptp.image_1215581382706833972nteger G S)) T)) (= (tptp.groups3188404863801439024er_int (tptp.aa_fun2934847258012291773er_int (tptp.aa_fun2579177667528128868er_int (tptp.aTP_Lamm_aad S) G) H) T) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int H) S)))))) (forall ((S tptp.set_int) (T tptp.set_Code_integer) (G tptp.fun_int_Code_integer) (H tptp.fun_int_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger (tptp.image_1587234942943678608nteger G S)) T)) (= (tptp.groups3188404863801439024er_int (tptp.aa_fun2092574682676764953er_int (tptp.aa_fun9146121993134396956er_int (tptp.aTP_Lamm_aae S) G) H) T) (tptp.groups1705073143266064639nt_int H S)))))) (forall ((S tptp.set_bool) (T tptp.set_nat) (G tptp.fun_bool_nat) (H tptp.fun_bool_nat)) (=> (tptp.finite_finite_bool S) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.image_bool_nat G S)) T)) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_fun9158115899668126683at_nat (tptp.aa_fun3360519976762538604at_nat (tptp.aTP_Lamm_aaf S) G) H)) T) (tptp.groups1894949261696196098ol_nat H S)))))) (forall ((S tptp.set_int) (T tptp.set_nat) (G tptp.fun_int_nat) (H tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.image_int_nat G S)) T)) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_fun5507398438843482068at_nat (tptp.aa_fun3220669823809117514at_nat (tptp.aTP_Lamm_aag S) G) H)) T) (tptp.groups1707563613775114915nt_nat H S)))))) (forall ((S tptp.set_Code_integer) (T tptp.set_nat) (G tptp.fun_Code_integer_nat) (H tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.image_951025933927791156er_nat G S)) T)) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_fun1707803128846032901at_nat (tptp.aa_fun2075405564639334828at_nat (tptp.aTP_Lamm_aah S) G) H)) T) (tptp.groups3190895334310489300er_nat H S)))))) (forall ((S tptp.set_nat) (T tptp.set_nat) (G tptp.fun_nat_nat) (H tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.image_nat_nat G S)) T)) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aa_fun6854695580826382482at_nat (tptp.aTP_Lamm_aai S) G) H)) T) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat H) S)))))) (forall ((S tptp.set_bool) (T tptp.set_nat) (G tptp.fun_bool_nat) (H tptp.fun_bool_int)) (=> (tptp.finite_finite_bool S) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.image_bool_nat G S)) T)) (= (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_fun8931709508574639251at_int (tptp.aa_fun4821881460246521124at_int (tptp.aTP_Lamm_aaj S) G) H)) T) (tptp.groups1892458791187145822ol_int H S)))))) (forall ((S tptp.set_Code_integer) (T tptp.set_nat) (G tptp.fun_Code_integer_nat) (H tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.image_951025933927791156er_nat G S)) T)) (= (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_fun1481396737752545469at_int (tptp.aa_fun3536767048123317348at_int (tptp.aTP_Lamm_aak S) G) H)) T) (tptp.groups3188404863801439024er_int H S)))))) (forall ((N7 tptp.set_nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat N7) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat N7)))) (forall ((A3 tptp.set_bool) (G tptp.fun_bo7282069421189217543nteger) (B3 tptp.set_bool)) (=> (tptp.finite_finite_bool A3) (= (tptp.groups7272450149305381519nteger G (tptp.inf_inf_set_bool A3 B3)) (tptp.groups7272450149305381519nteger (tptp.aa_set2829807854720747148nteger (tptp.aTP_Lamm_aal G) B3) A3)))) (forall ((A3 tptp.set_int) (G tptp.fun_int_Code_integer) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups3827104343326376752nteger G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3)) (tptp.groups3827104343326376752nteger (tptp.aa_set5517701783735052070nteger (tptp.aTP_Lamm_aam G) B3) A3)))) (forall ((A3 tptp.set_Code_integer) (G tptp.fun_Co8499238673658658103nteger) (B3 tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups3674199335183972705nteger G (tptp.inf_in1364745209274528805nteger A3 B3)) (tptp.groups3674199335183972705nteger (tptp.aa_set4294055438810586376nteger (tptp.aTP_Lamm_aan G) B3) A3)))) (forall ((A3 tptp.set_bool) (G tptp.fun_bool_assn) (B3 tptp.set_bool)) (=> (tptp.finite_finite_bool A3) (= (tptp.groups4835110720589548378l_assn G (tptp.inf_inf_set_bool A3 B3)) (tptp.groups4835110720589548378l_assn (tptp.aa_set3043482617886199255l_assn (tptp.aTP_Lamm_aao G) B3) A3)))) (forall ((A3 tptp.set_int) (G tptp.fun_int_assn) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups7882442080178216443t_assn G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3)) (tptp.groups7882442080178216443t_assn (tptp.aa_set5310648174735401585t_assn (tptp.aTP_Lamm_aap G) B3) A3)))) (forall ((A3 tptp.set_Code_integer) (G tptp.fun_Co4490034186337852034r_assn) (B3 tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups1304777262505850412r_assn G (tptp.inf_in1364745209274528805nteger A3 B3)) (tptp.groups1304777262505850412r_assn (tptp.aa_set2437433236263590995r_assn (tptp.aTP_Lamm_aaq G) B3) A3)))) (forall ((A3 tptp.set_bool) (G tptp.fun_bool_rat) (B3 tptp.set_bool)) (=> (tptp.finite_finite_bool A3) (= (tptp.groups1259819201609700362ol_rat G (tptp.inf_inf_set_bool A3 B3)) (tptp.groups1259819201609700362ol_rat (tptp.aa_set1787953457065026183ol_rat (tptp.aTP_Lamm_aar G) B3) A3)))) (forall ((A3 tptp.set_int) (G tptp.fun_int_rat) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups1072433553688619179nt_rat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3)) (tptp.groups1072433553688619179nt_rat (tptp.aa_set7979663334043413281nt_rat (tptp.aTP_Lamm_aas G) B3) A3)))) (forall ((A3 tptp.set_Code_integer) (G tptp.fun_Code_integer_rat) (B3 tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups2555765274223993564er_rat G (tptp.inf_in1364745209274528805nteger A3 B3)) (tptp.groups2555765274223993564er_rat (tptp.aa_set7344733238996822275er_rat (tptp.aTP_Lamm_aat G) B3) A3)))) (forall ((A3 tptp.set_bool) (G tptp.fun_bool_nat) (B3 tptp.set_bool)) (=> (tptp.finite_finite_bool A3) (= (tptp.groups1894949261696196098ol_nat G (tptp.inf_inf_set_bool A3 B3)) (tptp.groups1894949261696196098ol_nat (tptp.aa_set5296182015458422911ol_nat (tptp.aTP_Lamm_aau G) B3) A3)))) (forall ((Z tptp.code_integer) (W2 tptp.num)) (let ((_let_1 (tptp.power_8256067586552552935nteger Z))) (let ((_let_2 (tptp.aa_nat_Code_integer _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W2)))) (= (tptp.aa_nat_Code_integer _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 W2))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_2) _let_2))))) (forall ((Z tptp.assn) (W2 tptp.num)) (let ((_let_1 (tptp.power_power_assn Z))) (let ((_let_2 (tptp.aa_nat_assn _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W2)))) (= (tptp.aa_nat_assn _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 W2))) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn _let_2) _let_2))))) (forall ((Z tptp.rat) (W2 tptp.num)) (let ((_let_1 (tptp.power_power_rat Z))) (let ((_let_2 (tptp.aa_nat_rat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W2)))) (= (tptp.aa_nat_rat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 W2))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_2) _let_2))))) (forall ((Z tptp.nat) (W2 tptp.num)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Z))) (let ((_let_2 (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W2)))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 W2))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_2) _let_2))))) (forall ((Z tptp.int) (W2 tptp.num)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int Z))) (let ((_let_2 (tptp.aa_nat_int _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W2)))) (= (tptp.aa_nat_int _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 W2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_2) _let_2))))) (forall ((A3 tptp.set_int) (G tptp.fun_int_Code_integer)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups3827104343326376752nteger G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) (tptp.collect_int (tptp.aTP_Lamm_aav G)))) (tptp.groups3827104343326376752nteger G A3)))) (forall ((A3 tptp.set_Code_integer) (G tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups3674199335183972705nteger G (tptp.minus_2355218937544613996nteger A3 (tptp.collect_Code_integer (tptp.aTP_Lamm_aaw G)))) (tptp.groups3674199335183972705nteger G A3)))) (forall ((A3 tptp.set_int) (G tptp.fun_int_assn)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups7882442080178216443t_assn G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) (tptp.collect_int (tptp.aTP_Lamm_aax G)))) (tptp.groups7882442080178216443t_assn G A3)))) (forall ((A3 tptp.set_Code_integer) (G tptp.fun_Co4490034186337852034r_assn)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups1304777262505850412r_assn G (tptp.minus_2355218937544613996nteger A3 (tptp.collect_Code_integer (tptp.aTP_Lamm_aay G)))) (tptp.groups1304777262505850412r_assn G A3)))) (forall ((A3 tptp.set_int) (G tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups1072433553688619179nt_rat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) (tptp.collect_int (tptp.aTP_Lamm_aaz G)))) (tptp.groups1072433553688619179nt_rat G A3)))) (forall ((A3 tptp.set_Code_integer) (G tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups2555765274223993564er_rat G (tptp.minus_2355218937544613996nteger A3 (tptp.collect_Code_integer (tptp.aTP_Lamm_aba G)))) (tptp.groups2555765274223993564er_rat G A3)))) (forall ((A3 tptp.set_int) (G tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups1707563613775114915nt_nat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) (tptp.collect_int (tptp.aTP_Lamm_abb G)))) (tptp.groups1707563613775114915nt_nat G A3)))) (forall ((A3 tptp.set_Code_integer) (G tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups3190895334310489300er_nat G (tptp.minus_2355218937544613996nteger A3 (tptp.collect_Code_integer (tptp.aTP_Lamm_abc G)))) (tptp.groups3190895334310489300er_nat G A3)))) (forall ((A3 tptp.set_Code_integer) (G tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups3188404863801439024er_int G (tptp.minus_2355218937544613996nteger A3 (tptp.collect_Code_integer (tptp.aTP_Lamm_abd G)))) (tptp.groups3188404863801439024er_int G A3)))) (forall ((A3 tptp.set_nat) (G tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.groups3455450783089532116nteger G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.aa_set871585252387937313nteger _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) (tptp.collect_nat (tptp.aTP_Lamm_abe G)))) (tptp.aa_set871585252387937313nteger _let_1 A3))))) (forall ((A tptp.rat)) (tptp.finite_finite_rat (tptp.collect_rat (tptp.aa_rat_fun_rat_bool tptp.aTP_Lamm_abf A)))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.aa_int_int _let_1 B))) (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) tptp.one_one_int)) A))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.aa_int_int _let_1 B))) (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) A))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int _let_2 (tptp.aa_int_int _let_1 B))) (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_2 (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int B) A)))))))) (forall ((A tptp.nat) (D2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_abg A) D2)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) D2)))) _let_1)))) (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn) (D2 tptp.assn)) (= (tptp.ord_less_eq_set_assn (tptp.set_or7959216805967363635t_assn A B) (tptp.set_or5523502641901747543n_assn C D2)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn A) B)) (and (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn C) A)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn B) D2)))))) (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int) (D2 tptp.set_int)) (= (tptp.ord_le4403425263959731960et_int (tptp.set_or370866239135849197et_int A B) (tptp.set_or8585797421378605585et_int C D2)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) B)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int C) A)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int B) D2)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (= (tptp.ord_less_eq_set_rat (tptp.set_or633870826150836451st_rat A B) (tptp.set_or4029947393144176647an_rat C D2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) D2)))))) (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D2 tptp.num)) (= (tptp.ord_less_eq_set_num (tptp.set_or7049704709247886629st_num A B) (tptp.set_or1222409239386451017an_num C D2)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num C) A)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) D2)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat A) B)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat C) D2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) D2)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.set_or1266510415728281911st_int A B)) (tptp.set_or4662586982721622107an_int C D2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) D2)))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (= (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger (tptp.set_or189985376899183464nteger A B)) (tptp.set_or8404916559141939852nteger C D2))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger C) A)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger B) D2)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (= (tptp.ord_less_eq_set_rat (tptp.set_or4029947393144176647an_rat A B) (tptp.set_or633870826150836451st_rat C D2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) D2)))))) (forall ((L tptp.rat) (M tptp.rat) (U tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat L) M)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat M) U)) (= (tptp.sup_sup_set_rat (tptp.set_or633870826150836451st_rat L M) (tptp.set_or4029947393144176647an_rat M U)) (tptp.set_or4029947393144176647an_rat L U))))) (forall ((L tptp.num) (M tptp.num) (U tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num L) M)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) U)) (= (tptp.sup_sup_set_num (tptp.set_or7049704709247886629st_num L M) (tptp.set_or1222409239386451017an_num M U)) (tptp.set_or1222409239386451017an_num L U))))) (forall ((L tptp.nat) (M tptp.nat) (U tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat L) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) U)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat L) M)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) U)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat L) U))))) (forall ((L tptp.int) (M tptp.int) (U tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int L) M)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int M) U)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int (tptp.set_or1266510415728281911st_int L M)) (tptp.set_or4662586982721622107an_int M U)) (tptp.set_or4662586982721622107an_int L U))))) (forall ((L tptp.code_integer) (M tptp.code_integer) (U tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger L) M)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger M) U)) (= (tptp.sup_su848401254843788991nteger (tptp.set_or189985376899183464nteger L M) (tptp.set_or8404916559141939852nteger M U)) (tptp.set_or8404916559141939852nteger L U))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat tptp.aTP_Lamm_fu) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) tptp.one_one_nat))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat)))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_na2338080690716861136at_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (= (tptp.groups6857163185585827899at_nat G (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2)) (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat (tptp.aa_nat2240542744625857721at_nat G M)) (tptp.groups6857163185585827899at_nat G (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat (tptp.aa_nat_nat tptp.suc M)) N2)))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups2906978787729119204at_rat G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (= (tptp.aa_set_nat_rat _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat G M)) (tptp.aa_set_nat_rat _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat (tptp.aa_nat_nat tptp.suc M)) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.groups3539618377306564664at_int G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (= (tptp.aa_set_nat_int _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int G M)) (tptp.aa_set_nat_int _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat (tptp.aa_nat_nat tptp.suc M)) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.groups3542108847815614940at_nat G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (= (tptp.aa_set_nat_nat _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat G M)) (tptp.aa_set_nat_nat _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat (tptp.aa_nat_nat tptp.suc M)) N2))))))) (forall ((A tptp.nat) (B tptp.nat) (G tptp.fun_na2338080690716861136at_nat)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= (tptp.groups6857163185585827899at_nat G (tptp.aa_nat_set_nat _let_1 (tptp.aa_nat_nat tptp.suc B))) (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat (tptp.groups6857163185585827899at_nat G (tptp.aa_nat_set_nat _let_1 B))) (tptp.aa_nat2240542744625857721at_nat G B)))))) (forall ((A tptp.nat) (B tptp.nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat A))) (let ((_let_2 (tptp.groups2906978787729119204at_rat G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= (tptp.aa_set_nat_rat _let_2 (tptp.aa_nat_set_nat _let_1 (tptp.aa_nat_nat tptp.suc B))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_set_nat_rat _let_2 (tptp.aa_nat_set_nat _let_1 B))) (tptp.aa_nat_rat G B))))))) (forall ((A tptp.nat) (B tptp.nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat A))) (let ((_let_2 (tptp.groups3539618377306564664at_int G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= (tptp.aa_set_nat_int _let_2 (tptp.aa_nat_set_nat _let_1 (tptp.aa_nat_nat tptp.suc B))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_set_nat_int _let_2 (tptp.aa_nat_set_nat _let_1 B))) (tptp.aa_nat_int G B))))))) (forall ((A tptp.nat) (B tptp.nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat A))) (let ((_let_2 (tptp.groups3542108847815614940at_nat G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= (tptp.aa_set_nat_nat _let_2 (tptp.aa_nat_set_nat _let_1 (tptp.aa_nat_nat tptp.suc B))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_set_nat_nat _let_2 (tptp.aa_nat_set_nat _let_1 B))) (tptp.aa_nat_nat G B))))))) (forall ((G tptp.fun_nat_Code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (let ((_let_2 (tptp.groups3455450783089532116nteger G))) (= (tptp.aa_set871585252387937313nteger _let_2 (tptp.aa_nat_set_nat _let_1 (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_set871585252387937313nteger _let_2 (tptp.aa_nat_set_nat _let_1 N2))) (tptp.aa_nat_Code_integer G N2)))))) (forall ((G tptp.fun_nat_assn) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat _let_1 (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat _let_1 N2))) (tptp.aa_nat_assn G N2))))) (forall ((G tptp.fun_nat_rat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (let ((_let_2 (tptp.groups73079841787564623at_rat G))) (= (tptp.aa_set_nat_rat _let_2 (tptp.aa_nat_set_nat _let_1 (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_set_nat_rat _let_2 (tptp.aa_nat_set_nat _let_1 N2))) (tptp.aa_nat_rat G N2)))))) (forall ((G tptp.fun_nat_nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (let ((_let_2 (tptp.groups708209901874060359at_nat G))) (= (tptp.aa_set_nat_nat _let_2 (tptp.aa_nat_set_nat _let_1 (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_set_nat_nat _let_2 (tptp.aa_nat_set_nat _let_1 N2))) (tptp.aa_nat_nat G N2)))))) (forall ((G tptp.fun_nat_int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (let ((_let_2 (tptp.groups705719431365010083at_int G))) (= (tptp.aa_set_nat_int _let_2 (tptp.aa_nat_set_nat _let_1 (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_set_nat_int _let_2 (tptp.aa_nat_set_nat _let_1 N2))) (tptp.aa_nat_int G N2)))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.groups3455450783089532116nteger G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (= (tptp.aa_set871585252387937313nteger _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer G M)) (tptp.aa_set871585252387937313nteger _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat (tptp.aa_nat_nat tptp.suc M)) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_assn)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (= (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.aa_nat_assn G M)) (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat (tptp.aa_nat_nat tptp.suc M)) N2)))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups73079841787564623at_rat G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (= (tptp.aa_set_nat_rat _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat G M)) (tptp.aa_set_nat_rat _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat (tptp.aa_nat_nat tptp.suc M)) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.groups708209901874060359at_nat G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (= (tptp.aa_set_nat_nat _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat G M)) (tptp.aa_set_nat_nat _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat (tptp.aa_nat_nat tptp.suc M)) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.groups705719431365010083at_int G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (= (tptp.aa_set_nat_int _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int G M)) (tptp.aa_set_nat_int _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat (tptp.aa_nat_nat tptp.suc M)) N2))))))) (forall ((A tptp.nat) (B tptp.nat) (G tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat A))) (let ((_let_2 (tptp.groups3455450783089532116nteger G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= (tptp.aa_set871585252387937313nteger _let_2 (tptp.aa_nat_set_nat _let_1 (tptp.aa_nat_nat tptp.suc B))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_set871585252387937313nteger _let_2 (tptp.aa_nat_set_nat _let_1 B))) (tptp.aa_nat_Code_integer G B))))))) (forall ((A tptp.nat) (B tptp.nat) (G tptp.fun_nat_assn)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat _let_1 (tptp.aa_nat_nat tptp.suc B))) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat _let_1 B))) (tptp.aa_nat_assn G B)))))) (forall ((A tptp.nat) (B tptp.nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat A))) (let ((_let_2 (tptp.groups73079841787564623at_rat G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= (tptp.aa_set_nat_rat _let_2 (tptp.aa_nat_set_nat _let_1 (tptp.aa_nat_nat tptp.suc B))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_set_nat_rat _let_2 (tptp.aa_nat_set_nat _let_1 B))) (tptp.aa_nat_rat G B))))))) (forall ((A tptp.nat) (B tptp.nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat A))) (let ((_let_2 (tptp.groups708209901874060359at_nat G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= (tptp.aa_set_nat_nat _let_2 (tptp.aa_nat_set_nat _let_1 (tptp.aa_nat_nat tptp.suc B))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_set_nat_nat _let_2 (tptp.aa_nat_set_nat _let_1 B))) (tptp.aa_nat_nat G B))))))) (forall ((A tptp.nat) (B tptp.nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat A))) (let ((_let_2 (tptp.groups705719431365010083at_int G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= (tptp.aa_set_nat_int _let_2 (tptp.aa_nat_set_nat _let_1 (tptp.aa_nat_nat tptp.suc B))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_set_nat_int _let_2 (tptp.aa_nat_set_nat _let_1 B))) (tptp.aa_nat_int G B))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_na2338080690716861136at_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.groups6857163185585827899at_nat G (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)) (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat (tptp.aa_nat2240542744625857721at_nat G N2)) (tptp.groups6857163185585827899at_nat G (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2)))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups2906978787729119204at_rat G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_set_nat_rat _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat G N2)) (tptp.aa_set_nat_rat _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.groups3539618377306564664at_int G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_set_nat_int _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int G N2)) (tptp.aa_set_nat_int _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.groups3542108847815614940at_nat G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_set_nat_nat _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat G N2)) (tptp.aa_set_nat_nat _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.groups3455450783089532116nteger G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_set871585252387937313nteger _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer G N2)) (tptp.aa_set871585252387937313nteger _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_assn)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.aa_nat_assn G N2)) (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2)))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups73079841787564623at_rat G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_set_nat_rat _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat G N2)) (tptp.aa_set_nat_rat _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.groups708209901874060359at_nat G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_set_nat_nat _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat G N2)) (tptp.aa_set_nat_nat _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.groups705719431365010083at_int G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_set_nat_int _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int G N2)) (tptp.aa_set_nat_int _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2))))))) (forall ((I5 tptp.set_bool) (I2 tptp.bool) (F tptp.fun_bo7282069421189217543nteger)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (tptp.finite_finite_bool I5) (=> (tptp.pp (tptp.member_bool I2 I5)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_bool_Code_integer F I2))) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 I5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_bool_Code_integer F I3))))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.groups1682264926906508858nteger F I5))))))))) (forall ((I5 tptp.set_nat) (I2 tptp.nat) (F tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat I5)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I2) I5)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_nat_Code_integer F I2))) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer F I3))))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger F) I5))))))))) (forall ((I5 tptp.set_int) (I2 tptp.int) (F tptp.fun_int_Code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int I5)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I2) I5)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_int_Code_integer F I2))) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_int_Code_integer F I3))))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.groups7873554091576472773nteger F I5))))))))) (forall ((I5 tptp.set_Code_integer) (I2 tptp.code_integer) (F tptp.fun_Co8499238673658658103nteger)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger I5)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I2) I5)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger F I2))) (=> (forall ((I3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I3) I5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger F I3))))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.groups879477027807139574nteger F I5))))))))) (forall ((I5 tptp.set_bool) (I2 tptp.bool) (F tptp.fun_bool_rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.finite_finite_bool I5) (=> (tptp.pp (tptp.member_bool I2 I5)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_bool_rat F I2))) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_bool_rat F I3))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.groups5133371213642249141ol_rat F I5))))))))) (forall ((I5 tptp.set_nat) (I2 tptp.nat) (F tptp.fun_nat_rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat I5)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I2) I5)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat F I2))) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat F I3))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat F) I5))))))))) (forall ((I5 tptp.set_int) (I2 tptp.int) (F tptp.fun_int_rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int I5)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I2) I5)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_int_rat F I2))) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_int_rat F I3))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.groups3906332499630173760nt_rat F I5))))))))) (forall ((I5 tptp.set_Code_integer) (I2 tptp.code_integer) (F tptp.fun_Code_integer_rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger I5)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I2) I5)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_Code_integer_rat F I2))) (=> (forall ((I3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_Code_integer_rat F I3))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.groups6602215022474089585er_rat F I5))))))))) (forall ((I5 tptp.set_bool) (I2 tptp.bool) (F tptp.fun_bool_nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.finite_finite_bool I5) (=> (tptp.pp (tptp.member_bool I2 I5)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_bool_nat F I2))) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 I5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_bool_nat F I3))))) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.groups5768501273728744877ol_nat F I5))))))))) (forall ((I5 tptp.set_int) (I2 tptp.int) (F tptp.fun_int_nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int I5)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I2) I5)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_int_nat F I2))) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_int_nat F I3))))) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.groups4541462559716669496nt_nat F I5))))))))) (forall ((I5 tptp.set_Code_integer) (F tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger I5)) (=> (not (= I5 tptp.bot_bo3990330152332043303nteger)) (=> (forall ((I3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I3) I5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger F I3))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.groups879477027807139574nteger F I5))))))) (forall ((I5 tptp.set_bool) (F tptp.fun_bo7282069421189217543nteger)) (=> (tptp.finite_finite_bool I5) (=> (not (= I5 tptp.bot_bot_set_bool)) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 I5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_bool_Code_integer F I3))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.groups1682264926906508858nteger F I5))))))) (forall ((I5 tptp.set_nat) (F tptp.fun_nat_Code_integer)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat I5)) (=> (not (= I5 tptp.bot_bot_set_nat)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer F I3))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger F) I5))))))) (forall ((I5 tptp.set_int) (F tptp.fun_int_Code_integer)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int I5)) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_int_Code_integer F I3))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.groups7873554091576472773nteger F I5))))))) (forall ((I5 tptp.set_Code_integer) (F tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger I5)) (=> (not (= I5 tptp.bot_bo3990330152332043303nteger)) (=> (forall ((I3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_Code_integer_rat F I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.groups6602215022474089585er_rat F I5))))))) (forall ((I5 tptp.set_bool) (F tptp.fun_bool_rat)) (=> (tptp.finite_finite_bool I5) (=> (not (= I5 tptp.bot_bot_set_bool)) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_bool_rat F I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.groups5133371213642249141ol_rat F I5))))))) (forall ((I5 tptp.set_nat) (F tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat I5)) (=> (not (= I5 tptp.bot_bot_set_nat)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_nat_rat F I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat F) I5))))))) (forall ((I5 tptp.set_int) (F tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int I5)) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_int_rat F I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.groups3906332499630173760nt_rat F I5))))))) (forall ((I5 tptp.set_Code_integer) (F tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger I5)) (=> (not (= I5 tptp.bot_bo3990330152332043303nteger)) (=> (forall ((I3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I3) I5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_Code_integer_nat F I3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.groups7237345082560585321er_nat F I5))))))) (forall ((I5 tptp.set_bool) (F tptp.fun_bool_nat)) (=> (tptp.finite_finite_bool I5) (=> (not (= I5 tptp.bot_bot_set_bool)) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 I5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_bool_nat F I3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.groups5768501273728744877ol_nat F I5))))))) (forall ((I5 tptp.set_bool) (I2 tptp.bool) (F tptp.fun_bo7282069421189217543nteger)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (tptp.finite_finite_bool I5) (=> (tptp.pp (tptp.member_bool I2 I5)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_bool_Code_integer F I2))) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 I5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (tptp.aa_bool_Code_integer F I3))))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.groups7272450149305381519nteger F I5))))))))) (forall ((I5 tptp.set_nat) (I2 tptp.nat) (F tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat I5)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I2) I5)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_nat_Code_integer F I2))) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (tptp.aa_nat_Code_integer F I3))))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger F) I5))))))))) (forall ((I5 tptp.set_int) (I2 tptp.int) (F tptp.fun_int_Code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int I5)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I2) I5)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_int_Code_integer F I2))) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (tptp.aa_int_Code_integer F I3))))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.groups3827104343326376752nteger F I5))))))))) (forall ((I5 tptp.set_Code_integer) (I2 tptp.code_integer) (F tptp.fun_Co8499238673658658103nteger)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger I5)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I2) I5)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger F I2))) (=> (forall ((I3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I3) I5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger F I3))))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.groups3674199335183972705nteger F I5))))))))) (forall ((I5 tptp.set_bool) (I2 tptp.bool) (F tptp.fun_bool_rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat))) (=> (tptp.finite_finite_bool I5) (=> (tptp.pp (tptp.member_bool I2 I5)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_bool_rat F I2))) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_bool_rat F I3))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.groups1259819201609700362ol_rat F I5))))))))) (forall ((I5 tptp.set_nat) (I2 tptp.nat) (F tptp.fun_nat_rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat I5)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I2) I5)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat F I2))) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_nat_rat F I3))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat F) I5))))))))) (forall ((I5 tptp.set_int) (I2 tptp.int) (F tptp.fun_int_rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int I5)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I2) I5)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_int_rat F I2))) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_int_rat F I3))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.groups1072433553688619179nt_rat F I5))))))))) (forall ((I5 tptp.set_Code_integer) (I2 tptp.code_integer) (F tptp.fun_Code_integer_rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger I5)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I2) I5)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_Code_integer_rat F I2))) (=> (forall ((I3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_Code_integer_rat F I3))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.groups2555765274223993564er_rat F I5))))))))) (forall ((I5 tptp.set_bool) (I2 tptp.bool) (F tptp.fun_bool_int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int))) (=> (tptp.finite_finite_bool I5) (=> (tptp.pp (tptp.member_bool I2 I5)) (=> (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_bool_int F I2))) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 I5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) (tptp.aa_bool_int F I3))))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.groups1892458791187145822ol_int F I5))))))))) (forall ((I5 tptp.set_Code_integer) (I2 tptp.code_integer) (F tptp.fun_Code_integer_int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger I5)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I2) I5)) (=> (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_Code_integer_int F I2))) (=> (forall ((I3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I3) I5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) (tptp.aa_Code_integer_int F I3))))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.groups3188404863801439024er_int F I5))))))))) (forall ((I5 tptp.set_Code_integer) (F tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger I5)) (=> (not (= I5 tptp.bot_bo3990330152332043303nteger)) (=> (forall ((I3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I3) I5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger F I3))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (tptp.groups3674199335183972705nteger F I5))))))) (forall ((I5 tptp.set_bool) (F tptp.fun_bo7282069421189217543nteger)) (=> (tptp.finite_finite_bool I5) (=> (not (= I5 tptp.bot_bot_set_bool)) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 I5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (tptp.aa_bool_Code_integer F I3))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (tptp.groups7272450149305381519nteger F I5))))))) (forall ((I5 tptp.set_nat) (F tptp.fun_nat_Code_integer)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat I5)) (=> (not (= I5 tptp.bot_bot_set_nat)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (tptp.aa_nat_Code_integer F I3))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger F) I5))))))) (forall ((I5 tptp.set_int) (F tptp.fun_int_Code_integer)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int I5)) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (tptp.aa_int_Code_integer F I3))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (tptp.groups3827104343326376752nteger F I5))))))) (forall ((I5 tptp.set_Code_integer) (F tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger I5)) (=> (not (= I5 tptp.bot_bo3990330152332043303nteger)) (=> (forall ((I3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.aa_Code_integer_rat F I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.groups2555765274223993564er_rat F I5))))))) (forall ((I5 tptp.set_bool) (F tptp.fun_bool_rat)) (=> (tptp.finite_finite_bool I5) (=> (not (= I5 tptp.bot_bot_set_bool)) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.aa_bool_rat F I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.groups1259819201609700362ol_rat F I5))))))) (forall ((I5 tptp.set_nat) (F tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat I5)) (=> (not (= I5 tptp.bot_bot_set_nat)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.aa_nat_rat F I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat F) I5))))))) (forall ((I5 tptp.set_int) (F tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int I5)) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) I5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.aa_int_rat F I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.groups1072433553688619179nt_rat F I5))))))) (forall ((I5 tptp.set_Code_integer) (F tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger I5)) (=> (not (= I5 tptp.bot_bo3990330152332043303nteger)) (=> (forall ((I3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I3) I5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) (tptp.aa_Code_integer_int F I3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) (tptp.groups3188404863801439024er_int F I5))))))) (forall ((I5 tptp.set_bool) (F tptp.fun_bool_int)) (=> (tptp.finite_finite_bool I5) (=> (not (= I5 tptp.bot_bot_set_bool)) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 I5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) (tptp.aa_bool_int F I3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) (tptp.groups1892458791187145822ol_int F I5))))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat K)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K)))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N2) K)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2)))) (forall ((C3 tptp.set_bool) (A3 tptp.set_bool) (B3 tptp.set_bool) (G tptp.fun_bo7282069421189217543nteger) (H tptp.fun_bo7282069421189217543nteger)) (=> (tptp.finite_finite_bool C3) (=> (tptp.ord_less_eq_set_bool A3 C3) (=> (tptp.ord_less_eq_set_bool B3 C3) (=> (forall ((A4 tptp.bool)) (=> (tptp.pp (tptp.member_bool A4 (tptp.minus_minus_set_bool C3 A3))) (= (tptp.aa_bool_Code_integer G A4) tptp.zero_z3403309356797280102nteger))) (=> (forall ((B4 tptp.bool)) (=> (tptp.pp (tptp.member_bool B4 (tptp.minus_minus_set_bool C3 B3))) (= (tptp.aa_bool_Code_integer H B4) tptp.zero_z3403309356797280102nteger))) (= (= (tptp.groups1682264926906508858nteger G A3) (tptp.groups1682264926906508858nteger H B3)) (= (tptp.groups1682264926906508858nteger G C3) (tptp.groups1682264926906508858nteger H C3))))))))) (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Co8499238673658658103nteger) (H tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) C3)) (=> (forall ((A4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A4) (tptp.minus_2355218937544613996nteger C3 A3))) (= (tptp.aa_Cod1783974652533396728nteger G A4) tptp.zero_z3403309356797280102nteger))) (=> (forall ((B4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer B4) (tptp.minus_2355218937544613996nteger C3 B3))) (= (tptp.aa_Cod1783974652533396728nteger H B4) tptp.zero_z3403309356797280102nteger))) (= (= (tptp.groups879477027807139574nteger G A3) (tptp.groups879477027807139574nteger H B3)) (= (tptp.groups879477027807139574nteger G C3) (tptp.groups879477027807139574nteger H C3))))))))) (forall ((C3 tptp.set_bool) (A3 tptp.set_bool) (B3 tptp.set_bool) (G tptp.fun_bool_rat) (H tptp.fun_bool_rat)) (=> (tptp.finite_finite_bool C3) (=> (tptp.ord_less_eq_set_bool A3 C3) (=> (tptp.ord_less_eq_set_bool B3 C3) (=> (forall ((A4 tptp.bool)) (=> (tptp.pp (tptp.member_bool A4 (tptp.minus_minus_set_bool C3 A3))) (= (tptp.aa_bool_rat G A4) tptp.zero_zero_rat))) (=> (forall ((B4 tptp.bool)) (=> (tptp.pp (tptp.member_bool B4 (tptp.minus_minus_set_bool C3 B3))) (= (tptp.aa_bool_rat H B4) tptp.zero_zero_rat))) (= (= (tptp.groups5133371213642249141ol_rat G A3) (tptp.groups5133371213642249141ol_rat H B3)) (= (tptp.groups5133371213642249141ol_rat G C3) (tptp.groups5133371213642249141ol_rat H C3))))))))) (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Code_integer_rat) (H tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) C3)) (=> (forall ((A4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A4) (tptp.minus_2355218937544613996nteger C3 A3))) (= (tptp.aa_Code_integer_rat G A4) tptp.zero_zero_rat))) (=> (forall ((B4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer B4) (tptp.minus_2355218937544613996nteger C3 B3))) (= (tptp.aa_Code_integer_rat H B4) tptp.zero_zero_rat))) (= (= (tptp.groups6602215022474089585er_rat G A3) (tptp.groups6602215022474089585er_rat H B3)) (= (tptp.groups6602215022474089585er_rat G C3) (tptp.groups6602215022474089585er_rat H C3))))))))) (forall ((C3 tptp.set_bool) (A3 tptp.set_bool) (B3 tptp.set_bool) (G tptp.fun_bool_nat) (H tptp.fun_bool_nat)) (=> (tptp.finite_finite_bool C3) (=> (tptp.ord_less_eq_set_bool A3 C3) (=> (tptp.ord_less_eq_set_bool B3 C3) (=> (forall ((A4 tptp.bool)) (=> (tptp.pp (tptp.member_bool A4 (tptp.minus_minus_set_bool C3 A3))) (= (tptp.aa_bool_nat G A4) tptp.zero_zero_nat))) (=> (forall ((B4 tptp.bool)) (=> (tptp.pp (tptp.member_bool B4 (tptp.minus_minus_set_bool C3 B3))) (= (tptp.aa_bool_nat H B4) tptp.zero_zero_nat))) (= (= (tptp.groups5768501273728744877ol_nat G A3) (tptp.groups5768501273728744877ol_nat H B3)) (= (tptp.groups5768501273728744877ol_nat G C3) (tptp.groups5768501273728744877ol_nat H C3))))))))) (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Code_integer_nat) (H tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) C3)) (=> (forall ((A4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A4) (tptp.minus_2355218937544613996nteger C3 A3))) (= (tptp.aa_Code_integer_nat G A4) tptp.zero_zero_nat))) (=> (forall ((B4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer B4) (tptp.minus_2355218937544613996nteger C3 B3))) (= (tptp.aa_Code_integer_nat H B4) tptp.zero_zero_nat))) (= (= (tptp.groups7237345082560585321er_nat G A3) (tptp.groups7237345082560585321er_nat H B3)) (= (tptp.groups7237345082560585321er_nat G C3) (tptp.groups7237345082560585321er_nat H C3))))))))) (forall ((C3 tptp.set_bool) (A3 tptp.set_bool) (B3 tptp.set_bool) (G tptp.fun_bool_int) (H tptp.fun_bool_int)) (=> (tptp.finite_finite_bool C3) (=> (tptp.ord_less_eq_set_bool A3 C3) (=> (tptp.ord_less_eq_set_bool B3 C3) (=> (forall ((A4 tptp.bool)) (=> (tptp.pp (tptp.member_bool A4 (tptp.minus_minus_set_bool C3 A3))) (= (tptp.aa_bool_int G A4) tptp.zero_zero_int))) (=> (forall ((B4 tptp.bool)) (=> (tptp.pp (tptp.member_bool B4 (tptp.minus_minus_set_bool C3 B3))) (= (tptp.aa_bool_int H B4) tptp.zero_zero_int))) (= (= (tptp.groups5766010803219694601ol_int G A3) (tptp.groups5766010803219694601ol_int H B3)) (= (tptp.groups5766010803219694601ol_int G C3) (tptp.groups5766010803219694601ol_int H C3))))))))) (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Code_integer_int) (H tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) C3)) (=> (forall ((A4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A4) (tptp.minus_2355218937544613996nteger C3 A3))) (= (tptp.aa_Code_integer_int G A4) tptp.zero_zero_int))) (=> (forall ((B4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer B4) (tptp.minus_2355218937544613996nteger C3 B3))) (= (tptp.aa_Code_integer_int H B4) tptp.zero_zero_int))) (= (= (tptp.groups7234854612051535045er_int G A3) (tptp.groups7234854612051535045er_int H B3)) (= (tptp.groups7234854612051535045er_int G C3) (tptp.groups7234854612051535045er_int H C3))))))))) (forall ((C3 tptp.set_nat) (A3 tptp.set_nat) (B3 tptp.set_nat) (G tptp.fun_nat_Code_integer) (H tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.groups7501900531339628137nteger H))) (let ((_let_2 (tptp.groups7501900531339628137nteger G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat C3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) C3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B3) C3)) (=> (forall ((A4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A4) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat C3) A3))) (= (tptp.aa_nat_Code_integer G A4) tptp.zero_z3403309356797280102nteger))) (=> (forall ((B4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B4) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat C3) B3))) (= (tptp.aa_nat_Code_integer H B4) tptp.zero_z3403309356797280102nteger))) (= (= (tptp.aa_set871585252387937313nteger _let_2 A3) (tptp.aa_set871585252387937313nteger _let_1 B3)) (= (tptp.aa_set871585252387937313nteger _let_2 C3) (tptp.aa_set871585252387937313nteger _let_1 C3))))))))))) (forall ((C3 tptp.set_nat) (A3 tptp.set_nat) (B3 tptp.set_nat) (G tptp.fun_nat_rat) (H tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups2906978787729119204at_rat H))) (let ((_let_2 (tptp.groups2906978787729119204at_rat G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat C3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) C3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B3) C3)) (=> (forall ((A4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A4) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat C3) A3))) (= (tptp.aa_nat_rat G A4) tptp.zero_zero_rat))) (=> (forall ((B4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B4) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat C3) B3))) (= (tptp.aa_nat_rat H B4) tptp.zero_zero_rat))) (= (= (tptp.aa_set_nat_rat _let_2 A3) (tptp.aa_set_nat_rat _let_1 B3)) (= (tptp.aa_set_nat_rat _let_2 C3) (tptp.aa_set_nat_rat _let_1 C3))))))))))) (forall ((C3 tptp.set_bool) (A3 tptp.set_bool) (B3 tptp.set_bool) (G tptp.fun_bo7282069421189217543nteger) (H tptp.fun_bo7282069421189217543nteger)) (=> (tptp.finite_finite_bool C3) (=> (tptp.ord_less_eq_set_bool A3 C3) (=> (tptp.ord_less_eq_set_bool B3 C3) (=> (forall ((A4 tptp.bool)) (=> (tptp.pp (tptp.member_bool A4 (tptp.minus_minus_set_bool C3 A3))) (= (tptp.aa_bool_Code_integer G A4) tptp.zero_z3403309356797280102nteger))) (=> (forall ((B4 tptp.bool)) (=> (tptp.pp (tptp.member_bool B4 (tptp.minus_minus_set_bool C3 B3))) (= (tptp.aa_bool_Code_integer H B4) tptp.zero_z3403309356797280102nteger))) (=> (= (tptp.groups1682264926906508858nteger G C3) (tptp.groups1682264926906508858nteger H C3)) (= (tptp.groups1682264926906508858nteger G A3) (tptp.groups1682264926906508858nteger H B3))))))))) (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Co8499238673658658103nteger) (H tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) C3)) (=> (forall ((A4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A4) (tptp.minus_2355218937544613996nteger C3 A3))) (= (tptp.aa_Cod1783974652533396728nteger G A4) tptp.zero_z3403309356797280102nteger))) (=> (forall ((B4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer B4) (tptp.minus_2355218937544613996nteger C3 B3))) (= (tptp.aa_Cod1783974652533396728nteger H B4) tptp.zero_z3403309356797280102nteger))) (=> (= (tptp.groups879477027807139574nteger G C3) (tptp.groups879477027807139574nteger H C3)) (= (tptp.groups879477027807139574nteger G A3) (tptp.groups879477027807139574nteger H B3))))))))) (forall ((C3 tptp.set_bool) (A3 tptp.set_bool) (B3 tptp.set_bool) (G tptp.fun_bool_rat) (H tptp.fun_bool_rat)) (=> (tptp.finite_finite_bool C3) (=> (tptp.ord_less_eq_set_bool A3 C3) (=> (tptp.ord_less_eq_set_bool B3 C3) (=> (forall ((A4 tptp.bool)) (=> (tptp.pp (tptp.member_bool A4 (tptp.minus_minus_set_bool C3 A3))) (= (tptp.aa_bool_rat G A4) tptp.zero_zero_rat))) (=> (forall ((B4 tptp.bool)) (=> (tptp.pp (tptp.member_bool B4 (tptp.minus_minus_set_bool C3 B3))) (= (tptp.aa_bool_rat H B4) tptp.zero_zero_rat))) (=> (= (tptp.groups5133371213642249141ol_rat G C3) (tptp.groups5133371213642249141ol_rat H C3)) (= (tptp.groups5133371213642249141ol_rat G A3) (tptp.groups5133371213642249141ol_rat H B3))))))))) (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Code_integer_rat) (H tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) C3)) (=> (forall ((A4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A4) (tptp.minus_2355218937544613996nteger C3 A3))) (= (tptp.aa_Code_integer_rat G A4) tptp.zero_zero_rat))) (=> (forall ((B4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer B4) (tptp.minus_2355218937544613996nteger C3 B3))) (= (tptp.aa_Code_integer_rat H B4) tptp.zero_zero_rat))) (=> (= (tptp.groups6602215022474089585er_rat G C3) (tptp.groups6602215022474089585er_rat H C3)) (= (tptp.groups6602215022474089585er_rat G A3) (tptp.groups6602215022474089585er_rat H B3))))))))) (forall ((C3 tptp.set_bool) (A3 tptp.set_bool) (B3 tptp.set_bool) (G tptp.fun_bool_nat) (H tptp.fun_bool_nat)) (=> (tptp.finite_finite_bool C3) (=> (tptp.ord_less_eq_set_bool A3 C3) (=> (tptp.ord_less_eq_set_bool B3 C3) (=> (forall ((A4 tptp.bool)) (=> (tptp.pp (tptp.member_bool A4 (tptp.minus_minus_set_bool C3 A3))) (= (tptp.aa_bool_nat G A4) tptp.zero_zero_nat))) (=> (forall ((B4 tptp.bool)) (=> (tptp.pp (tptp.member_bool B4 (tptp.minus_minus_set_bool C3 B3))) (= (tptp.aa_bool_nat H B4) tptp.zero_zero_nat))) (=> (= (tptp.groups5768501273728744877ol_nat G C3) (tptp.groups5768501273728744877ol_nat H C3)) (= (tptp.groups5768501273728744877ol_nat G A3) (tptp.groups5768501273728744877ol_nat H B3))))))))) (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Code_integer_nat) (H tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) C3)) (=> (forall ((A4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A4) (tptp.minus_2355218937544613996nteger C3 A3))) (= (tptp.aa_Code_integer_nat G A4) tptp.zero_zero_nat))) (=> (forall ((B4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer B4) (tptp.minus_2355218937544613996nteger C3 B3))) (= (tptp.aa_Code_integer_nat H B4) tptp.zero_zero_nat))) (=> (= (tptp.groups7237345082560585321er_nat G C3) (tptp.groups7237345082560585321er_nat H C3)) (= (tptp.groups7237345082560585321er_nat G A3) (tptp.groups7237345082560585321er_nat H B3))))))))) (forall ((C3 tptp.set_bool) (A3 tptp.set_bool) (B3 tptp.set_bool) (G tptp.fun_bool_int) (H tptp.fun_bool_int)) (=> (tptp.finite_finite_bool C3) (=> (tptp.ord_less_eq_set_bool A3 C3) (=> (tptp.ord_less_eq_set_bool B3 C3) (=> (forall ((A4 tptp.bool)) (=> (tptp.pp (tptp.member_bool A4 (tptp.minus_minus_set_bool C3 A3))) (= (tptp.aa_bool_int G A4) tptp.zero_zero_int))) (=> (forall ((B4 tptp.bool)) (=> (tptp.pp (tptp.member_bool B4 (tptp.minus_minus_set_bool C3 B3))) (= (tptp.aa_bool_int H B4) tptp.zero_zero_int))) (=> (= (tptp.groups5766010803219694601ol_int G C3) (tptp.groups5766010803219694601ol_int H C3)) (= (tptp.groups5766010803219694601ol_int G A3) (tptp.groups5766010803219694601ol_int H B3))))))))) (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Code_integer_int) (H tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) C3)) (=> (forall ((A4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A4) (tptp.minus_2355218937544613996nteger C3 A3))) (= (tptp.aa_Code_integer_int G A4) tptp.zero_zero_int))) (=> (forall ((B4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer B4) (tptp.minus_2355218937544613996nteger C3 B3))) (= (tptp.aa_Code_integer_int H B4) tptp.zero_zero_int))) (=> (= (tptp.groups7234854612051535045er_int G C3) (tptp.groups7234854612051535045er_int H C3)) (= (tptp.groups7234854612051535045er_int G A3) (tptp.groups7234854612051535045er_int H B3))))))))) (forall ((C3 tptp.set_nat) (A3 tptp.set_nat) (B3 tptp.set_nat) (G tptp.fun_nat_Code_integer) (H tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.groups7501900531339628137nteger H))) (let ((_let_2 (tptp.groups7501900531339628137nteger G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat C3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) C3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B3) C3)) (=> (forall ((A4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A4) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat C3) A3))) (= (tptp.aa_nat_Code_integer G A4) tptp.zero_z3403309356797280102nteger))) (=> (forall ((B4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B4) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat C3) B3))) (= (tptp.aa_nat_Code_integer H B4) tptp.zero_z3403309356797280102nteger))) (=> (= (tptp.aa_set871585252387937313nteger _let_2 C3) (tptp.aa_set871585252387937313nteger _let_1 C3)) (= (tptp.aa_set871585252387937313nteger _let_2 A3) (tptp.aa_set871585252387937313nteger _let_1 B3))))))))))) (forall ((C3 tptp.set_nat) (A3 tptp.set_nat) (B3 tptp.set_nat) (G tptp.fun_nat_rat) (H tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups2906978787729119204at_rat H))) (let ((_let_2 (tptp.groups2906978787729119204at_rat G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat C3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) C3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B3) C3)) (=> (forall ((A4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A4) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat C3) A3))) (= (tptp.aa_nat_rat G A4) tptp.zero_zero_rat))) (=> (forall ((B4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B4) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat C3) B3))) (= (tptp.aa_nat_rat H B4) tptp.zero_zero_rat))) (=> (= (tptp.aa_set_nat_rat _let_2 C3) (tptp.aa_set_nat_rat _let_1 C3)) (= (tptp.aa_set_nat_rat _let_2 A3) (tptp.aa_set_nat_rat _let_1 B3))))))))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Cod1783974652533396728nteger G X3) tptp.zero_z3403309356797280102nteger))) (= (tptp.groups879477027807139574nteger G S) (tptp.groups879477027807139574nteger G T)))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Code_integer_rat G X3) tptp.zero_zero_rat))) (= (tptp.groups6602215022474089585er_rat G S) (tptp.groups6602215022474089585er_rat G T)))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Code_integer_nat G X3) tptp.zero_zero_nat))) (= (tptp.groups7237345082560585321er_nat G S) (tptp.groups7237345082560585321er_nat G T)))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Code_integer_int G X3) tptp.zero_zero_int))) (= (tptp.groups7234854612051535045er_int G S) (tptp.groups7234854612051535045er_int G T)))))) (forall ((T tptp.set_nat) (S tptp.set_nat) (G tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.groups7501900531339628137nteger G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat S) T)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat T) S))) (= (tptp.aa_nat_Code_integer G X3) tptp.zero_z3403309356797280102nteger))) (= (tptp.aa_set871585252387937313nteger _let_1 S) (tptp.aa_set871585252387937313nteger _let_1 T))))))) (forall ((T tptp.set_nat) (S tptp.set_nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups2906978787729119204at_rat G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat S) T)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat T) S))) (= (tptp.aa_nat_rat G X3) tptp.zero_zero_rat))) (= (tptp.aa_set_nat_rat _let_1 S) (tptp.aa_set_nat_rat _let_1 T))))))) (forall ((T tptp.set_nat) (S tptp.set_nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.groups3539618377306564664at_int G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat S) T)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat T) S))) (= (tptp.aa_nat_int G X3) tptp.zero_zero_int))) (= (tptp.aa_set_nat_int _let_1 S) (tptp.aa_set_nat_int _let_1 T))))))) (forall ((T tptp.set_int) (S tptp.set_int) (G tptp.fun_int_Code_integer)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int S) T)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int T) S))) (= (tptp.aa_int_Code_integer G X3) tptp.zero_z3403309356797280102nteger))) (= (tptp.groups7873554091576472773nteger G S) (tptp.groups7873554091576472773nteger G T)))))) (forall ((T tptp.set_int) (S tptp.set_int) (G tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int S) T)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int T) S))) (= (tptp.aa_int_rat G X3) tptp.zero_zero_rat))) (= (tptp.groups3906332499630173760nt_rat G S) (tptp.groups3906332499630173760nt_rat G T)))))) (forall ((T tptp.set_int) (S tptp.set_int) (G tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int S) T)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int T) S))) (= (tptp.aa_int_nat G X3) tptp.zero_zero_nat))) (= (tptp.groups4541462559716669496nt_nat G S) (tptp.groups4541462559716669496nt_nat G T)))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Cod1783974652533396728nteger G X3) tptp.zero_z3403309356797280102nteger))) (= (tptp.groups879477027807139574nteger G T) (tptp.groups879477027807139574nteger G S)))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Code_integer_rat G X3) tptp.zero_zero_rat))) (= (tptp.groups6602215022474089585er_rat G T) (tptp.groups6602215022474089585er_rat G S)))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Code_integer_nat G X3) tptp.zero_zero_nat))) (= (tptp.groups7237345082560585321er_nat G T) (tptp.groups7237345082560585321er_nat G S)))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Code_integer_int G X3) tptp.zero_zero_int))) (= (tptp.groups7234854612051535045er_int G T) (tptp.groups7234854612051535045er_int G S)))))) (forall ((T tptp.set_nat) (S tptp.set_nat) (G tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.groups7501900531339628137nteger G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat S) T)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat T) S))) (= (tptp.aa_nat_Code_integer G X3) tptp.zero_z3403309356797280102nteger))) (= (tptp.aa_set871585252387937313nteger _let_1 T) (tptp.aa_set871585252387937313nteger _let_1 S))))))) (forall ((T tptp.set_nat) (S tptp.set_nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups2906978787729119204at_rat G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat S) T)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat T) S))) (= (tptp.aa_nat_rat G X3) tptp.zero_zero_rat))) (= (tptp.aa_set_nat_rat _let_1 T) (tptp.aa_set_nat_rat _let_1 S))))))) (forall ((T tptp.set_nat) (S tptp.set_nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.groups3539618377306564664at_int G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat S) T)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat T) S))) (= (tptp.aa_nat_int G X3) tptp.zero_zero_int))) (= (tptp.aa_set_nat_int _let_1 T) (tptp.aa_set_nat_int _let_1 S))))))) (forall ((T tptp.set_int) (S tptp.set_int) (G tptp.fun_int_Code_integer)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int S) T)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int T) S))) (= (tptp.aa_int_Code_integer G X3) tptp.zero_z3403309356797280102nteger))) (= (tptp.groups7873554091576472773nteger G T) (tptp.groups7873554091576472773nteger G S)))))) (forall ((T tptp.set_int) (S tptp.set_int) (G tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int S) T)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int T) S))) (= (tptp.aa_int_rat G X3) tptp.zero_zero_rat))) (= (tptp.groups3906332499630173760nt_rat G T) (tptp.groups3906332499630173760nt_rat G S)))))) (forall ((T tptp.set_int) (S tptp.set_int) (G tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int S) T)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int T) S))) (= (tptp.aa_int_nat G X3) tptp.zero_zero_nat))) (= (tptp.groups4541462559716669496nt_nat G T) (tptp.groups4541462559716669496nt_nat G S)))))) (forall ((T tptp.set_bool) (S tptp.set_bool) (H tptp.fun_bo7282069421189217543nteger) (G tptp.fun_bo7282069421189217543nteger)) (=> (tptp.finite_finite_bool T) (=> (tptp.ord_less_eq_set_bool S T) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 (tptp.minus_minus_set_bool T S))) (= (tptp.aa_bool_Code_integer H X3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 S)) (= (tptp.aa_bool_Code_integer G X3) (tptp.aa_bool_Code_integer H X3)))) (= (tptp.groups1682264926906508858nteger G S) (tptp.groups1682264926906508858nteger H T))))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (H tptp.fun_Co8499238673658658103nteger) (G tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Cod1783974652533396728nteger H X3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) S)) (= (tptp.aa_Cod1783974652533396728nteger G X3) (tptp.aa_Cod1783974652533396728nteger H X3)))) (= (tptp.groups879477027807139574nteger G S) (tptp.groups879477027807139574nteger H T))))))) (forall ((T tptp.set_bool) (S tptp.set_bool) (H tptp.fun_bool_rat) (G tptp.fun_bool_rat)) (=> (tptp.finite_finite_bool T) (=> (tptp.ord_less_eq_set_bool S T) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 (tptp.minus_minus_set_bool T S))) (= (tptp.aa_bool_rat H X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 S)) (= (tptp.aa_bool_rat G X3) (tptp.aa_bool_rat H X3)))) (= (tptp.groups5133371213642249141ol_rat G S) (tptp.groups5133371213642249141ol_rat H T))))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (H tptp.fun_Code_integer_rat) (G tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Code_integer_rat H X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) S)) (= (tptp.aa_Code_integer_rat G X3) (tptp.aa_Code_integer_rat H X3)))) (= (tptp.groups6602215022474089585er_rat G S) (tptp.groups6602215022474089585er_rat H T))))))) (forall ((T tptp.set_bool) (S tptp.set_bool) (H tptp.fun_bool_nat) (G tptp.fun_bool_nat)) (=> (tptp.finite_finite_bool T) (=> (tptp.ord_less_eq_set_bool S T) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 (tptp.minus_minus_set_bool T S))) (= (tptp.aa_bool_nat H X3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 S)) (= (tptp.aa_bool_nat G X3) (tptp.aa_bool_nat H X3)))) (= (tptp.groups5768501273728744877ol_nat G S) (tptp.groups5768501273728744877ol_nat H T))))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (H tptp.fun_Code_integer_nat) (G tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Code_integer_nat H X3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) S)) (= (tptp.aa_Code_integer_nat G X3) (tptp.aa_Code_integer_nat H X3)))) (= (tptp.groups7237345082560585321er_nat G S) (tptp.groups7237345082560585321er_nat H T))))))) (forall ((T tptp.set_bool) (S tptp.set_bool) (H tptp.fun_bool_int) (G tptp.fun_bool_int)) (=> (tptp.finite_finite_bool T) (=> (tptp.ord_less_eq_set_bool S T) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 (tptp.minus_minus_set_bool T S))) (= (tptp.aa_bool_int H X3) tptp.zero_zero_int))) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 S)) (= (tptp.aa_bool_int G X3) (tptp.aa_bool_int H X3)))) (= (tptp.groups5766010803219694601ol_int G S) (tptp.groups5766010803219694601ol_int H T))))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (H tptp.fun_Code_integer_int) (G tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Code_integer_int H X3) tptp.zero_zero_int))) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) S)) (= (tptp.aa_Code_integer_int G X3) (tptp.aa_Code_integer_int H X3)))) (= (tptp.groups7234854612051535045er_int G S) (tptp.groups7234854612051535045er_int H T))))))) (forall ((T tptp.set_nat) (S tptp.set_nat) (H tptp.fun_nat_Code_integer) (G tptp.fun_nat_Code_integer)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat S) T)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat T) S))) (= (tptp.aa_nat_Code_integer H X3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) S)) (= (tptp.aa_nat_Code_integer G X3) (tptp.aa_nat_Code_integer H X3)))) (= (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger G) S) (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger H) T))))))) (forall ((T tptp.set_nat) (S tptp.set_nat) (H tptp.fun_nat_rat) (G tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat S) T)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat T) S))) (= (tptp.aa_nat_rat H X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) S)) (= (tptp.aa_nat_rat G X3) (tptp.aa_nat_rat H X3)))) (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat G) S) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat H) T))))))) (forall ((T tptp.set_bool) (S tptp.set_bool) (G tptp.fun_bo7282069421189217543nteger) (H tptp.fun_bo7282069421189217543nteger)) (=> (tptp.finite_finite_bool T) (=> (tptp.ord_less_eq_set_bool S T) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 (tptp.minus_minus_set_bool T S))) (= (tptp.aa_bool_Code_integer G X3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 S)) (= (tptp.aa_bool_Code_integer G X3) (tptp.aa_bool_Code_integer H X3)))) (= (tptp.groups1682264926906508858nteger G T) (tptp.groups1682264926906508858nteger H S))))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G tptp.fun_Co8499238673658658103nteger) (H tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Cod1783974652533396728nteger G X3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) S)) (= (tptp.aa_Cod1783974652533396728nteger G X3) (tptp.aa_Cod1783974652533396728nteger H X3)))) (= (tptp.groups879477027807139574nteger G T) (tptp.groups879477027807139574nteger H S))))))) (forall ((T tptp.set_bool) (S tptp.set_bool) (G tptp.fun_bool_rat) (H tptp.fun_bool_rat)) (=> (tptp.finite_finite_bool T) (=> (tptp.ord_less_eq_set_bool S T) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 (tptp.minus_minus_set_bool T S))) (= (tptp.aa_bool_rat G X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 S)) (= (tptp.aa_bool_rat G X3) (tptp.aa_bool_rat H X3)))) (= (tptp.groups5133371213642249141ol_rat G T) (tptp.groups5133371213642249141ol_rat H S))))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G tptp.fun_Code_integer_rat) (H tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Code_integer_rat G X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) S)) (= (tptp.aa_Code_integer_rat G X3) (tptp.aa_Code_integer_rat H X3)))) (= (tptp.groups6602215022474089585er_rat G T) (tptp.groups6602215022474089585er_rat H S))))))) (forall ((T tptp.set_bool) (S tptp.set_bool) (G tptp.fun_bool_nat) (H tptp.fun_bool_nat)) (=> (tptp.finite_finite_bool T) (=> (tptp.ord_less_eq_set_bool S T) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 (tptp.minus_minus_set_bool T S))) (= (tptp.aa_bool_nat G X3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 S)) (= (tptp.aa_bool_nat G X3) (tptp.aa_bool_nat H X3)))) (= (tptp.groups5768501273728744877ol_nat G T) (tptp.groups5768501273728744877ol_nat H S))))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G tptp.fun_Code_integer_nat) (H tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Code_integer_nat G X3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) S)) (= (tptp.aa_Code_integer_nat G X3) (tptp.aa_Code_integer_nat H X3)))) (= (tptp.groups7237345082560585321er_nat G T) (tptp.groups7237345082560585321er_nat H S))))))) (forall ((T tptp.set_bool) (S tptp.set_bool) (G tptp.fun_bool_int) (H tptp.fun_bool_int)) (=> (tptp.finite_finite_bool T) (=> (tptp.ord_less_eq_set_bool S T) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 (tptp.minus_minus_set_bool T S))) (= (tptp.aa_bool_int G X3) tptp.zero_zero_int))) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 S)) (= (tptp.aa_bool_int G X3) (tptp.aa_bool_int H X3)))) (= (tptp.groups5766010803219694601ol_int G T) (tptp.groups5766010803219694601ol_int H S))))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G tptp.fun_Code_integer_int) (H tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Code_integer_int G X3) tptp.zero_zero_int))) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) S)) (= (tptp.aa_Code_integer_int G X3) (tptp.aa_Code_integer_int H X3)))) (= (tptp.groups7234854612051535045er_int G T) (tptp.groups7234854612051535045er_int H S))))))) (forall ((T tptp.set_nat) (S tptp.set_nat) (G tptp.fun_nat_Code_integer) (H tptp.fun_nat_Code_integer)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat S) T)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat T) S))) (= (tptp.aa_nat_Code_integer G X3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) S)) (= (tptp.aa_nat_Code_integer G X3) (tptp.aa_nat_Code_integer H X3)))) (= (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger G) T) (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger H) S))))))) (forall ((T tptp.set_nat) (S tptp.set_nat) (G tptp.fun_nat_rat) (H tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat S) T)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat T) S))) (= (tptp.aa_nat_rat G X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) S)) (= (tptp.aa_nat_rat G X3) (tptp.aa_nat_rat H X3)))) (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat G) T) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat H) S))))))) (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (G tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups6602215022474089585er_rat G A3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups6602215022474089585er_rat G (tptp.minus_2355218937544613996nteger A3 B3))) (tptp.groups6602215022474089585er_rat G B3)))))) (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (G tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups7237345082560585321er_nat G A3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.groups7237345082560585321er_nat G (tptp.minus_2355218937544613996nteger A3 B3))) (tptp.groups7237345082560585321er_nat G B3)))))) (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (G tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups7234854612051535045er_int G A3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups7234854612051535045er_int G (tptp.minus_2355218937544613996nteger A3 B3))) (tptp.groups7234854612051535045er_int G B3)))))) (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups2906978787729119204at_rat G))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B3) A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.aa_set_nat_rat _let_1 A3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_set_nat_rat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3))) (tptp.aa_set_nat_rat _let_1 B3))))))) (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.groups3539618377306564664at_int G))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B3) A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.aa_set_nat_int _let_1 A3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_set_nat_int _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3))) (tptp.aa_set_nat_int _let_1 B3))))))) (forall ((B3 tptp.set_int) (A3 tptp.set_int) (G tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups3906332499630173760nt_rat G A3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups3906332499630173760nt_rat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3))) (tptp.groups3906332499630173760nt_rat G B3)))))) (forall ((B3 tptp.set_int) (A3 tptp.set_int) (G tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups4541462559716669496nt_nat G A3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.groups4541462559716669496nt_nat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3))) (tptp.groups4541462559716669496nt_nat G B3)))))) (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.groups3542108847815614940at_nat G))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B3) A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.aa_set_nat_nat _let_1 A3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_set_nat_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3))) (tptp.aa_set_nat_nat _let_1 B3))))))) (forall ((B3 tptp.set_int) (A3 tptp.set_int) (G tptp.fun_int_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups4538972089207619220nt_int G A3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups4538972089207619220nt_int G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3))) (tptp.groups4538972089207619220nt_int G B3)))))) (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (G tptp.fun_Pr8317260874932935276at_rat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat B3) A3)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat A3)) (= (tptp.groups342789780944988191at_rat G A3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups342789780944988191at_rat G (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat A3) B3))) (tptp.groups342789780944988191at_rat G B3)))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (F tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) A3)) (= (tptp.groups6602215022474089585er_rat F (tptp.minus_2355218937544613996nteger A3 B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.groups6602215022474089585er_rat F A3)) (tptp.groups6602215022474089585er_rat F B3)))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (F tptp.fun_Pr8317260874932935276at_rat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat A3)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat B3) A3)) (= (tptp.groups342789780944988191at_rat F (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat A3) B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.groups342789780944988191at_rat F A3)) (tptp.groups342789780944988191at_rat F B3)))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (F tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) A3)) (= (tptp.groups7234854612051535045er_int F (tptp.minus_2355218937544613996nteger A3 B3)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.groups7234854612051535045er_int F A3)) (tptp.groups7234854612051535045er_int F B3)))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (F tptp.fun_Pr7647638413817135296at_int)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat A3)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat B3) A3)) (= (tptp.groups975429370522433651at_int F (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat A3) B3)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.groups975429370522433651at_int F A3)) (tptp.groups975429370522433651at_int F B3)))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (F tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups2906978787729119204at_rat F))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B3) A3)) (= (tptp.aa_set_nat_rat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_set_nat_rat _let_1 A3)) (tptp.aa_set_nat_rat _let_1 B3))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (F tptp.fun_nat_int)) (let ((_let_1 (tptp.groups3539618377306564664at_int F))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B3) A3)) (= (tptp.aa_set_nat_int _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_set_nat_int _let_1 A3)) (tptp.aa_set_nat_int _let_1 B3))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (F tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) A3)) (= (tptp.groups3906332499630173760nt_rat F (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.groups3906332499630173760nt_rat F A3)) (tptp.groups3906332499630173760nt_rat F B3)))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (F tptp.fun_int_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) A3)) (= (tptp.groups4538972089207619220nt_int F (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.groups4538972089207619220nt_int F A3)) (tptp.groups4538972089207619220nt_int F B3)))))) (forall ((T tptp.set_bool) (S tptp.set_bool) (H tptp.fun_bo7282069421189217543nteger) (G tptp.fun_bo7282069421189217543nteger)) (=> (tptp.finite_finite_bool T) (=> (tptp.finite_finite_bool S) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 (tptp.minus_minus_set_bool T S))) (= (tptp.aa_bool_Code_integer H I3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 (tptp.minus_minus_set_bool S T))) (= (tptp.aa_bool_Code_integer G I3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 (tptp.inf_inf_set_bool S T))) (= (tptp.aa_bool_Code_integer G X3) (tptp.aa_bool_Code_integer H X3)))) (= (tptp.groups1682264926906508858nteger G S) (tptp.groups1682264926906508858nteger H T)))))))) (forall ((T tptp.set_int) (S tptp.set_int) (H tptp.fun_int_Code_integer) (G tptp.fun_int_Code_integer)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int T) S))) (= (tptp.aa_int_Code_integer H I3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int S) T))) (= (tptp.aa_int_Code_integer G I3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int S) T))) (= (tptp.aa_int_Code_integer G X3) (tptp.aa_int_Code_integer H X3)))) (= (tptp.groups7873554091576472773nteger G S) (tptp.groups7873554091576472773nteger H T)))))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (H tptp.fun_Co8499238673658658103nteger) (G tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S)) (=> (forall ((I3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Cod1783974652533396728nteger H I3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((I3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I3) (tptp.minus_2355218937544613996nteger S T))) (= (tptp.aa_Cod1783974652533396728nteger G I3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.inf_in1364745209274528805nteger S T))) (= (tptp.aa_Cod1783974652533396728nteger G X3) (tptp.aa_Cod1783974652533396728nteger H X3)))) (= (tptp.groups879477027807139574nteger G S) (tptp.groups879477027807139574nteger H T)))))))) (forall ((T tptp.set_bool) (S tptp.set_bool) (H tptp.fun_bool_rat) (G tptp.fun_bool_rat)) (=> (tptp.finite_finite_bool T) (=> (tptp.finite_finite_bool S) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 (tptp.minus_minus_set_bool T S))) (= (tptp.aa_bool_rat H I3) tptp.zero_zero_rat))) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 (tptp.minus_minus_set_bool S T))) (= (tptp.aa_bool_rat G I3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 (tptp.inf_inf_set_bool S T))) (= (tptp.aa_bool_rat G X3) (tptp.aa_bool_rat H X3)))) (= (tptp.groups5133371213642249141ol_rat G S) (tptp.groups5133371213642249141ol_rat H T)))))))) (forall ((T tptp.set_int) (S tptp.set_int) (H tptp.fun_int_rat) (G tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int T) S))) (= (tptp.aa_int_rat H I3) tptp.zero_zero_rat))) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int S) T))) (= (tptp.aa_int_rat G I3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int S) T))) (= (tptp.aa_int_rat G X3) (tptp.aa_int_rat H X3)))) (= (tptp.groups3906332499630173760nt_rat G S) (tptp.groups3906332499630173760nt_rat H T)))))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (H tptp.fun_Code_integer_rat) (G tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S)) (=> (forall ((I3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Code_integer_rat H I3) tptp.zero_zero_rat))) (=> (forall ((I3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I3) (tptp.minus_2355218937544613996nteger S T))) (= (tptp.aa_Code_integer_rat G I3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.inf_in1364745209274528805nteger S T))) (= (tptp.aa_Code_integer_rat G X3) (tptp.aa_Code_integer_rat H X3)))) (= (tptp.groups6602215022474089585er_rat G S) (tptp.groups6602215022474089585er_rat H T)))))))) (forall ((T tptp.set_bool) (S tptp.set_bool) (H tptp.fun_bool_nat) (G tptp.fun_bool_nat)) (=> (tptp.finite_finite_bool T) (=> (tptp.finite_finite_bool S) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 (tptp.minus_minus_set_bool T S))) (= (tptp.aa_bool_nat H I3) tptp.zero_zero_nat))) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 (tptp.minus_minus_set_bool S T))) (= (tptp.aa_bool_nat G I3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 (tptp.inf_inf_set_bool S T))) (= (tptp.aa_bool_nat G X3) (tptp.aa_bool_nat H X3)))) (= (tptp.groups5768501273728744877ol_nat G S) (tptp.groups5768501273728744877ol_nat H T)))))))) (forall ((T tptp.set_int) (S tptp.set_int) (H tptp.fun_int_nat) (G tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int T) S))) (= (tptp.aa_int_nat H I3) tptp.zero_zero_nat))) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int S) T))) (= (tptp.aa_int_nat G I3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int S) T))) (= (tptp.aa_int_nat G X3) (tptp.aa_int_nat H X3)))) (= (tptp.groups4541462559716669496nt_nat G S) (tptp.groups4541462559716669496nt_nat H T)))))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (H tptp.fun_Code_integer_nat) (G tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S)) (=> (forall ((I3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Code_integer_nat H I3) tptp.zero_zero_nat))) (=> (forall ((I3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I3) (tptp.minus_2355218937544613996nteger S T))) (= (tptp.aa_Code_integer_nat G I3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.inf_in1364745209274528805nteger S T))) (= (tptp.aa_Code_integer_nat G X3) (tptp.aa_Code_integer_nat H X3)))) (= (tptp.groups7237345082560585321er_nat G S) (tptp.groups7237345082560585321er_nat H T)))))))) (forall ((T tptp.set_bool) (S tptp.set_bool) (H tptp.fun_bool_int) (G tptp.fun_bool_int)) (=> (tptp.finite_finite_bool T) (=> (tptp.finite_finite_bool S) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 (tptp.minus_minus_set_bool T S))) (= (tptp.aa_bool_int H I3) tptp.zero_zero_int))) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 (tptp.minus_minus_set_bool S T))) (= (tptp.aa_bool_int G I3) tptp.zero_zero_int))) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 (tptp.inf_inf_set_bool S T))) (= (tptp.aa_bool_int G X3) (tptp.aa_bool_int H X3)))) (= (tptp.groups5766010803219694601ol_int G S) (tptp.groups5766010803219694601ol_int H T)))))))) (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (G tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups3674199335183972705nteger G A3) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.groups3674199335183972705nteger G (tptp.minus_2355218937544613996nteger A3 B3))) (tptp.groups3674199335183972705nteger G B3)))))) (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (G tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.groups3455450783089532116nteger G))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B3) A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.aa_set871585252387937313nteger _let_1 A3) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_set871585252387937313nteger _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3))) (tptp.aa_set871585252387937313nteger _let_1 B3))))))) (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (G tptp.fun_Co4490034186337852034r_assn)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups1304777262505850412r_assn G A3) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups1304777262505850412r_assn G (tptp.minus_2355218937544613996nteger A3 B3))) (tptp.groups1304777262505850412r_assn G B3)))))) (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (G tptp.fun_nat_assn)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B3) A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.groups6906906614972039071t_assn G A3) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups6906906614972039071t_assn G (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3))) (tptp.groups6906906614972039071t_assn G B3)))))) (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (G tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups2555765274223993564er_rat G A3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.groups2555765274223993564er_rat G (tptp.minus_2355218937544613996nteger A3 B3))) (tptp.groups2555765274223993564er_rat G B3)))))) (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups73079841787564623at_rat G))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B3) A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.aa_set_nat_rat _let_1 A3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_set_nat_rat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3))) (tptp.aa_set_nat_rat _let_1 B3))))))) (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (G tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups3190895334310489300er_nat G A3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.groups3190895334310489300er_nat G (tptp.minus_2355218937544613996nteger A3 B3))) (tptp.groups3190895334310489300er_nat G B3)))))) (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (G tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups3188404863801439024er_int G A3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.groups3188404863801439024er_int G (tptp.minus_2355218937544613996nteger A3 B3))) (tptp.groups3188404863801439024er_int G B3)))))) (forall ((B3 tptp.set_int) (A3 tptp.set_int) (G tptp.fun_int_Code_integer)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups3827104343326376752nteger G A3) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.groups3827104343326376752nteger G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3))) (tptp.groups3827104343326376752nteger G B3)))))) (forall ((B3 tptp.set_int) (A3 tptp.set_int) (G tptp.fun_int_assn)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups7882442080178216443t_assn G A3) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups7882442080178216443t_assn G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3))) (tptp.groups7882442080178216443t_assn G B3)))))) (forall ((C3 tptp.set_bool) (A3 tptp.set_bool) (B3 tptp.set_bool) (G tptp.fun_bo7282069421189217543nteger) (H tptp.fun_bo7282069421189217543nteger)) (=> (tptp.finite_finite_bool C3) (=> (tptp.ord_less_eq_set_bool A3 C3) (=> (tptp.ord_less_eq_set_bool B3 C3) (=> (forall ((A4 tptp.bool)) (=> (tptp.pp (tptp.member_bool A4 (tptp.minus_minus_set_bool C3 A3))) (= (tptp.aa_bool_Code_integer G A4) tptp.one_one_Code_integer))) (=> (forall ((B4 tptp.bool)) (=> (tptp.pp (tptp.member_bool B4 (tptp.minus_minus_set_bool C3 B3))) (= (tptp.aa_bool_Code_integer H B4) tptp.one_one_Code_integer))) (= (= (tptp.groups7272450149305381519nteger G A3) (tptp.groups7272450149305381519nteger H B3)) (= (tptp.groups7272450149305381519nteger G C3) (tptp.groups7272450149305381519nteger H C3))))))))) (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Co8499238673658658103nteger) (H tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) C3)) (=> (forall ((A4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A4) (tptp.minus_2355218937544613996nteger C3 A3))) (= (tptp.aa_Cod1783974652533396728nteger G A4) tptp.one_one_Code_integer))) (=> (forall ((B4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer B4) (tptp.minus_2355218937544613996nteger C3 B3))) (= (tptp.aa_Cod1783974652533396728nteger H B4) tptp.one_one_Code_integer))) (= (= (tptp.groups3674199335183972705nteger G A3) (tptp.groups3674199335183972705nteger H B3)) (= (tptp.groups3674199335183972705nteger G C3) (tptp.groups3674199335183972705nteger H C3))))))))) (forall ((C3 tptp.set_bool) (A3 tptp.set_bool) (B3 tptp.set_bool) (G tptp.fun_bool_assn) (H tptp.fun_bool_assn)) (=> (tptp.finite_finite_bool C3) (=> (tptp.ord_less_eq_set_bool A3 C3) (=> (tptp.ord_less_eq_set_bool B3 C3) (=> (forall ((A4 tptp.bool)) (=> (tptp.pp (tptp.member_bool A4 (tptp.minus_minus_set_bool C3 A3))) (= (tptp.aa_bool_assn G A4) tptp.one_one_assn))) (=> (forall ((B4 tptp.bool)) (=> (tptp.pp (tptp.member_bool B4 (tptp.minus_minus_set_bool C3 B3))) (= (tptp.aa_bool_assn H B4) tptp.one_one_assn))) (= (= (tptp.groups4835110720589548378l_assn G A3) (tptp.groups4835110720589548378l_assn H B3)) (= (tptp.groups4835110720589548378l_assn G C3) (tptp.groups4835110720589548378l_assn H C3))))))))) (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Co4490034186337852034r_assn) (H tptp.fun_Co4490034186337852034r_assn)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) C3)) (=> (forall ((A4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A4) (tptp.minus_2355218937544613996nteger C3 A3))) (= (tptp.aa_Code_integer_assn G A4) tptp.one_one_assn))) (=> (forall ((B4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer B4) (tptp.minus_2355218937544613996nteger C3 B3))) (= (tptp.aa_Code_integer_assn H B4) tptp.one_one_assn))) (= (= (tptp.groups1304777262505850412r_assn G A3) (tptp.groups1304777262505850412r_assn H B3)) (= (tptp.groups1304777262505850412r_assn G C3) (tptp.groups1304777262505850412r_assn H C3))))))))) (forall ((C3 tptp.set_bool) (A3 tptp.set_bool) (B3 tptp.set_bool) (G tptp.fun_bool_rat) (H tptp.fun_bool_rat)) (=> (tptp.finite_finite_bool C3) (=> (tptp.ord_less_eq_set_bool A3 C3) (=> (tptp.ord_less_eq_set_bool B3 C3) (=> (forall ((A4 tptp.bool)) (=> (tptp.pp (tptp.member_bool A4 (tptp.minus_minus_set_bool C3 A3))) (= (tptp.aa_bool_rat G A4) tptp.one_one_rat))) (=> (forall ((B4 tptp.bool)) (=> (tptp.pp (tptp.member_bool B4 (tptp.minus_minus_set_bool C3 B3))) (= (tptp.aa_bool_rat H B4) tptp.one_one_rat))) (= (= (tptp.groups1259819201609700362ol_rat G A3) (tptp.groups1259819201609700362ol_rat H B3)) (= (tptp.groups1259819201609700362ol_rat G C3) (tptp.groups1259819201609700362ol_rat H C3))))))))) (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Code_integer_rat) (H tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) C3)) (=> (forall ((A4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A4) (tptp.minus_2355218937544613996nteger C3 A3))) (= (tptp.aa_Code_integer_rat G A4) tptp.one_one_rat))) (=> (forall ((B4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer B4) (tptp.minus_2355218937544613996nteger C3 B3))) (= (tptp.aa_Code_integer_rat H B4) tptp.one_one_rat))) (= (= (tptp.groups2555765274223993564er_rat G A3) (tptp.groups2555765274223993564er_rat H B3)) (= (tptp.groups2555765274223993564er_rat G C3) (tptp.groups2555765274223993564er_rat H C3))))))))) (forall ((C3 tptp.set_bool) (A3 tptp.set_bool) (B3 tptp.set_bool) (G tptp.fun_bool_nat) (H tptp.fun_bool_nat)) (=> (tptp.finite_finite_bool C3) (=> (tptp.ord_less_eq_set_bool A3 C3) (=> (tptp.ord_less_eq_set_bool B3 C3) (=> (forall ((A4 tptp.bool)) (=> (tptp.pp (tptp.member_bool A4 (tptp.minus_minus_set_bool C3 A3))) (= (tptp.aa_bool_nat G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.bool)) (=> (tptp.pp (tptp.member_bool B4 (tptp.minus_minus_set_bool C3 B3))) (= (tptp.aa_bool_nat H B4) tptp.one_one_nat))) (= (= (tptp.groups1894949261696196098ol_nat G A3) (tptp.groups1894949261696196098ol_nat H B3)) (= (tptp.groups1894949261696196098ol_nat G C3) (tptp.groups1894949261696196098ol_nat H C3))))))))) (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Code_integer_nat) (H tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) C3)) (=> (forall ((A4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A4) (tptp.minus_2355218937544613996nteger C3 A3))) (= (tptp.aa_Code_integer_nat G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer B4) (tptp.minus_2355218937544613996nteger C3 B3))) (= (tptp.aa_Code_integer_nat H B4) tptp.one_one_nat))) (= (= (tptp.groups3190895334310489300er_nat G A3) (tptp.groups3190895334310489300er_nat H B3)) (= (tptp.groups3190895334310489300er_nat G C3) (tptp.groups3190895334310489300er_nat H C3))))))))) (forall ((C3 tptp.set_bool) (A3 tptp.set_bool) (B3 tptp.set_bool) (G tptp.fun_bool_int) (H tptp.fun_bool_int)) (=> (tptp.finite_finite_bool C3) (=> (tptp.ord_less_eq_set_bool A3 C3) (=> (tptp.ord_less_eq_set_bool B3 C3) (=> (forall ((A4 tptp.bool)) (=> (tptp.pp (tptp.member_bool A4 (tptp.minus_minus_set_bool C3 A3))) (= (tptp.aa_bool_int G A4) tptp.one_one_int))) (=> (forall ((B4 tptp.bool)) (=> (tptp.pp (tptp.member_bool B4 (tptp.minus_minus_set_bool C3 B3))) (= (tptp.aa_bool_int H B4) tptp.one_one_int))) (= (= (tptp.groups1892458791187145822ol_int G A3) (tptp.groups1892458791187145822ol_int H B3)) (= (tptp.groups1892458791187145822ol_int G C3) (tptp.groups1892458791187145822ol_int H C3))))))))) (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Code_integer_int) (H tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) C3)) (=> (forall ((A4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A4) (tptp.minus_2355218937544613996nteger C3 A3))) (= (tptp.aa_Code_integer_int G A4) tptp.one_one_int))) (=> (forall ((B4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer B4) (tptp.minus_2355218937544613996nteger C3 B3))) (= (tptp.aa_Code_integer_int H B4) tptp.one_one_int))) (= (= (tptp.groups3188404863801439024er_int G A3) (tptp.groups3188404863801439024er_int H B3)) (= (tptp.groups3188404863801439024er_int G C3) (tptp.groups3188404863801439024er_int H C3))))))))) (forall ((C3 tptp.set_bool) (A3 tptp.set_bool) (B3 tptp.set_bool) (G tptp.fun_bo7282069421189217543nteger) (H tptp.fun_bo7282069421189217543nteger)) (=> (tptp.finite_finite_bool C3) (=> (tptp.ord_less_eq_set_bool A3 C3) (=> (tptp.ord_less_eq_set_bool B3 C3) (=> (forall ((A4 tptp.bool)) (=> (tptp.pp (tptp.member_bool A4 (tptp.minus_minus_set_bool C3 A3))) (= (tptp.aa_bool_Code_integer G A4) tptp.one_one_Code_integer))) (=> (forall ((B4 tptp.bool)) (=> (tptp.pp (tptp.member_bool B4 (tptp.minus_minus_set_bool C3 B3))) (= (tptp.aa_bool_Code_integer H B4) tptp.one_one_Code_integer))) (=> (= (tptp.groups7272450149305381519nteger G C3) (tptp.groups7272450149305381519nteger H C3)) (= (tptp.groups7272450149305381519nteger G A3) (tptp.groups7272450149305381519nteger H B3))))))))) (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Co8499238673658658103nteger) (H tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) C3)) (=> (forall ((A4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A4) (tptp.minus_2355218937544613996nteger C3 A3))) (= (tptp.aa_Cod1783974652533396728nteger G A4) tptp.one_one_Code_integer))) (=> (forall ((B4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer B4) (tptp.minus_2355218937544613996nteger C3 B3))) (= (tptp.aa_Cod1783974652533396728nteger H B4) tptp.one_one_Code_integer))) (=> (= (tptp.groups3674199335183972705nteger G C3) (tptp.groups3674199335183972705nteger H C3)) (= (tptp.groups3674199335183972705nteger G A3) (tptp.groups3674199335183972705nteger H B3))))))))) (forall ((C3 tptp.set_bool) (A3 tptp.set_bool) (B3 tptp.set_bool) (G tptp.fun_bool_assn) (H tptp.fun_bool_assn)) (=> (tptp.finite_finite_bool C3) (=> (tptp.ord_less_eq_set_bool A3 C3) (=> (tptp.ord_less_eq_set_bool B3 C3) (=> (forall ((A4 tptp.bool)) (=> (tptp.pp (tptp.member_bool A4 (tptp.minus_minus_set_bool C3 A3))) (= (tptp.aa_bool_assn G A4) tptp.one_one_assn))) (=> (forall ((B4 tptp.bool)) (=> (tptp.pp (tptp.member_bool B4 (tptp.minus_minus_set_bool C3 B3))) (= (tptp.aa_bool_assn H B4) tptp.one_one_assn))) (=> (= (tptp.groups4835110720589548378l_assn G C3) (tptp.groups4835110720589548378l_assn H C3)) (= (tptp.groups4835110720589548378l_assn G A3) (tptp.groups4835110720589548378l_assn H B3))))))))) (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Co4490034186337852034r_assn) (H tptp.fun_Co4490034186337852034r_assn)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) C3)) (=> (forall ((A4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A4) (tptp.minus_2355218937544613996nteger C3 A3))) (= (tptp.aa_Code_integer_assn G A4) tptp.one_one_assn))) (=> (forall ((B4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer B4) (tptp.minus_2355218937544613996nteger C3 B3))) (= (tptp.aa_Code_integer_assn H B4) tptp.one_one_assn))) (=> (= (tptp.groups1304777262505850412r_assn G C3) (tptp.groups1304777262505850412r_assn H C3)) (= (tptp.groups1304777262505850412r_assn G A3) (tptp.groups1304777262505850412r_assn H B3))))))))) (forall ((C3 tptp.set_bool) (A3 tptp.set_bool) (B3 tptp.set_bool) (G tptp.fun_bool_rat) (H tptp.fun_bool_rat)) (=> (tptp.finite_finite_bool C3) (=> (tptp.ord_less_eq_set_bool A3 C3) (=> (tptp.ord_less_eq_set_bool B3 C3) (=> (forall ((A4 tptp.bool)) (=> (tptp.pp (tptp.member_bool A4 (tptp.minus_minus_set_bool C3 A3))) (= (tptp.aa_bool_rat G A4) tptp.one_one_rat))) (=> (forall ((B4 tptp.bool)) (=> (tptp.pp (tptp.member_bool B4 (tptp.minus_minus_set_bool C3 B3))) (= (tptp.aa_bool_rat H B4) tptp.one_one_rat))) (=> (= (tptp.groups1259819201609700362ol_rat G C3) (tptp.groups1259819201609700362ol_rat H C3)) (= (tptp.groups1259819201609700362ol_rat G A3) (tptp.groups1259819201609700362ol_rat H B3))))))))) (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Code_integer_rat) (H tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) C3)) (=> (forall ((A4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A4) (tptp.minus_2355218937544613996nteger C3 A3))) (= (tptp.aa_Code_integer_rat G A4) tptp.one_one_rat))) (=> (forall ((B4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer B4) (tptp.minus_2355218937544613996nteger C3 B3))) (= (tptp.aa_Code_integer_rat H B4) tptp.one_one_rat))) (=> (= (tptp.groups2555765274223993564er_rat G C3) (tptp.groups2555765274223993564er_rat H C3)) (= (tptp.groups2555765274223993564er_rat G A3) (tptp.groups2555765274223993564er_rat H B3))))))))) (forall ((C3 tptp.set_bool) (A3 tptp.set_bool) (B3 tptp.set_bool) (G tptp.fun_bool_nat) (H tptp.fun_bool_nat)) (=> (tptp.finite_finite_bool C3) (=> (tptp.ord_less_eq_set_bool A3 C3) (=> (tptp.ord_less_eq_set_bool B3 C3) (=> (forall ((A4 tptp.bool)) (=> (tptp.pp (tptp.member_bool A4 (tptp.minus_minus_set_bool C3 A3))) (= (tptp.aa_bool_nat G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.bool)) (=> (tptp.pp (tptp.member_bool B4 (tptp.minus_minus_set_bool C3 B3))) (= (tptp.aa_bool_nat H B4) tptp.one_one_nat))) (=> (= (tptp.groups1894949261696196098ol_nat G C3) (tptp.groups1894949261696196098ol_nat H C3)) (= (tptp.groups1894949261696196098ol_nat G A3) (tptp.groups1894949261696196098ol_nat H B3))))))))) (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Code_integer_nat) (H tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) C3)) (=> (forall ((A4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A4) (tptp.minus_2355218937544613996nteger C3 A3))) (= (tptp.aa_Code_integer_nat G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer B4) (tptp.minus_2355218937544613996nteger C3 B3))) (= (tptp.aa_Code_integer_nat H B4) tptp.one_one_nat))) (=> (= (tptp.groups3190895334310489300er_nat G C3) (tptp.groups3190895334310489300er_nat H C3)) (= (tptp.groups3190895334310489300er_nat G A3) (tptp.groups3190895334310489300er_nat H B3))))))))) (forall ((C3 tptp.set_bool) (A3 tptp.set_bool) (B3 tptp.set_bool) (G tptp.fun_bool_int) (H tptp.fun_bool_int)) (=> (tptp.finite_finite_bool C3) (=> (tptp.ord_less_eq_set_bool A3 C3) (=> (tptp.ord_less_eq_set_bool B3 C3) (=> (forall ((A4 tptp.bool)) (=> (tptp.pp (tptp.member_bool A4 (tptp.minus_minus_set_bool C3 A3))) (= (tptp.aa_bool_int G A4) tptp.one_one_int))) (=> (forall ((B4 tptp.bool)) (=> (tptp.pp (tptp.member_bool B4 (tptp.minus_minus_set_bool C3 B3))) (= (tptp.aa_bool_int H B4) tptp.one_one_int))) (=> (= (tptp.groups1892458791187145822ol_int G C3) (tptp.groups1892458791187145822ol_int H C3)) (= (tptp.groups1892458791187145822ol_int G A3) (tptp.groups1892458791187145822ol_int H B3))))))))) (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Code_integer_int) (H tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) C3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) C3)) (=> (forall ((A4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A4) (tptp.minus_2355218937544613996nteger C3 A3))) (= (tptp.aa_Code_integer_int G A4) tptp.one_one_int))) (=> (forall ((B4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer B4) (tptp.minus_2355218937544613996nteger C3 B3))) (= (tptp.aa_Code_integer_int H B4) tptp.one_one_int))) (=> (= (tptp.groups3188404863801439024er_int G C3) (tptp.groups3188404863801439024er_int H C3)) (= (tptp.groups3188404863801439024er_int G A3) (tptp.groups3188404863801439024er_int H B3))))))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Cod1783974652533396728nteger G X3) tptp.one_one_Code_integer))) (= (tptp.groups3674199335183972705nteger G S) (tptp.groups3674199335183972705nteger G T)))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G tptp.fun_Co4490034186337852034r_assn)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Code_integer_assn G X3) tptp.one_one_assn))) (= (tptp.groups1304777262505850412r_assn G S) (tptp.groups1304777262505850412r_assn G T)))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Code_integer_rat G X3) tptp.one_one_rat))) (= (tptp.groups2555765274223993564er_rat G S) (tptp.groups2555765274223993564er_rat G T)))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Code_integer_nat G X3) tptp.one_one_nat))) (= (tptp.groups3190895334310489300er_nat G S) (tptp.groups3190895334310489300er_nat G T)))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Code_integer_int G X3) tptp.one_one_int))) (= (tptp.groups3188404863801439024er_int G S) (tptp.groups3188404863801439024er_int G T)))))) (forall ((T tptp.set_nat) (S tptp.set_nat) (G tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.groups3455450783089532116nteger G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat S) T)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat T) S))) (= (tptp.aa_nat_Code_integer G X3) tptp.one_one_Code_integer))) (= (tptp.aa_set871585252387937313nteger _let_1 S) (tptp.aa_set871585252387937313nteger _let_1 T))))))) (forall ((T tptp.set_nat) (S tptp.set_nat) (G tptp.fun_nat_assn)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat S) T)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat T) S))) (= (tptp.aa_nat_assn G X3) tptp.one_one_assn))) (= (tptp.groups6906906614972039071t_assn G S) (tptp.groups6906906614972039071t_assn G T)))))) (forall ((T tptp.set_nat) (S tptp.set_nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups73079841787564623at_rat G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat S) T)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat T) S))) (= (tptp.aa_nat_rat G X3) tptp.one_one_rat))) (= (tptp.aa_set_nat_rat _let_1 S) (tptp.aa_set_nat_rat _let_1 T))))))) (forall ((T tptp.set_int) (S tptp.set_int) (G tptp.fun_int_Code_integer)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int S) T)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int T) S))) (= (tptp.aa_int_Code_integer G X3) tptp.one_one_Code_integer))) (= (tptp.groups3827104343326376752nteger G S) (tptp.groups3827104343326376752nteger G T)))))) (forall ((T tptp.set_int) (S tptp.set_int) (G tptp.fun_int_assn)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int S) T)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int T) S))) (= (tptp.aa_int_assn G X3) tptp.one_one_assn))) (= (tptp.groups7882442080178216443t_assn G S) (tptp.groups7882442080178216443t_assn G T)))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Cod1783974652533396728nteger G X3) tptp.one_one_Code_integer))) (= (tptp.groups3674199335183972705nteger G T) (tptp.groups3674199335183972705nteger G S)))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G tptp.fun_Co4490034186337852034r_assn)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Code_integer_assn G X3) tptp.one_one_assn))) (= (tptp.groups1304777262505850412r_assn G T) (tptp.groups1304777262505850412r_assn G S)))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Code_integer_rat G X3) tptp.one_one_rat))) (= (tptp.groups2555765274223993564er_rat G T) (tptp.groups2555765274223993564er_rat G S)))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Code_integer_nat G X3) tptp.one_one_nat))) (= (tptp.groups3190895334310489300er_nat G T) (tptp.groups3190895334310489300er_nat G S)))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Code_integer_int G X3) tptp.one_one_int))) (= (tptp.groups3188404863801439024er_int G T) (tptp.groups3188404863801439024er_int G S)))))) (forall ((T tptp.set_nat) (S tptp.set_nat) (G tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.groups3455450783089532116nteger G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat S) T)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat T) S))) (= (tptp.aa_nat_Code_integer G X3) tptp.one_one_Code_integer))) (= (tptp.aa_set871585252387937313nteger _let_1 T) (tptp.aa_set871585252387937313nteger _let_1 S))))))) (forall ((T tptp.set_nat) (S tptp.set_nat) (G tptp.fun_nat_assn)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat S) T)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat T) S))) (= (tptp.aa_nat_assn G X3) tptp.one_one_assn))) (= (tptp.groups6906906614972039071t_assn G T) (tptp.groups6906906614972039071t_assn G S)))))) (forall ((T tptp.set_nat) (S tptp.set_nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups73079841787564623at_rat G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat S) T)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat T) S))) (= (tptp.aa_nat_rat G X3) tptp.one_one_rat))) (= (tptp.aa_set_nat_rat _let_1 T) (tptp.aa_set_nat_rat _let_1 S))))))) (forall ((T tptp.set_int) (S tptp.set_int) (G tptp.fun_int_Code_integer)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int S) T)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int T) S))) (= (tptp.aa_int_Code_integer G X3) tptp.one_one_Code_integer))) (= (tptp.groups3827104343326376752nteger G T) (tptp.groups3827104343326376752nteger G S)))))) (forall ((T tptp.set_int) (S tptp.set_int) (G tptp.fun_int_assn)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int S) T)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int T) S))) (= (tptp.aa_int_assn G X3) tptp.one_one_assn))) (= (tptp.groups7882442080178216443t_assn G T) (tptp.groups7882442080178216443t_assn G S)))))) (forall ((T tptp.set_bool) (S tptp.set_bool) (H tptp.fun_bo7282069421189217543nteger) (G tptp.fun_bo7282069421189217543nteger)) (=> (tptp.finite_finite_bool T) (=> (tptp.ord_less_eq_set_bool S T) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 (tptp.minus_minus_set_bool T S))) (= (tptp.aa_bool_Code_integer H X3) tptp.one_one_Code_integer))) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 S)) (= (tptp.aa_bool_Code_integer G X3) (tptp.aa_bool_Code_integer H X3)))) (= (tptp.groups7272450149305381519nteger G S) (tptp.groups7272450149305381519nteger H T))))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (H tptp.fun_Co8499238673658658103nteger) (G tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Cod1783974652533396728nteger H X3) tptp.one_one_Code_integer))) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) S)) (= (tptp.aa_Cod1783974652533396728nteger G X3) (tptp.aa_Cod1783974652533396728nteger H X3)))) (= (tptp.groups3674199335183972705nteger G S) (tptp.groups3674199335183972705nteger H T))))))) (forall ((T tptp.set_bool) (S tptp.set_bool) (H tptp.fun_bool_assn) (G tptp.fun_bool_assn)) (=> (tptp.finite_finite_bool T) (=> (tptp.ord_less_eq_set_bool S T) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 (tptp.minus_minus_set_bool T S))) (= (tptp.aa_bool_assn H X3) tptp.one_one_assn))) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 S)) (= (tptp.aa_bool_assn G X3) (tptp.aa_bool_assn H X3)))) (= (tptp.groups4835110720589548378l_assn G S) (tptp.groups4835110720589548378l_assn H T))))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (H tptp.fun_Co4490034186337852034r_assn) (G tptp.fun_Co4490034186337852034r_assn)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Code_integer_assn H X3) tptp.one_one_assn))) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) S)) (= (tptp.aa_Code_integer_assn G X3) (tptp.aa_Code_integer_assn H X3)))) (= (tptp.groups1304777262505850412r_assn G S) (tptp.groups1304777262505850412r_assn H T))))))) (forall ((T tptp.set_bool) (S tptp.set_bool) (H tptp.fun_bool_rat) (G tptp.fun_bool_rat)) (=> (tptp.finite_finite_bool T) (=> (tptp.ord_less_eq_set_bool S T) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 (tptp.minus_minus_set_bool T S))) (= (tptp.aa_bool_rat H X3) tptp.one_one_rat))) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 S)) (= (tptp.aa_bool_rat G X3) (tptp.aa_bool_rat H X3)))) (= (tptp.groups1259819201609700362ol_rat G S) (tptp.groups1259819201609700362ol_rat H T))))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (H tptp.fun_Code_integer_rat) (G tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Code_integer_rat H X3) tptp.one_one_rat))) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) S)) (= (tptp.aa_Code_integer_rat G X3) (tptp.aa_Code_integer_rat H X3)))) (= (tptp.groups2555765274223993564er_rat G S) (tptp.groups2555765274223993564er_rat H T))))))) (forall ((T tptp.set_bool) (S tptp.set_bool) (H tptp.fun_bool_nat) (G tptp.fun_bool_nat)) (=> (tptp.finite_finite_bool T) (=> (tptp.ord_less_eq_set_bool S T) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 (tptp.minus_minus_set_bool T S))) (= (tptp.aa_bool_nat H X3) tptp.one_one_nat))) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 S)) (= (tptp.aa_bool_nat G X3) (tptp.aa_bool_nat H X3)))) (= (tptp.groups1894949261696196098ol_nat G S) (tptp.groups1894949261696196098ol_nat H T))))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (H tptp.fun_Code_integer_nat) (G tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Code_integer_nat H X3) tptp.one_one_nat))) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) S)) (= (tptp.aa_Code_integer_nat G X3) (tptp.aa_Code_integer_nat H X3)))) (= (tptp.groups3190895334310489300er_nat G S) (tptp.groups3190895334310489300er_nat H T))))))) (forall ((T tptp.set_bool) (S tptp.set_bool) (H tptp.fun_bool_int) (G tptp.fun_bool_int)) (=> (tptp.finite_finite_bool T) (=> (tptp.ord_less_eq_set_bool S T) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 (tptp.minus_minus_set_bool T S))) (= (tptp.aa_bool_int H X3) tptp.one_one_int))) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 S)) (= (tptp.aa_bool_int G X3) (tptp.aa_bool_int H X3)))) (= (tptp.groups1892458791187145822ol_int G S) (tptp.groups1892458791187145822ol_int H T))))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (H tptp.fun_Code_integer_int) (G tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Code_integer_int H X3) tptp.one_one_int))) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) S)) (= (tptp.aa_Code_integer_int G X3) (tptp.aa_Code_integer_int H X3)))) (= (tptp.groups3188404863801439024er_int G S) (tptp.groups3188404863801439024er_int H T))))))) (forall ((T tptp.set_bool) (S tptp.set_bool) (G tptp.fun_bo7282069421189217543nteger) (H tptp.fun_bo7282069421189217543nteger)) (=> (tptp.finite_finite_bool T) (=> (tptp.ord_less_eq_set_bool S T) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 (tptp.minus_minus_set_bool T S))) (= (tptp.aa_bool_Code_integer G X3) tptp.one_one_Code_integer))) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 S)) (= (tptp.aa_bool_Code_integer G X3) (tptp.aa_bool_Code_integer H X3)))) (= (tptp.groups7272450149305381519nteger G T) (tptp.groups7272450149305381519nteger H S))))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G tptp.fun_Co8499238673658658103nteger) (H tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Cod1783974652533396728nteger G X3) tptp.one_one_Code_integer))) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) S)) (= (tptp.aa_Cod1783974652533396728nteger G X3) (tptp.aa_Cod1783974652533396728nteger H X3)))) (= (tptp.groups3674199335183972705nteger G T) (tptp.groups3674199335183972705nteger H S))))))) (forall ((T tptp.set_bool) (S tptp.set_bool) (G tptp.fun_bool_assn) (H tptp.fun_bool_assn)) (=> (tptp.finite_finite_bool T) (=> (tptp.ord_less_eq_set_bool S T) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 (tptp.minus_minus_set_bool T S))) (= (tptp.aa_bool_assn G X3) tptp.one_one_assn))) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 S)) (= (tptp.aa_bool_assn G X3) (tptp.aa_bool_assn H X3)))) (= (tptp.groups4835110720589548378l_assn G T) (tptp.groups4835110720589548378l_assn H S))))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G tptp.fun_Co4490034186337852034r_assn) (H tptp.fun_Co4490034186337852034r_assn)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Code_integer_assn G X3) tptp.one_one_assn))) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) S)) (= (tptp.aa_Code_integer_assn G X3) (tptp.aa_Code_integer_assn H X3)))) (= (tptp.groups1304777262505850412r_assn G T) (tptp.groups1304777262505850412r_assn H S))))))) (forall ((T tptp.set_bool) (S tptp.set_bool) (G tptp.fun_bool_rat) (H tptp.fun_bool_rat)) (=> (tptp.finite_finite_bool T) (=> (tptp.ord_less_eq_set_bool S T) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 (tptp.minus_minus_set_bool T S))) (= (tptp.aa_bool_rat G X3) tptp.one_one_rat))) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 S)) (= (tptp.aa_bool_rat G X3) (tptp.aa_bool_rat H X3)))) (= (tptp.groups1259819201609700362ol_rat G T) (tptp.groups1259819201609700362ol_rat H S))))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G tptp.fun_Code_integer_rat) (H tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Code_integer_rat G X3) tptp.one_one_rat))) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) S)) (= (tptp.aa_Code_integer_rat G X3) (tptp.aa_Code_integer_rat H X3)))) (= (tptp.groups2555765274223993564er_rat G T) (tptp.groups2555765274223993564er_rat H S))))))) (forall ((T tptp.set_bool) (S tptp.set_bool) (G tptp.fun_bool_nat) (H tptp.fun_bool_nat)) (=> (tptp.finite_finite_bool T) (=> (tptp.ord_less_eq_set_bool S T) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 (tptp.minus_minus_set_bool T S))) (= (tptp.aa_bool_nat G X3) tptp.one_one_nat))) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 S)) (= (tptp.aa_bool_nat G X3) (tptp.aa_bool_nat H X3)))) (= (tptp.groups1894949261696196098ol_nat G T) (tptp.groups1894949261696196098ol_nat H S))))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G tptp.fun_Code_integer_nat) (H tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Code_integer_nat G X3) tptp.one_one_nat))) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) S)) (= (tptp.aa_Code_integer_nat G X3) (tptp.aa_Code_integer_nat H X3)))) (= (tptp.groups3190895334310489300er_nat G T) (tptp.groups3190895334310489300er_nat H S))))))) (forall ((T tptp.set_bool) (S tptp.set_bool) (G tptp.fun_bool_int) (H tptp.fun_bool_int)) (=> (tptp.finite_finite_bool T) (=> (tptp.ord_less_eq_set_bool S T) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 (tptp.minus_minus_set_bool T S))) (= (tptp.aa_bool_int G X3) tptp.one_one_int))) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 S)) (= (tptp.aa_bool_int G X3) (tptp.aa_bool_int H X3)))) (= (tptp.groups1892458791187145822ol_int G T) (tptp.groups1892458791187145822ol_int H S))))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G tptp.fun_Code_integer_int) (H tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Code_integer_int G X3) tptp.one_one_int))) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) S)) (= (tptp.aa_Code_integer_int G X3) (tptp.aa_Code_integer_int H X3)))) (= (tptp.groups3188404863801439024er_int G T) (tptp.groups3188404863801439024er_int H S))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups3906332499630173760nt_rat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3))) (tptp.groups3906332499630173760nt_rat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups3906332499630173760nt_rat G A3)) (tptp.groups3906332499630173760nt_rat G B3)))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups6602215022474089585er_rat G (tptp.sup_su848401254843788991nteger A3 B3))) (tptp.groups6602215022474089585er_rat G (tptp.inf_in1364745209274528805nteger A3 B3))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups6602215022474089585er_rat G A3)) (tptp.groups6602215022474089585er_rat G B3)))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.groups4541462559716669496nt_nat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3))) (tptp.groups4541462559716669496nt_nat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.groups4541462559716669496nt_nat G A3)) (tptp.groups4541462559716669496nt_nat G B3)))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.groups7237345082560585321er_nat G (tptp.sup_su848401254843788991nteger A3 B3))) (tptp.groups7237345082560585321er_nat G (tptp.inf_in1364745209274528805nteger A3 B3))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.groups7237345082560585321er_nat G A3)) (tptp.groups7237345082560585321er_nat G B3)))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups7234854612051535045er_int G (tptp.sup_su848401254843788991nteger A3 B3))) (tptp.groups7234854612051535045er_int G (tptp.inf_in1364745209274528805nteger A3 B3))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups7234854612051535045er_int G A3)) (tptp.groups7234854612051535045er_int G B3)))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups2906978787729119204at_rat G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_set_nat_rat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3))) (tptp.aa_set_nat_rat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_set_nat_rat _let_1 A3)) (tptp.aa_set_nat_rat _let_1 B3))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.groups3539618377306564664at_int G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_set_nat_int _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3))) (tptp.aa_set_nat_int _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_set_nat_int _let_1 A3)) (tptp.aa_set_nat_int _let_1 B3))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.groups3542108847815614940at_nat G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_set_nat_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3))) (tptp.aa_set_nat_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_set_nat_nat _let_1 A3)) (tptp.aa_set_nat_nat _let_1 B3))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G tptp.fun_int_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups4538972089207619220nt_int G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3))) (tptp.groups4538972089207619220nt_int G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups4538972089207619220nt_int G A3)) (tptp.groups4538972089207619220nt_int G B3)))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (G tptp.fun_Pr8317260874932935276at_rat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat A3)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat B3)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups342789780944988191at_rat G (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat A3) B3))) (tptp.groups342789780944988191at_rat G (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups342789780944988191at_rat G A3)) (tptp.groups342789780944988191at_rat G B3)))))) (forall ((A3 tptp.set_int) (G tptp.fun_int_rat) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups3906332499630173760nt_rat G A3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups3906332499630173760nt_rat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))) (tptp.groups3906332499630173760nt_rat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3)))))) (forall ((A3 tptp.set_Code_integer) (G tptp.fun_Code_integer_rat) (B3 tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups6602215022474089585er_rat G A3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups6602215022474089585er_rat G (tptp.inf_in1364745209274528805nteger A3 B3))) (tptp.groups6602215022474089585er_rat G (tptp.minus_2355218937544613996nteger A3 B3)))))) (forall ((A3 tptp.set_int) (G tptp.fun_int_nat) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups4541462559716669496nt_nat G A3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.groups4541462559716669496nt_nat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))) (tptp.groups4541462559716669496nt_nat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3)))))) (forall ((A3 tptp.set_Code_integer) (G tptp.fun_Code_integer_nat) (B3 tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups7237345082560585321er_nat G A3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.groups7237345082560585321er_nat G (tptp.inf_in1364745209274528805nteger A3 B3))) (tptp.groups7237345082560585321er_nat G (tptp.minus_2355218937544613996nteger A3 B3)))))) (forall ((A3 tptp.set_Code_integer) (G tptp.fun_Code_integer_int) (B3 tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups7234854612051535045er_int G A3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups7234854612051535045er_int G (tptp.inf_in1364745209274528805nteger A3 B3))) (tptp.groups7234854612051535045er_int G (tptp.minus_2355218937544613996nteger A3 B3)))))) (forall ((A3 tptp.set_nat) (G tptp.fun_nat_rat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.groups2906978787729119204at_rat G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.aa_set_nat_rat _let_1 A3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_set_nat_rat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3))) (tptp.aa_set_nat_rat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3))))))) (forall ((A3 tptp.set_nat) (G tptp.fun_nat_int) (B3 tptp.set_nat)) (let ((_let_1 (tptp.groups3539618377306564664at_int G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.aa_set_nat_int _let_1 A3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_set_nat_int _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3))) (tptp.aa_set_nat_int _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3))))))) (forall ((A3 tptp.set_nat) (G tptp.fun_nat_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.groups3542108847815614940at_nat G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.aa_set_nat_nat _let_1 A3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_set_nat_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3))) (tptp.aa_set_nat_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3))))))) (forall ((A3 tptp.set_int) (G tptp.fun_int_int) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups4538972089207619220nt_int G A3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups4538972089207619220nt_int G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))) (tptp.groups4538972089207619220nt_int G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3)))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (G tptp.fun_Pr8317260874932935276at_rat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat A3)) (= (tptp.groups342789780944988191at_rat G A3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups342789780944988191at_rat G (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3))) (tptp.groups342789780944988191at_rat G (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat A3) B3)))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G tptp.fun_int_Code_integer)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.groups3827104343326376752nteger G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3))) (tptp.groups3827104343326376752nteger G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.groups3827104343326376752nteger G A3)) (tptp.groups3827104343326376752nteger G B3)))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.groups3674199335183972705nteger G (tptp.sup_su848401254843788991nteger A3 B3))) (tptp.groups3674199335183972705nteger G (tptp.inf_in1364745209274528805nteger A3 B3))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.groups3674199335183972705nteger G A3)) (tptp.groups3674199335183972705nteger G B3)))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.groups3455450783089532116nteger G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_set871585252387937313nteger _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3))) (tptp.aa_set871585252387937313nteger _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_set871585252387937313nteger _let_1 A3)) (tptp.aa_set871585252387937313nteger _let_1 B3))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G tptp.fun_int_assn)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups7882442080178216443t_assn G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3))) (tptp.groups7882442080178216443t_assn G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups7882442080178216443t_assn G A3)) (tptp.groups7882442080178216443t_assn G B3)))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Co4490034186337852034r_assn)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups1304777262505850412r_assn G (tptp.sup_su848401254843788991nteger A3 B3))) (tptp.groups1304777262505850412r_assn G (tptp.inf_in1364745209274528805nteger A3 B3))) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups1304777262505850412r_assn G A3)) (tptp.groups1304777262505850412r_assn G B3)))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G tptp.fun_nat_assn)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups6906906614972039071t_assn G (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3))) (tptp.groups6906906614972039071t_assn G (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3))) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups6906906614972039071t_assn G A3)) (tptp.groups6906906614972039071t_assn G B3)))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.groups1072433553688619179nt_rat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3))) (tptp.groups1072433553688619179nt_rat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.groups1072433553688619179nt_rat G A3)) (tptp.groups1072433553688619179nt_rat G B3)))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.groups2555765274223993564er_rat G (tptp.sup_su848401254843788991nteger A3 B3))) (tptp.groups2555765274223993564er_rat G (tptp.inf_in1364745209274528805nteger A3 B3))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.groups2555765274223993564er_rat G A3)) (tptp.groups2555765274223993564er_rat G B3)))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups73079841787564623at_rat G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_set_nat_rat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3))) (tptp.aa_set_nat_rat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_set_nat_rat _let_1 A3)) (tptp.aa_set_nat_rat _let_1 B3))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.groups1707563613775114915nt_nat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3))) (tptp.groups1707563613775114915nt_nat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.groups1707563613775114915nt_nat G A3)) (tptp.groups1707563613775114915nt_nat G B3)))))) (forall ((A3 tptp.set_int) (G tptp.fun_int_Code_integer) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups3827104343326376752nteger G A3) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.groups3827104343326376752nteger G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))) (tptp.groups3827104343326376752nteger G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3)))))) (forall ((A3 tptp.set_Code_integer) (G tptp.fun_Co8499238673658658103nteger) (B3 tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups3674199335183972705nteger G A3) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.groups3674199335183972705nteger G (tptp.inf_in1364745209274528805nteger A3 B3))) (tptp.groups3674199335183972705nteger G (tptp.minus_2355218937544613996nteger A3 B3)))))) (forall ((A3 tptp.set_nat) (G tptp.fun_nat_Code_integer) (B3 tptp.set_nat)) (let ((_let_1 (tptp.groups3455450783089532116nteger G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.aa_set871585252387937313nteger _let_1 A3) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_set871585252387937313nteger _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3))) (tptp.aa_set871585252387937313nteger _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3))))))) (forall ((A3 tptp.set_int) (G tptp.fun_int_assn) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups7882442080178216443t_assn G A3) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups7882442080178216443t_assn G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))) (tptp.groups7882442080178216443t_assn G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3)))))) (forall ((A3 tptp.set_Code_integer) (G tptp.fun_Co4490034186337852034r_assn) (B3 tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups1304777262505850412r_assn G A3) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups1304777262505850412r_assn G (tptp.inf_in1364745209274528805nteger A3 B3))) (tptp.groups1304777262505850412r_assn G (tptp.minus_2355218937544613996nteger A3 B3)))))) (forall ((A3 tptp.set_nat) (G tptp.fun_nat_assn) (B3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.groups6906906614972039071t_assn G A3) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups6906906614972039071t_assn G (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3))) (tptp.groups6906906614972039071t_assn G (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3)))))) (forall ((A3 tptp.set_int) (G tptp.fun_int_rat) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups1072433553688619179nt_rat G A3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.groups1072433553688619179nt_rat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))) (tptp.groups1072433553688619179nt_rat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3)))))) (forall ((A3 tptp.set_Code_integer) (G tptp.fun_Code_integer_rat) (B3 tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups2555765274223993564er_rat G A3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.groups2555765274223993564er_rat G (tptp.inf_in1364745209274528805nteger A3 B3))) (tptp.groups2555765274223993564er_rat G (tptp.minus_2355218937544613996nteger A3 B3)))))) (forall ((A3 tptp.set_nat) (G tptp.fun_nat_rat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.groups73079841787564623at_rat G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.aa_set_nat_rat _let_1 A3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_set_nat_rat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3))) (tptp.aa_set_nat_rat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3))))))) (forall ((A3 tptp.set_int) (G tptp.fun_int_nat) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups1707563613775114915nt_nat G A3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.groups1707563613775114915nt_nat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))) (tptp.groups1707563613775114915nt_nat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3)))))) (forall ((T tptp.set_bool) (S tptp.set_bool) (H tptp.fun_bo7282069421189217543nteger) (G tptp.fun_bo7282069421189217543nteger)) (=> (tptp.finite_finite_bool T) (=> (tptp.finite_finite_bool S) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 (tptp.minus_minus_set_bool T S))) (= (tptp.aa_bool_Code_integer H I3) tptp.one_one_Code_integer))) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 (tptp.minus_minus_set_bool S T))) (= (tptp.aa_bool_Code_integer G I3) tptp.one_one_Code_integer))) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 (tptp.inf_inf_set_bool S T))) (= (tptp.aa_bool_Code_integer G X3) (tptp.aa_bool_Code_integer H X3)))) (= (tptp.groups7272450149305381519nteger G S) (tptp.groups7272450149305381519nteger H T)))))))) (forall ((T tptp.set_int) (S tptp.set_int) (H tptp.fun_int_Code_integer) (G tptp.fun_int_Code_integer)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int T) S))) (= (tptp.aa_int_Code_integer H I3) tptp.one_one_Code_integer))) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int S) T))) (= (tptp.aa_int_Code_integer G I3) tptp.one_one_Code_integer))) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int S) T))) (= (tptp.aa_int_Code_integer G X3) (tptp.aa_int_Code_integer H X3)))) (= (tptp.groups3827104343326376752nteger G S) (tptp.groups3827104343326376752nteger H T)))))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (H tptp.fun_Co8499238673658658103nteger) (G tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S)) (=> (forall ((I3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Cod1783974652533396728nteger H I3) tptp.one_one_Code_integer))) (=> (forall ((I3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I3) (tptp.minus_2355218937544613996nteger S T))) (= (tptp.aa_Cod1783974652533396728nteger G I3) tptp.one_one_Code_integer))) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.inf_in1364745209274528805nteger S T))) (= (tptp.aa_Cod1783974652533396728nteger G X3) (tptp.aa_Cod1783974652533396728nteger H X3)))) (= (tptp.groups3674199335183972705nteger G S) (tptp.groups3674199335183972705nteger H T)))))))) (forall ((T tptp.set_bool) (S tptp.set_bool) (H tptp.fun_bool_assn) (G tptp.fun_bool_assn)) (=> (tptp.finite_finite_bool T) (=> (tptp.finite_finite_bool S) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 (tptp.minus_minus_set_bool T S))) (= (tptp.aa_bool_assn H I3) tptp.one_one_assn))) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 (tptp.minus_minus_set_bool S T))) (= (tptp.aa_bool_assn G I3) tptp.one_one_assn))) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 (tptp.inf_inf_set_bool S T))) (= (tptp.aa_bool_assn G X3) (tptp.aa_bool_assn H X3)))) (= (tptp.groups4835110720589548378l_assn G S) (tptp.groups4835110720589548378l_assn H T)))))))) (forall ((T tptp.set_int) (S tptp.set_int) (H tptp.fun_int_assn) (G tptp.fun_int_assn)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int T) S))) (= (tptp.aa_int_assn H I3) tptp.one_one_assn))) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int S) T))) (= (tptp.aa_int_assn G I3) tptp.one_one_assn))) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int S) T))) (= (tptp.aa_int_assn G X3) (tptp.aa_int_assn H X3)))) (= (tptp.groups7882442080178216443t_assn G S) (tptp.groups7882442080178216443t_assn H T)))))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (H tptp.fun_Co4490034186337852034r_assn) (G tptp.fun_Co4490034186337852034r_assn)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S)) (=> (forall ((I3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Code_integer_assn H I3) tptp.one_one_assn))) (=> (forall ((I3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I3) (tptp.minus_2355218937544613996nteger S T))) (= (tptp.aa_Code_integer_assn G I3) tptp.one_one_assn))) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.inf_in1364745209274528805nteger S T))) (= (tptp.aa_Code_integer_assn G X3) (tptp.aa_Code_integer_assn H X3)))) (= (tptp.groups1304777262505850412r_assn G S) (tptp.groups1304777262505850412r_assn H T)))))))) (forall ((T tptp.set_bool) (S tptp.set_bool) (H tptp.fun_bool_rat) (G tptp.fun_bool_rat)) (=> (tptp.finite_finite_bool T) (=> (tptp.finite_finite_bool S) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 (tptp.minus_minus_set_bool T S))) (= (tptp.aa_bool_rat H I3) tptp.one_one_rat))) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 (tptp.minus_minus_set_bool S T))) (= (tptp.aa_bool_rat G I3) tptp.one_one_rat))) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 (tptp.inf_inf_set_bool S T))) (= (tptp.aa_bool_rat G X3) (tptp.aa_bool_rat H X3)))) (= (tptp.groups1259819201609700362ol_rat G S) (tptp.groups1259819201609700362ol_rat H T)))))))) (forall ((T tptp.set_int) (S tptp.set_int) (H tptp.fun_int_rat) (G tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int T) S))) (= (tptp.aa_int_rat H I3) tptp.one_one_rat))) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int S) T))) (= (tptp.aa_int_rat G I3) tptp.one_one_rat))) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int S) T))) (= (tptp.aa_int_rat G X3) (tptp.aa_int_rat H X3)))) (= (tptp.groups1072433553688619179nt_rat G S) (tptp.groups1072433553688619179nt_rat H T)))))))) (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (H tptp.fun_Code_integer_rat) (G tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S)) (=> (forall ((I3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I3) (tptp.minus_2355218937544613996nteger T S))) (= (tptp.aa_Code_integer_rat H I3) tptp.one_one_rat))) (=> (forall ((I3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I3) (tptp.minus_2355218937544613996nteger S T))) (= (tptp.aa_Code_integer_rat G I3) tptp.one_one_rat))) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.inf_in1364745209274528805nteger S T))) (= (tptp.aa_Code_integer_rat G X3) (tptp.aa_Code_integer_rat H X3)))) (= (tptp.groups2555765274223993564er_rat G S) (tptp.groups2555765274223993564er_rat H T)))))))) (forall ((T tptp.set_bool) (S tptp.set_bool) (H tptp.fun_bool_nat) (G tptp.fun_bool_nat)) (=> (tptp.finite_finite_bool T) (=> (tptp.finite_finite_bool S) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 (tptp.minus_minus_set_bool T S))) (= (tptp.aa_bool_nat H I3) tptp.one_one_nat))) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 (tptp.minus_minus_set_bool S T))) (= (tptp.aa_bool_nat G I3) tptp.one_one_nat))) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 (tptp.inf_inf_set_bool S T))) (= (tptp.aa_bool_nat G X3) (tptp.aa_bool_nat H X3)))) (= (tptp.groups1894949261696196098ol_nat G S) (tptp.groups1894949261696196098ol_nat H T)))))))) (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) J))) (= (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat I2) _let_1)) (tptp.groups1705073143266064639nt_int tptp.aTP_Lamm_fv (tptp.set_or1266510415728281911st_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int I2) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int _let_1)))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.aa_int_int _let_1 B))) (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) tptp.one_one_int)) A))) tptp.one_one_int))))) (forall ((A tptp.rat) (D2 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))) (let ((_let_2 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_rat_rat _let_2 (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aTP_Lamm_abh A) D2)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat _let_2 A)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) D2))))))) (forall ((A tptp.code_natural) (D2 tptp.code_natural) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_natural tptp.semiri3763490453095760265atural N2))) (let ((_let_2 (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.times_2397367101498566445atural _let_2 (tptp.groups6325495683096345652atural (tptp.aa_Cod5320533616963873627atural (tptp.aTP_Lamm_abi A) D2) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (tptp.times_2397367101498566445atural (tptp.plus_p4538020629002901425atural _let_1 tptp.one_one_Code_natural) (tptp.plus_p4538020629002901425atural (tptp.times_2397367101498566445atural _let_2 A) (tptp.times_2397367101498566445atural _let_1 D2))))))) (forall ((A tptp.int) (D2 tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_int_int _let_2 (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_abj A) D2)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_2 A)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) D2))))))) (forall ((A tptp.code_integer) (D2 tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) (let ((_let_2 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_Cod1783974652533396728nteger _let_2 (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger (tptp.aa_Cod1578151519121547077nteger (tptp.aTP_Lamm_abk A) D2)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger _let_2 A)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) D2))))))) (forall ((A tptp.nat) (D2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_nat_nat _let_2 (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_abl A) D2)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_2 A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) D2))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat tptp.semiri681578069525770553at_rat) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat _let_1) tptp.one_one_rat))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_natural tptp.semiri3763490453095760265atural N2))) (= (tptp.times_2397367101498566445atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)) (tptp.groups6325495683096345652atural tptp.semiri3763490453095760265atural (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (tptp.times_2397367101498566445atural _let_1 (tptp.plus_p4538020629002901425atural _let_1 tptp.one_one_Code_natural))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_abm M) N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat tptp.suc N2)) M)))) (forall ((M tptp.nat) (N2 tptp.nat) (F tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_kd F)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_nat_rat F N2)) (tptp.aa_nat_rat F M))))) (forall ((M tptp.nat) (N2 tptp.nat) (F tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_ke F)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int F N2)) (tptp.aa_nat_int F M))))) (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (F tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) A3)) (= (tptp.groups7237345082560585321er_nat F (tptp.minus_2355218937544613996nteger A3 B3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.groups7237345082560585321er_nat F A3)) (tptp.groups7237345082560585321er_nat F B3)))))) (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (F tptp.fun_Pr2602117396471556196at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat B3)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat B3) A3)) (= (tptp.groups977919841031483927at_nat F (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat A3) B3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.groups977919841031483927at_nat F A3)) (tptp.groups977919841031483927at_nat F B3)))))) (forall ((B3 tptp.set_int) (A3 tptp.set_int) (F tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) A3)) (= (tptp.groups4541462559716669496nt_nat F (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.groups4541462559716669496nt_nat F A3)) (tptp.groups4541462559716669496nt_nat F B3)))))) (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (F tptp.fun_nat_nat)) (let ((_let_1 (tptp.groups3542108847815614940at_nat F))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B3) A3)) (= (tptp.aa_set_nat_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_set_nat_nat _let_1 A3)) (tptp.aa_set_nat_nat _let_1 B3))))))) (forall ((M tptp.nat) (N2 tptp.nat) (R3 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_nat3783148529270815480at_nat (tptp.aTP_Lamm_abn M) N2) R3)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat R3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2)) R3))) (forall ((G tptp.fun_nat_nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat N2) M))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) _let_1) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_nat3783148529270815480at_nat (tptp.aTP_Lamm_abo G) N2) M)) _let_1)))) (forall ((B tptp.int) (A tptp.int) (Q5 tptp.int) (R3 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int))) (let ((_let_3 (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q5))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) B)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int A B) (tptp.aa_int7462565939943104719nt_int _let_3 R3))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int (tptp.aa_int_int _let_2 (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B)) (tptp.aa_int7462565939943104719nt_int _let_3 (tptp.aa_int_int _let_2 (tptp.aa_int_int _let_1 R3))))))))))) (forall ((A tptp.fun_nat_fun_nat_nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_abp A)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_abq A) N2)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)))) (forall ((G tptp.fun_nat_nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat N2) M))) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat G) _let_1) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_nat3783148529270815480at_nat (tptp.aTP_Lamm_abo G) N2) M)) _let_1)))) (forall ((G tptp.fun_nat_int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat N2) M))) (= (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int G) _let_1) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_nat_fun_nat_int (tptp.aa_nat1293065384339088724at_int (tptp.aTP_Lamm_abr G) N2) M)) _let_1)))) (forall ((A tptp.fun_nat_fun_nat_nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aTP_Lamm_abs A)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_abt A) N2)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)))) (forall ((A tptp.fun_nat_fun_nat_int) (N2 tptp.nat)) (= (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aTP_Lamm_abu A)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_abv A) N2)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N2) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2))))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger N2) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2))))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2))))) (forall ((M tptp.nat)) (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_abw M)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))) M))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.divide6298287555418463151nteger A))) (let ((_let_2 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_Cod1783974652533396728nteger _let_2 B))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) _let_3))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger _let_2 (tptp.aa_Cod1783974652533396728nteger _let_1 _let_3))) tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger _let_1 B))))))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_nat_nat _let_2 B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_3))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat _let_1 _let_3))) tptp.one_one_nat) (tptp.aa_nat_nat _let_1 B))))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.divide_divide_int A))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_int_int _let_2 B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) _let_3))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_2 (tptp.aa_int_int _let_1 _let_3))) tptp.one_one_int) (tptp.aa_int_int _let_1 B))))))))) (forall ((M tptp.int) (N2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int M) N2)) (= (tptp.groups4538972089207619220nt_int tptp.aTP_Lamm_fv (tptp.set_or1266510415728281911st_int M N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int N2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int N2) tptp.one_one_int))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int M) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int M) tptp.one_one_int)))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((A3 tptp.set_int) (P tptp.fun_int_bool) (H tptp.fun_int_rat) (G tptp.fun_int_rat)) (let ((_let_1 (tptp.collect_int P))) (let ((_let_2 (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups3906332499630173760nt_rat (tptp.aa_fun1481061427733998144nt_rat (tptp.aa_fun2191249852558612414nt_rat (tptp.aTP_Lamm_abx P) H) G) A3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups3906332499630173760nt_rat H (tptp.aa_set_int_set_int _let_2 _let_1))) (tptp.groups3906332499630173760nt_rat G (tptp.aa_set_int_set_int _let_2 (tptp.uminus1532241313380277803et_int _let_1))))))))) (forall ((A3 tptp.set_Code_integer) (P tptp.fun_Co8822979462182099027r_bool) (H tptp.fun_Code_integer_rat) (G tptp.fun_Code_integer_rat)) (let ((_let_1 (tptp.collect_Code_integer P))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups6602215022474089585er_rat (tptp.aa_fun8169474305930283170er_rat (tptp.aa_fun1894662059565830609er_rat (tptp.aTP_Lamm_aby P) H) G) A3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups6602215022474089585er_rat H (tptp.inf_in1364745209274528805nteger A3 _let_1))) (tptp.groups6602215022474089585er_rat G (tptp.inf_in1364745209274528805nteger A3 (tptp.uminus804700908173204444nteger _let_1)))))))) (forall ((A3 tptp.set_int) (P tptp.fun_int_bool) (H tptp.fun_int_nat) (G tptp.fun_int_nat)) (let ((_let_1 (tptp.collect_int P))) (let ((_let_2 (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups4541462559716669496nt_nat (tptp.aa_fun6506752150744536624nt_nat (tptp.aa_fun5407591398502139302nt_nat (tptp.aTP_Lamm_ib P) H) G) A3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.groups4541462559716669496nt_nat H (tptp.aa_set_int_set_int _let_2 _let_1))) (tptp.groups4541462559716669496nt_nat G (tptp.aa_set_int_set_int _let_2 (tptp.uminus1532241313380277803et_int _let_1))))))))) (forall ((A3 tptp.set_Code_integer) (P tptp.fun_Co8822979462182099027r_bool) (H tptp.fun_Code_integer_nat) (G tptp.fun_Code_integer_nat)) (let ((_let_1 (tptp.collect_Code_integer P))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups7237345082560585321er_nat (tptp.aa_fun3076867170244285586er_nat (tptp.aa_fun7635586485349294009er_nat (tptp.aTP_Lamm_abz P) H) G) A3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.groups7237345082560585321er_nat H (tptp.inf_in1364745209274528805nteger A3 _let_1))) (tptp.groups7237345082560585321er_nat G (tptp.inf_in1364745209274528805nteger A3 (tptp.uminus804700908173204444nteger _let_1)))))))) (forall ((A3 tptp.set_Code_integer) (P tptp.fun_Co8822979462182099027r_bool) (H tptp.fun_Code_integer_int) (G tptp.fun_Code_integer_int)) (let ((_let_1 (tptp.collect_Code_integer P))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups7234854612051535045er_int (tptp.aa_fun3291479149765983562er_int (tptp.aa_fun4411173778969602765er_int (tptp.aTP_Lamm_aca P) H) G) A3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups7234854612051535045er_int H (tptp.inf_in1364745209274528805nteger A3 _let_1))) (tptp.groups7234854612051535045er_int G (tptp.inf_in1364745209274528805nteger A3 (tptp.uminus804700908173204444nteger _let_1)))))))) (forall ((A3 tptp.set_nat) (P tptp.fun_nat_bool) (H tptp.fun_nat_rat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.collect_nat P))) (let ((_let_2 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aa_fun765758790203053448at_rat (tptp.aa_fun3638354034882855594at_rat (tptp.aTP_Lamm_acb P) H) G)) A3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat H) (tptp.aa_set_nat_set_nat _let_2 _let_1))) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat G) (tptp.aa_set_nat_set_nat _let_2 (tptp.uminus5710092332889474511et_nat _let_1))))))))) (forall ((A3 tptp.set_nat) (P tptp.fun_nat_bool) (H tptp.fun_nat_int) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.collect_nat P))) (let ((_let_2 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aa_fun5565043122120104496at_int (tptp.aa_fun5140708168904641446at_int (tptp.aTP_Lamm_ia P) H) G)) A3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int H) (tptp.aa_set_nat_set_nat _let_2 _let_1))) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int G) (tptp.aa_set_nat_set_nat _let_2 (tptp.uminus5710092332889474511et_nat _let_1))))))))) (forall ((A3 tptp.set_nat) (P tptp.fun_nat_bool) (H tptp.fun_nat_nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.collect_nat P))) (let ((_let_2 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aa_fun6854695580826382482at_nat (tptp.aTP_Lamm_ic P) H) G)) A3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat H) (tptp.aa_set_nat_set_nat _let_2 _let_1))) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) (tptp.aa_set_nat_set_nat _let_2 (tptp.uminus5710092332889474511et_nat _let_1))))))))) (forall ((A3 tptp.set_int) (P tptp.fun_int_bool) (H tptp.fun_int_int) (G tptp.fun_int_int)) (let ((_let_1 (tptp.collect_int P))) (let ((_let_2 (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups4538972089207619220nt_int (tptp.aa_fun6280345759651049192nt_int (tptp.aa_fun3693603986580398266nt_int (tptp.aTP_Lamm_hz P) H) G) A3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups4538972089207619220nt_int H (tptp.aa_set_int_set_int _let_2 _let_1))) (tptp.groups4538972089207619220nt_int G (tptp.aa_set_int_set_int _let_2 (tptp.uminus1532241313380277803et_int _let_1))))))))) (forall ((A3 tptp.set_list_nat) (P tptp.fun_list_nat_bool) (H tptp.fun_list_nat_rat) (G tptp.fun_list_nat_rat)) (let ((_let_1 (tptp.collect_list_nat P))) (=> (tptp.finite8100373058378681591st_nat A3) (= (tptp.groups3760926236672600436at_rat (tptp.aa_fun1630595088783574696at_rat (tptp.aa_fun6629217458047550682at_rat (tptp.aTP_Lamm_acc P) H) G) A3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups3760926236672600436at_rat H (tptp.inf_inf_set_list_nat A3 _let_1))) (tptp.groups3760926236672600436at_rat G (tptp.inf_inf_set_list_nat A3 (tptp.uminus3195874150345416415st_nat _let_1)))))))) (forall ((A3 tptp.set_int) (P tptp.fun_int_bool) (H tptp.fun_int_Code_integer) (G tptp.fun_int_Code_integer)) (let ((_let_1 (tptp.collect_int P))) (let ((_let_2 (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups3827104343326376752nteger (tptp.aa_fun5304498221708291146nteger (tptp.aa_fun3938006231294128461nteger (tptp.aTP_Lamm_acd P) H) G) A3) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.groups3827104343326376752nteger H (tptp.aa_set_int_set_int _let_2 _let_1))) (tptp.groups3827104343326376752nteger G (tptp.aa_set_int_set_int _let_2 (tptp.uminus1532241313380277803et_int _let_1))))))))) (forall ((A3 tptp.set_Code_integer) (P tptp.fun_Co8822979462182099027r_bool) (H tptp.fun_Co8499238673658658103nteger) (G tptp.fun_Co8499238673658658103nteger)) (let ((_let_1 (tptp.collect_Code_integer P))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups3674199335183972705nteger (tptp.aa_fun4435975922079263404nteger (tptp.aa_fun2957433868855875424nteger (tptp.aTP_Lamm_ace P) H) G) A3) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.groups3674199335183972705nteger H (tptp.inf_in1364745209274528805nteger A3 _let_1))) (tptp.groups3674199335183972705nteger G (tptp.inf_in1364745209274528805nteger A3 (tptp.uminus804700908173204444nteger _let_1)))))))) (forall ((A3 tptp.set_nat) (P tptp.fun_nat_bool) (H tptp.fun_nat_Code_integer) (G tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.collect_nat P))) (let ((_let_2 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger (tptp.aa_fun589076786913273746nteger (tptp.aa_fun3918145391673965625nteger (tptp.aTP_Lamm_acf P) H) G)) A3) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger H) (tptp.aa_set_nat_set_nat _let_2 _let_1))) (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger G) (tptp.aa_set_nat_set_nat _let_2 (tptp.uminus5710092332889474511et_nat _let_1))))))))) (forall ((A3 tptp.set_int) (P tptp.fun_int_bool) (H tptp.fun_int_assn) (G tptp.fun_int_assn)) (let ((_let_1 (tptp.collect_int P))) (let ((_let_2 (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups7882442080178216443t_assn (tptp.aa_fun919007281442365664t_assn (tptp.aa_fun7795160494388424622t_assn (tptp.aTP_Lamm_acg P) H) G) A3) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups7882442080178216443t_assn H (tptp.aa_set_int_set_int _let_2 _let_1))) (tptp.groups7882442080178216443t_assn G (tptp.aa_set_int_set_int _let_2 (tptp.uminus1532241313380277803et_int _let_1))))))))) (forall ((A3 tptp.set_Code_integer) (P tptp.fun_Co8822979462182099027r_bool) (H tptp.fun_Co4490034186337852034r_assn) (G tptp.fun_Co4490034186337852034r_assn)) (let ((_let_1 (tptp.collect_Code_integer P))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups1304777262505850412r_assn (tptp.aa_fun4119713415300323650r_assn (tptp.aa_fun8067317676786998721r_assn (tptp.aTP_Lamm_ach P) H) G) A3) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups1304777262505850412r_assn H (tptp.inf_in1364745209274528805nteger A3 _let_1))) (tptp.groups1304777262505850412r_assn G (tptp.inf_in1364745209274528805nteger A3 (tptp.uminus804700908173204444nteger _let_1)))))))) (forall ((A3 tptp.set_nat) (P tptp.fun_nat_bool) (H tptp.fun_nat_assn) (G tptp.fun_nat_assn)) (let ((_let_1 (tptp.collect_nat P))) (let ((_let_2 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.groups6906906614972039071t_assn (tptp.aa_fun785744391571715112t_assn (tptp.aa_fun6591345337174305434t_assn (tptp.aTP_Lamm_aci P) H) G) A3) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups6906906614972039071t_assn H (tptp.aa_set_nat_set_nat _let_2 _let_1))) (tptp.groups6906906614972039071t_assn G (tptp.aa_set_nat_set_nat _let_2 (tptp.uminus5710092332889474511et_nat _let_1))))))))) (forall ((A3 tptp.set_int) (P tptp.fun_int_bool) (H tptp.fun_int_rat) (G tptp.fun_int_rat)) (let ((_let_1 (tptp.collect_int P))) (let ((_let_2 (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups1072433553688619179nt_rat (tptp.aa_fun1481061427733998144nt_rat (tptp.aa_fun2191249852558612414nt_rat (tptp.aTP_Lamm_abx P) H) G) A3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.groups1072433553688619179nt_rat H (tptp.aa_set_int_set_int _let_2 _let_1))) (tptp.groups1072433553688619179nt_rat G (tptp.aa_set_int_set_int _let_2 (tptp.uminus1532241313380277803et_int _let_1))))))))) (forall ((A3 tptp.set_Code_integer) (P tptp.fun_Co8822979462182099027r_bool) (H tptp.fun_Code_integer_rat) (G tptp.fun_Code_integer_rat)) (let ((_let_1 (tptp.collect_Code_integer P))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups2555765274223993564er_rat (tptp.aa_fun8169474305930283170er_rat (tptp.aa_fun1894662059565830609er_rat (tptp.aTP_Lamm_aby P) H) G) A3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.groups2555765274223993564er_rat H (tptp.inf_in1364745209274528805nteger A3 _let_1))) (tptp.groups2555765274223993564er_rat G (tptp.inf_in1364745209274528805nteger A3 (tptp.uminus804700908173204444nteger _let_1)))))))) (forall ((A3 tptp.set_nat) (P tptp.fun_nat_bool) (H tptp.fun_nat_rat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.collect_nat P))) (let ((_let_2 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat (tptp.aa_fun765758790203053448at_rat (tptp.aa_fun3638354034882855594at_rat (tptp.aTP_Lamm_acb P) H) G)) A3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat H) (tptp.aa_set_nat_set_nat _let_2 _let_1))) (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat G) (tptp.aa_set_nat_set_nat _let_2 (tptp.uminus5710092332889474511et_nat _let_1))))))))) (forall ((A3 tptp.set_int) (P tptp.fun_int_bool) (H tptp.fun_int_nat) (G tptp.fun_int_nat)) (let ((_let_1 (tptp.collect_int P))) (let ((_let_2 (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups1707563613775114915nt_nat (tptp.aa_fun6506752150744536624nt_nat (tptp.aa_fun5407591398502139302nt_nat (tptp.aTP_Lamm_ib P) H) G) A3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.groups1707563613775114915nt_nat H (tptp.aa_set_int_set_int _let_2 _let_1))) (tptp.groups1707563613775114915nt_nat G (tptp.aa_set_int_set_int _let_2 (tptp.uminus1532241313380277803et_int _let_1))))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_rat tptp.numeral_numeral_rat _let_1))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N2))) (= (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat _let_3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat _let_2) _let_3)) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat tptp.one_one_rat) _let_2)) N2))) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N2))))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) K)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N2) K)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat tptp.semiri681578069525770553at_rat) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N2))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat _let_1) tptp.one_one_rat))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_natural tptp.semiri3763490453095760265atural N2))) (= (tptp.times_2397367101498566445atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)) (tptp.groups6325495683096345652atural tptp.semiri3763490453095760265atural (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N2))) (tptp.times_2397367101498566445atural _let_1 (tptp.plus_p4538020629002901425atural _let_1 tptp.one_one_Code_natural))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N2))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N2))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat))))) (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat)))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_2 N2)) (=> (tptp.pp (tptp.aa_nat_bool _let_2 K)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N2) K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat K) tptp.one_one_nat))) (tptp.aa_nat_nat _let_1 K)))))))) (forall ((A tptp.code_natural) (D2 tptp.code_natural) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_Code_natural tptp.semiri3763490453095760265atural N2))) (= (tptp.groups6325495683096345652atural (tptp.aa_Cod5320533616963873627atural (tptp.aTP_Lamm_abi A) D2) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (tptp.divide5121882707175180666atural (tptp.times_2397367101498566445atural (tptp.plus_p4538020629002901425atural _let_2 tptp.one_one_Code_natural) (tptp.plus_p4538020629002901425atural (tptp.times_2397367101498566445atural _let_1 A) (tptp.times_2397367101498566445atural _let_2 D2))) _let_1))))) (forall ((A tptp.int) (D2 tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) (= (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_abj A) D2)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_2) tptp.one_one_int)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) A)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_2) D2)))) _let_1))))) (forall ((A tptp.code_integer) (D2 tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) (= (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger (tptp.aa_Cod1578151519121547077nteger (tptp.aTP_Lamm_abk A) D2)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger _let_2) tptp.one_one_Code_integer)) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) A)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_2) D2)))) _let_1))))) (forall ((A tptp.nat) (D2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_abl A) D2)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_2) tptp.one_one_nat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_2) D2)))) _let_1))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_natural tptp.semiri3763490453095760265atural N2))) (= (tptp.groups6325495683096345652atural tptp.semiri3763490453095760265atural (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (tptp.divide5121882707175180666atural (tptp.times_2397367101498566445atural _let_1 (tptp.plus_p4538020629002901425atural _let_1 tptp.one_one_Code_natural)) (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) (= (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) (= (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat K) tptp.one_one_nat)))))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.groups7501900531339628137nteger G))) (let ((_let_2 (tptp.aa_set871585252387937313nteger _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)))) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_set871585252387937313nteger _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2))) (tptp.aa_nat_Code_integer G N2))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_na2338080690716861136at_nat)) (let ((_let_1 (tptp.groups6857163185585827899at_nat G (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)))) (and (=> _let_2 (= _let_1 tptp.zero_z1048942125864253310at_nat)) (=> (not _let_2) (= _let_1 (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat (tptp.groups6857163185585827899at_nat G (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2))) (tptp.aa_nat2240542744625857721at_nat G N2)))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups2906978787729119204at_rat G))) (let ((_let_2 (tptp.aa_set_nat_rat _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)))) (and (=> _let_3 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_3) (= _let_2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_set_nat_rat _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2))) (tptp.aa_nat_rat G N2))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.groups3539618377306564664at_int G))) (let ((_let_2 (tptp.aa_set_nat_int _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_set_nat_int _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2))) (tptp.aa_nat_int G N2))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.groups3542108847815614940at_nat G))) (let ((_let_2 (tptp.aa_set_nat_nat _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_set_nat_nat _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2))) (tptp.aa_nat_nat G N2))))))))) (forall ((B tptp.int) (A tptp.int) (Q5 tptp.int) (R3 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q5))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) tptp.one_one_int) B) (tptp.aa_int7462565939943104719nt_int _let_2 R3))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B)) (tptp.aa_int7462565939943104719nt_int _let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 R3)) tptp.one_one_int))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.groups3455450783089532116nteger G))) (let ((_let_2 (tptp.aa_set871585252387937313nteger _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)))) (and (=> _let_3 (= _let_2 tptp.one_one_Code_integer)) (=> (not _let_3) (= _let_2 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_set871585252387937313nteger _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2))) (tptp.aa_nat_Code_integer G N2))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_nat_assn)) (let ((_let_1 (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)))) (and (=> _let_2 (= _let_1 tptp.one_one_assn)) (=> (not _let_2) (= _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2))) (tptp.aa_nat_assn G N2)))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups73079841787564623at_rat G))) (let ((_let_2 (tptp.aa_set_nat_rat _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)))) (and (=> _let_3 (= _let_2 tptp.one_one_rat)) (=> (not _let_3) (= _let_2 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_set_nat_rat _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2))) (tptp.aa_nat_rat G N2))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.groups708209901874060359at_nat G))) (let ((_let_2 (tptp.aa_set_nat_nat _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)))) (and (=> _let_3 (= _let_2 tptp.one_one_nat)) (=> (not _let_3) (= _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_set_nat_nat _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2))) (tptp.aa_nat_nat G N2))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.groups705719431365010083at_int G))) (let ((_let_2 (tptp.aa_set_nat_int _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)))) (and (=> _let_3 (= _let_2 tptp.one_one_int)) (=> (not _let_3) (= _let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_set_nat_int _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2))) (tptp.aa_nat_int G N2))))))))) (forall ((A3 tptp.set_Code_integer) (F tptp.fun_Co8499238673658658103nteger) (G tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (forall ((I3 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger F I3))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I3) A3)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger _let_1) (tptp.aa_Cod1783974652533396728nteger G I3))))))) (=> (not (= A3 tptp.bot_bo3990330152332043303nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.groups3674199335183972705nteger F A3)) (tptp.groups3674199335183972705nteger G A3))))))) (forall ((A3 tptp.set_bool) (F tptp.fun_bo7282069421189217543nteger) (G tptp.fun_bo7282069421189217543nteger)) (=> (tptp.finite_finite_bool A3) (=> (forall ((I3 tptp.bool)) (let ((_let_1 (tptp.aa_bool_Code_integer F I3))) (=> (tptp.pp (tptp.member_bool I3 A3)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger _let_1) (tptp.aa_bool_Code_integer G I3))))))) (=> (not (= A3 tptp.bot_bot_set_bool)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.groups7272450149305381519nteger F A3)) (tptp.groups7272450149305381519nteger G A3))))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_Code_integer) (G tptp.fun_nat_Code_integer)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_integer F I3))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) A3)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger _let_1) (tptp.aa_nat_Code_integer G I3))))))) (=> (not (= A3 tptp.bot_bot_set_nat)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger F) A3)) (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger G) A3))))))) (forall ((A3 tptp.set_int) (F tptp.fun_int_Code_integer) (G tptp.fun_int_Code_integer)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (forall ((I3 tptp.int)) (let ((_let_1 (tptp.aa_int_Code_integer F I3))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) A3)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger _let_1) (tptp.aa_int_Code_integer G I3))))))) (=> (not (= A3 tptp.bot_bot_set_int)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.groups3827104343326376752nteger F A3)) (tptp.groups3827104343326376752nteger G A3))))))) (forall ((A3 tptp.set_Code_integer) (F tptp.fun_Code_integer_rat) (G tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (forall ((I3 tptp.code_integer)) (let ((_let_1 (tptp.aa_Code_integer_rat F I3))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I3) A3)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_1) (tptp.aa_Code_integer_rat G I3))))))) (=> (not (= A3 tptp.bot_bo3990330152332043303nteger)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups2555765274223993564er_rat F A3)) (tptp.groups2555765274223993564er_rat G A3))))))) (forall ((A3 tptp.set_bool) (F tptp.fun_bool_rat) (G tptp.fun_bool_rat)) (=> (tptp.finite_finite_bool A3) (=> (forall ((I3 tptp.bool)) (let ((_let_1 (tptp.aa_bool_rat F I3))) (=> (tptp.pp (tptp.member_bool I3 A3)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_1) (tptp.aa_bool_rat G I3))))))) (=> (not (= A3 tptp.bot_bot_set_bool)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups1259819201609700362ol_rat F A3)) (tptp.groups1259819201609700362ol_rat G A3))))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_rat) (G tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat F I3))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) A3)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_1) (tptp.aa_nat_rat G I3))))))) (=> (not (= A3 tptp.bot_bot_set_nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat F) A3)) (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat G) A3))))))) (forall ((A3 tptp.set_int) (F tptp.fun_int_rat) (G tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (forall ((I3 tptp.int)) (let ((_let_1 (tptp.aa_int_rat F I3))) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) A3)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_1) (tptp.aa_int_rat G I3))))))) (=> (not (= A3 tptp.bot_bot_set_int)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups1072433553688619179nt_rat F A3)) (tptp.groups1072433553688619179nt_rat G A3))))))) (forall ((A3 tptp.set_Code_integer) (F tptp.fun_Code_integer_nat) (G tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (forall ((I3 tptp.code_integer)) (let ((_let_1 (tptp.aa_Code_integer_nat F I3))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer I3) A3)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) (tptp.aa_Code_integer_nat G I3))))))) (=> (not (= A3 tptp.bot_bo3990330152332043303nteger)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.groups3190895334310489300er_nat F A3)) (tptp.groups3190895334310489300er_nat G A3))))))) (forall ((A3 tptp.set_bool) (F tptp.fun_bool_nat) (G tptp.fun_bool_nat)) (=> (tptp.finite_finite_bool A3) (=> (forall ((I3 tptp.bool)) (let ((_let_1 (tptp.aa_bool_nat F I3))) (=> (tptp.pp (tptp.member_bool I3 A3)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) (tptp.aa_bool_nat G I3))))))) (=> (not (= A3 tptp.bot_bot_set_bool)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.groups1894949261696196098ol_nat F A3)) (tptp.groups1894949261696196098ol_nat G A3))))))) (forall ((B3 tptp.set_bool) (A3 tptp.set_bool) (F tptp.fun_bo7282069421189217543nteger)) (=> (tptp.finite_finite_bool B3) (=> (tptp.ord_less_eq_set_bool A3 B3) (=> (forall ((B4 tptp.bool)) (=> (tptp.pp (tptp.member_bool B4 (tptp.minus_minus_set_bool B3 A3))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_bool_Code_integer F B4))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.groups1682264926906508858nteger F A3)) (tptp.groups1682264926906508858nteger F B3))))))) (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (F tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) B3)) (=> (forall ((B4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer B4) (tptp.minus_2355218937544613996nteger B3 A3))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger F B4))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.groups879477027807139574nteger F A3)) (tptp.groups879477027807139574nteger F B3))))))) (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (F tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.groups7501900531339628137nteger F))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) B3)) (=> (forall ((B4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B4) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat B3) A3))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer F B4))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_set871585252387937313nteger _let_1 A3)) (tptp.aa_set871585252387937313nteger _let_1 B3)))))))) (forall ((B3 tptp.set_bool) (A3 tptp.set_bool) (F tptp.fun_bool_rat)) (=> (tptp.finite_finite_bool B3) (=> (tptp.ord_less_eq_set_bool A3 B3) (=> (forall ((B4 tptp.bool)) (=> (tptp.pp (tptp.member_bool B4 (tptp.minus_minus_set_bool B3 A3))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_bool_rat F B4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups5133371213642249141ol_rat F A3)) (tptp.groups5133371213642249141ol_rat F B3))))))) (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (F tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) B3)) (=> (forall ((B4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer B4) (tptp.minus_2355218937544613996nteger B3 A3))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_Code_integer_rat F B4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups6602215022474089585er_rat F A3)) (tptp.groups6602215022474089585er_rat F B3))))))) (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (F tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups2906978787729119204at_rat F))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) B3)) (=> (forall ((B4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B4) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat B3) A3))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat F B4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_set_nat_rat _let_1 A3)) (tptp.aa_set_nat_rat _let_1 B3)))))))) (forall ((B3 tptp.set_bool) (A3 tptp.set_bool) (F tptp.fun_bool_nat)) (=> (tptp.finite_finite_bool B3) (=> (tptp.ord_less_eq_set_bool A3 B3) (=> (forall ((B4 tptp.bool)) (=> (tptp.pp (tptp.member_bool B4 (tptp.minus_minus_set_bool B3 A3))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_bool_nat F B4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.groups5768501273728744877ol_nat F A3)) (tptp.groups5768501273728744877ol_nat F B3))))))) (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (F tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) B3)) (=> (forall ((B4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer B4) (tptp.minus_2355218937544613996nteger B3 A3))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_Code_integer_nat F B4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.groups7237345082560585321er_nat F A3)) (tptp.groups7237345082560585321er_nat F B3))))))) (forall ((B3 tptp.set_bool) (A3 tptp.set_bool) (F tptp.fun_bool_int)) (=> (tptp.finite_finite_bool B3) (=> (tptp.ord_less_eq_set_bool A3 B3) (=> (forall ((B4 tptp.bool)) (=> (tptp.pp (tptp.member_bool B4 (tptp.minus_minus_set_bool B3 A3))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_bool_int F B4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.groups5766010803219694601ol_int F A3)) (tptp.groups5766010803219694601ol_int F B3))))))) (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (F tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) B3)) (=> (forall ((B4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer B4) (tptp.minus_2355218937544613996nteger B3 A3))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_Code_integer_int F B4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.groups7234854612051535045er_int F A3)) (tptp.groups7234854612051535045er_int F B3))))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N2) K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat K)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G tptp.fun_int_Code_integer)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))) (= (tptp.aa_int_Code_integer G X3) tptp.zero_z3403309356797280102nteger))) (= (tptp.groups7873554091576472773nteger G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3)) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.groups7873554091576472773nteger G A3)) (tptp.groups7873554091576472773nteger G B3))))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.inf_in1364745209274528805nteger A3 B3))) (= (tptp.aa_Cod1783974652533396728nteger G X3) tptp.zero_z3403309356797280102nteger))) (= (tptp.groups879477027807139574nteger G (tptp.sup_su848401254843788991nteger A3 B3)) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.groups879477027807139574nteger G A3)) (tptp.groups879477027807139574nteger G B3))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))) (= (tptp.aa_int_rat G X3) tptp.zero_zero_rat))) (= (tptp.groups3906332499630173760nt_rat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups3906332499630173760nt_rat G A3)) (tptp.groups3906332499630173760nt_rat G B3))))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.inf_in1364745209274528805nteger A3 B3))) (= (tptp.aa_Code_integer_rat G X3) tptp.zero_zero_rat))) (= (tptp.groups6602215022474089585er_rat G (tptp.sup_su848401254843788991nteger A3 B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups6602215022474089585er_rat G A3)) (tptp.groups6602215022474089585er_rat G B3))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))) (= (tptp.aa_int_nat G X3) tptp.zero_zero_nat))) (= (tptp.groups4541462559716669496nt_nat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.groups4541462559716669496nt_nat G A3)) (tptp.groups4541462559716669496nt_nat G B3))))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.inf_in1364745209274528805nteger A3 B3))) (= (tptp.aa_Code_integer_nat G X3) tptp.zero_zero_nat))) (= (tptp.groups7237345082560585321er_nat G (tptp.sup_su848401254843788991nteger A3 B3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.groups7237345082560585321er_nat G A3)) (tptp.groups7237345082560585321er_nat G B3))))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.inf_in1364745209274528805nteger A3 B3))) (= (tptp.aa_Code_integer_int G X3) tptp.zero_zero_int))) (= (tptp.groups7234854612051535045er_int G (tptp.sup_su848401254843788991nteger A3 B3)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups7234854612051535045er_int G A3)) (tptp.groups7234854612051535045er_int G B3))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.groups7501900531339628137nteger G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3))) (= (tptp.aa_nat_Code_integer G X3) tptp.zero_z3403309356797280102nteger))) (= (tptp.aa_set871585252387937313nteger _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_set871585252387937313nteger _let_1 A3)) (tptp.aa_set871585252387937313nteger _let_1 B3)))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups2906978787729119204at_rat G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3))) (= (tptp.aa_nat_rat G X3) tptp.zero_zero_rat))) (= (tptp.aa_set_nat_rat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_set_nat_rat _let_1 A3)) (tptp.aa_set_nat_rat _let_1 B3)))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.groups3539618377306564664at_int G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3))) (= (tptp.aa_nat_int G X3) tptp.zero_zero_int))) (= (tptp.aa_set_nat_int _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_set_nat_int _let_1 A3)) (tptp.aa_set_nat_int _let_1 B3)))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (F tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (= (tptp.groups3906332499630173760nt_rat F (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups3906332499630173760nt_rat F A3)) (tptp.groups3906332499630173760nt_rat F B3))) (tptp.groups3906332499630173760nt_rat F (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (F tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (= (tptp.groups6602215022474089585er_rat F (tptp.sup_su848401254843788991nteger A3 B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups6602215022474089585er_rat F A3)) (tptp.groups6602215022474089585er_rat F B3))) (tptp.groups6602215022474089585er_rat F (tptp.inf_in1364745209274528805nteger A3 B3))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (F tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups2906978787729119204at_rat F))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (= (tptp.aa_set_nat_rat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_set_nat_rat _let_1 A3)) (tptp.aa_set_nat_rat _let_1 B3))) (tptp.aa_set_nat_rat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3)))))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (F tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (= (tptp.groups7234854612051535045er_int F (tptp.sup_su848401254843788991nteger A3 B3)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups7234854612051535045er_int F A3)) (tptp.groups7234854612051535045er_int F B3))) (tptp.groups7234854612051535045er_int F (tptp.inf_in1364745209274528805nteger A3 B3))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (F tptp.fun_nat_int)) (let ((_let_1 (tptp.groups3539618377306564664at_int F))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (= (tptp.aa_set_nat_int _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_set_nat_int _let_1 A3)) (tptp.aa_set_nat_int _let_1 B3))) (tptp.aa_set_nat_int _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3)))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (F tptp.fun_int_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (= (tptp.groups4538972089207619220nt_int F (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups4538972089207619220nt_int F A3)) (tptp.groups4538972089207619220nt_int F B3))) (tptp.groups4538972089207619220nt_int F (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (F tptp.fun_Pr8317260874932935276at_rat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat A3)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat B3)) (= (tptp.groups342789780944988191at_rat F (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat A3) B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups342789780944988191at_rat F A3)) (tptp.groups342789780944988191at_rat F B3))) (tptp.groups342789780944988191at_rat F (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3))))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (F tptp.fun_Pr7647638413817135296at_int)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat A3)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat B3)) (= (tptp.groups975429370522433651at_int F (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat A3) B3)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups975429370522433651at_int F A3)) (tptp.groups975429370522433651at_int F B3))) (tptp.groups975429370522433651at_int F (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3))))))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (F tptp.fun_Pr8586684092290301266at_rat)) (=> (tptp.finite4392333629123659920at_nat A3) (=> (tptp.finite4392333629123659920at_nat B3) (= (tptp.groups1265588324298845189at_rat F (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3) B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups1265588324298845189at_rat F A3)) (tptp.groups1265588324298845189at_rat F B3))) (tptp.groups1265588324298845189at_rat F (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat A3) B3))))))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (F tptp.fun_Pr7917061631174501286at_int)) (=> (tptp.finite4392333629123659920at_nat A3) (=> (tptp.finite4392333629123659920at_nat B3) (= (tptp.groups1898227913876290649at_int F (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3) B3)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups1898227913876290649at_int F A3)) (tptp.groups1898227913876290649at_int F B3))) (tptp.groups1898227913876290649at_int F (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat A3) B3))))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (= (tptp.inf_in1364745209274528805nteger A3 B3) tptp.bot_bo3990330152332043303nteger) (= (tptp.groups6602215022474089585er_rat G (tptp.sup_su848401254843788991nteger A3 B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups6602215022474089585er_rat G A3)) (tptp.groups6602215022474089585er_rat G B3))))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (= (tptp.inf_in1364745209274528805nteger A3 B3) tptp.bot_bo3990330152332043303nteger) (= (tptp.groups7237345082560585321er_nat G (tptp.sup_su848401254843788991nteger A3 B3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.groups7237345082560585321er_nat G A3)) (tptp.groups7237345082560585321er_nat G B3))))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (= (tptp.inf_in1364745209274528805nteger A3 B3) tptp.bot_bo3990330152332043303nteger) (= (tptp.groups7234854612051535045er_int G (tptp.sup_su848401254843788991nteger A3 B3)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups7234854612051535045er_int G A3)) (tptp.groups7234854612051535045er_int G B3))))))) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool) (G tptp.fun_bool_rat)) (=> (tptp.finite_finite_bool A3) (=> (tptp.finite_finite_bool B3) (=> (= (tptp.inf_inf_set_bool A3 B3) tptp.bot_bot_set_bool) (= (tptp.groups5133371213642249141ol_rat G (tptp.aa_set_bool_set_bool (tptp.aa_set4734229006438377534t_bool tptp.sup_sup_set_bool A3) B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups5133371213642249141ol_rat G A3)) (tptp.groups5133371213642249141ol_rat G B3))))))) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool) (G tptp.fun_bool_nat)) (=> (tptp.finite_finite_bool A3) (=> (tptp.finite_finite_bool B3) (=> (= (tptp.inf_inf_set_bool A3 B3) tptp.bot_bot_set_bool) (= (tptp.groups5768501273728744877ol_nat G (tptp.aa_set_bool_set_bool (tptp.aa_set4734229006438377534t_bool tptp.sup_sup_set_bool A3) B3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.groups5768501273728744877ol_nat G A3)) (tptp.groups5768501273728744877ol_nat G B3))))))) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool) (G tptp.fun_bool_int)) (=> (tptp.finite_finite_bool A3) (=> (tptp.finite_finite_bool B3) (=> (= (tptp.inf_inf_set_bool A3 B3) tptp.bot_bot_set_bool) (= (tptp.groups5766010803219694601ol_int G (tptp.aa_set_bool_set_bool (tptp.aa_set4734229006438377534t_bool tptp.sup_sup_set_bool A3) B3)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups5766010803219694601ol_int G A3)) (tptp.groups5766010803219694601ol_int G B3))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups2906978787729119204at_rat G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3) tptp.bot_bot_set_nat) (= (tptp.aa_set_nat_rat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_set_nat_rat _let_1 A3)) (tptp.aa_set_nat_rat _let_1 B3)))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.groups3539618377306564664at_int G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3) tptp.bot_bot_set_nat) (= (tptp.aa_set_nat_int _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_set_nat_int _let_1 A3)) (tptp.aa_set_nat_int _let_1 B3)))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3) tptp.bot_bot_set_int) (= (tptp.groups3906332499630173760nt_rat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups3906332499630173760nt_rat G A3)) (tptp.groups3906332499630173760nt_rat G B3))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3) tptp.bot_bot_set_int) (= (tptp.groups4541462559716669496nt_nat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.groups4541462559716669496nt_nat G A3)) (tptp.groups4541462559716669496nt_nat G B3))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G tptp.fun_int_Code_integer)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))) (= (tptp.aa_int_Code_integer G X3) tptp.one_one_Code_integer))) (= (tptp.groups3827104343326376752nteger G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.groups3827104343326376752nteger G A3)) (tptp.groups3827104343326376752nteger G B3))))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.inf_in1364745209274528805nteger A3 B3))) (= (tptp.aa_Cod1783974652533396728nteger G X3) tptp.one_one_Code_integer))) (= (tptp.groups3674199335183972705nteger G (tptp.sup_su848401254843788991nteger A3 B3)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.groups3674199335183972705nteger G A3)) (tptp.groups3674199335183972705nteger G B3))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.groups3455450783089532116nteger G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3))) (= (tptp.aa_nat_Code_integer G X3) tptp.one_one_Code_integer))) (= (tptp.aa_set871585252387937313nteger _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_set871585252387937313nteger _let_1 A3)) (tptp.aa_set871585252387937313nteger _let_1 B3)))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G tptp.fun_int_assn)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))) (= (tptp.aa_int_assn G X3) tptp.one_one_assn))) (= (tptp.groups7882442080178216443t_assn G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups7882442080178216443t_assn G A3)) (tptp.groups7882442080178216443t_assn G B3))))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Co4490034186337852034r_assn)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.inf_in1364745209274528805nteger A3 B3))) (= (tptp.aa_Code_integer_assn G X3) tptp.one_one_assn))) (= (tptp.groups1304777262505850412r_assn G (tptp.sup_su848401254843788991nteger A3 B3)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups1304777262505850412r_assn G A3)) (tptp.groups1304777262505850412r_assn G B3))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G tptp.fun_nat_assn)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3))) (= (tptp.aa_nat_assn G X3) tptp.one_one_assn))) (= (tptp.groups6906906614972039071t_assn G (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups6906906614972039071t_assn G A3)) (tptp.groups6906906614972039071t_assn G B3))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))) (= (tptp.aa_int_rat G X3) tptp.one_one_rat))) (= (tptp.groups1072433553688619179nt_rat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.groups1072433553688619179nt_rat G A3)) (tptp.groups1072433553688619179nt_rat G B3))))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.inf_in1364745209274528805nteger A3 B3))) (= (tptp.aa_Code_integer_rat G X3) tptp.one_one_rat))) (= (tptp.groups2555765274223993564er_rat G (tptp.sup_su848401254843788991nteger A3 B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.groups2555765274223993564er_rat G A3)) (tptp.groups2555765274223993564er_rat G B3))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups73079841787564623at_rat G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3))) (= (tptp.aa_nat_rat G X3) tptp.one_one_rat))) (= (tptp.aa_set_nat_rat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_set_nat_rat _let_1 A3)) (tptp.aa_set_nat_rat _let_1 B3)))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))) (= (tptp.aa_int_nat G X3) tptp.one_one_nat))) (= (tptp.groups1707563613775114915nt_nat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.groups1707563613775114915nt_nat G A3)) (tptp.groups1707563613775114915nt_nat G B3))))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (= (tptp.inf_in1364745209274528805nteger A3 B3) tptp.bot_bo3990330152332043303nteger) (= (tptp.groups3674199335183972705nteger G (tptp.sup_su848401254843788991nteger A3 B3)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.groups3674199335183972705nteger G A3)) (tptp.groups3674199335183972705nteger G B3))))))) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool) (G tptp.fun_bo7282069421189217543nteger)) (=> (tptp.finite_finite_bool A3) (=> (tptp.finite_finite_bool B3) (=> (= (tptp.inf_inf_set_bool A3 B3) tptp.bot_bot_set_bool) (= (tptp.groups7272450149305381519nteger G (tptp.aa_set_bool_set_bool (tptp.aa_set4734229006438377534t_bool tptp.sup_sup_set_bool A3) B3)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.groups7272450149305381519nteger G A3)) (tptp.groups7272450149305381519nteger G B3))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.groups3455450783089532116nteger G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3) tptp.bot_bot_set_nat) (= (tptp.aa_set871585252387937313nteger _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_set871585252387937313nteger _let_1 A3)) (tptp.aa_set871585252387937313nteger _let_1 B3)))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G tptp.fun_int_Code_integer)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3) tptp.bot_bot_set_int) (= (tptp.groups3827104343326376752nteger G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.groups3827104343326376752nteger G A3)) (tptp.groups3827104343326376752nteger G B3))))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Co4490034186337852034r_assn)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (= (tptp.inf_in1364745209274528805nteger A3 B3) tptp.bot_bo3990330152332043303nteger) (= (tptp.groups1304777262505850412r_assn G (tptp.sup_su848401254843788991nteger A3 B3)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups1304777262505850412r_assn G A3)) (tptp.groups1304777262505850412r_assn G B3))))))) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool) (G tptp.fun_bool_assn)) (=> (tptp.finite_finite_bool A3) (=> (tptp.finite_finite_bool B3) (=> (= (tptp.inf_inf_set_bool A3 B3) tptp.bot_bot_set_bool) (= (tptp.groups4835110720589548378l_assn G (tptp.aa_set_bool_set_bool (tptp.aa_set4734229006438377534t_bool tptp.sup_sup_set_bool A3) B3)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups4835110720589548378l_assn G A3)) (tptp.groups4835110720589548378l_assn G B3))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G tptp.fun_nat_assn)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3) tptp.bot_bot_set_nat) (= (tptp.groups6906906614972039071t_assn G (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups6906906614972039071t_assn G A3)) (tptp.groups6906906614972039071t_assn G B3))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G tptp.fun_int_assn)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3) tptp.bot_bot_set_int) (= (tptp.groups7882442080178216443t_assn G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups7882442080178216443t_assn G A3)) (tptp.groups7882442080178216443t_assn G B3))))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (= (tptp.inf_in1364745209274528805nteger A3 B3) tptp.bot_bo3990330152332043303nteger) (= (tptp.groups2555765274223993564er_rat G (tptp.sup_su848401254843788991nteger A3 B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.groups2555765274223993564er_rat G A3)) (tptp.groups2555765274223993564er_rat G B3))))))) (forall ((A3 tptp.set_bool) (B3 tptp.set_bool) (G tptp.fun_bool_rat)) (=> (tptp.finite_finite_bool A3) (=> (tptp.finite_finite_bool B3) (=> (= (tptp.inf_inf_set_bool A3 B3) tptp.bot_bot_set_bool) (= (tptp.groups1259819201609700362ol_rat G (tptp.aa_set_bool_set_bool (tptp.aa_set4734229006438377534t_bool tptp.sup_sup_set_bool A3) B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.groups1259819201609700362ol_rat G A3)) (tptp.groups1259819201609700362ol_rat G B3))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (F tptp.fun_int_rat)) (let ((_let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int _let_1)) (= (tptp.groups3906332499630173760nt_rat F _let_1) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups3906332499630173760nt_rat F (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3))) (tptp.groups3906332499630173760nt_rat F (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int B3) A3)))) (tptp.groups3906332499630173760nt_rat F (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (F tptp.fun_Code_integer_rat)) (let ((_let_1 (tptp.sup_su848401254843788991nteger A3 B3))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger _let_1)) (= (tptp.groups6602215022474089585er_rat F _let_1) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups6602215022474089585er_rat F (tptp.minus_2355218937544613996nteger A3 B3))) (tptp.groups6602215022474089585er_rat F (tptp.minus_2355218937544613996nteger B3 A3)))) (tptp.groups6602215022474089585er_rat F (tptp.inf_in1364745209274528805nteger A3 B3))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (F tptp.fun_int_nat)) (let ((_let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int _let_1)) (= (tptp.groups4541462559716669496nt_nat F _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.groups4541462559716669496nt_nat F (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3))) (tptp.groups4541462559716669496nt_nat F (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int B3) A3)))) (tptp.groups4541462559716669496nt_nat F (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (F tptp.fun_Code_integer_nat)) (let ((_let_1 (tptp.sup_su848401254843788991nteger A3 B3))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger _let_1)) (= (tptp.groups7237345082560585321er_nat F _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.groups7237345082560585321er_nat F (tptp.minus_2355218937544613996nteger A3 B3))) (tptp.groups7237345082560585321er_nat F (tptp.minus_2355218937544613996nteger B3 A3)))) (tptp.groups7237345082560585321er_nat F (tptp.inf_in1364745209274528805nteger A3 B3))))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (F tptp.fun_Code_integer_int)) (let ((_let_1 (tptp.sup_su848401254843788991nteger A3 B3))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger _let_1)) (= (tptp.groups7234854612051535045er_int F _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups7234854612051535045er_int F (tptp.minus_2355218937544613996nteger A3 B3))) (tptp.groups7234854612051535045er_int F (tptp.minus_2355218937544613996nteger B3 A3)))) (tptp.groups7234854612051535045er_int F (tptp.inf_in1364745209274528805nteger A3 B3))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (F tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups2906978787729119204at_rat F))) (let ((_let_2 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat _let_2)) (= (tptp.aa_set_nat_rat _let_1 _let_2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_set_nat_rat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3))) (tptp.aa_set_nat_rat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat B3) A3)))) (tptp.aa_set_nat_rat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3)))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (F tptp.fun_nat_int)) (let ((_let_1 (tptp.groups3539618377306564664at_int F))) (let ((_let_2 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat _let_2)) (= (tptp.aa_set_nat_int _let_1 _let_2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_set_nat_int _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3))) (tptp.aa_set_nat_int _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat B3) A3)))) (tptp.aa_set_nat_int _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3)))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (F tptp.fun_nat_nat)) (let ((_let_1 (tptp.groups3542108847815614940at_nat F))) (let ((_let_2 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat _let_2)) (= (tptp.aa_set_nat_nat _let_1 _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_set_nat_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3))) (tptp.aa_set_nat_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat B3) A3)))) (tptp.aa_set_nat_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3)))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (F tptp.fun_int_int)) (let ((_let_1 (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int _let_1)) (= (tptp.groups4538972089207619220nt_int F _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups4538972089207619220nt_int F (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3))) (tptp.groups4538972089207619220nt_int F (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int B3) A3)))) (tptp.groups4538972089207619220nt_int F (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (F tptp.fun_Pr8317260874932935276at_rat)) (let ((_let_1 (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat A3) B3))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat _let_1)) (= (tptp.groups342789780944988191at_rat F _let_1) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups342789780944988191at_rat F (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat A3) B3))) (tptp.groups342789780944988191at_rat F (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat B3) A3)))) (tptp.groups342789780944988191at_rat F (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (= (tptp.groups3906332499630173760nt_rat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups3906332499630173760nt_rat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3))) (tptp.groups3906332499630173760nt_rat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int B3) A3)))) (tptp.groups3906332499630173760nt_rat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (= (tptp.groups6602215022474089585er_rat G (tptp.sup_su848401254843788991nteger A3 B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups6602215022474089585er_rat G (tptp.minus_2355218937544613996nteger A3 B3))) (tptp.groups6602215022474089585er_rat G (tptp.minus_2355218937544613996nteger B3 A3)))) (tptp.groups6602215022474089585er_rat G (tptp.inf_in1364745209274528805nteger A3 B3))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (= (tptp.groups4541462559716669496nt_nat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.groups4541462559716669496nt_nat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3))) (tptp.groups4541462559716669496nt_nat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int B3) A3)))) (tptp.groups4541462559716669496nt_nat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (= (tptp.groups7237345082560585321er_nat G (tptp.sup_su848401254843788991nteger A3 B3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.groups7237345082560585321er_nat G (tptp.minus_2355218937544613996nteger A3 B3))) (tptp.groups7237345082560585321er_nat G (tptp.minus_2355218937544613996nteger B3 A3)))) (tptp.groups7237345082560585321er_nat G (tptp.inf_in1364745209274528805nteger A3 B3))))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (= (tptp.groups7234854612051535045er_int G (tptp.sup_su848401254843788991nteger A3 B3)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups7234854612051535045er_int G (tptp.minus_2355218937544613996nteger A3 B3))) (tptp.groups7234854612051535045er_int G (tptp.minus_2355218937544613996nteger B3 A3)))) (tptp.groups7234854612051535045er_int G (tptp.inf_in1364745209274528805nteger A3 B3))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups2906978787729119204at_rat G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (= (tptp.aa_set_nat_rat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_set_nat_rat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3))) (tptp.aa_set_nat_rat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat B3) A3)))) (tptp.aa_set_nat_rat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3)))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.groups3539618377306564664at_int G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (= (tptp.aa_set_nat_int _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_set_nat_int _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3))) (tptp.aa_set_nat_int _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat B3) A3)))) (tptp.aa_set_nat_int _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3)))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.groups3542108847815614940at_nat G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (= (tptp.aa_set_nat_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_set_nat_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3))) (tptp.aa_set_nat_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat B3) A3)))) (tptp.aa_set_nat_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3)))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G tptp.fun_int_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (= (tptp.groups4538972089207619220nt_int G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups4538972089207619220nt_int G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3))) (tptp.groups4538972089207619220nt_int G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int B3) A3)))) (tptp.groups4538972089207619220nt_int G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (G tptp.fun_Pr8317260874932935276at_rat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat A3)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat B3)) (= (tptp.groups342789780944988191at_rat G (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat A3) B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.groups342789780944988191at_rat G (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat A3) B3))) (tptp.groups342789780944988191at_rat G (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat B3) A3)))) (tptp.groups342789780944988191at_rat G (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G tptp.fun_int_Code_integer)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (= (tptp.groups3827104343326376752nteger G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.groups3827104343326376752nteger G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3))) (tptp.groups3827104343326376752nteger G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int B3) A3)))) (tptp.groups3827104343326376752nteger G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (= (tptp.groups3674199335183972705nteger G (tptp.sup_su848401254843788991nteger A3 B3)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.groups3674199335183972705nteger G (tptp.minus_2355218937544613996nteger A3 B3))) (tptp.groups3674199335183972705nteger G (tptp.minus_2355218937544613996nteger B3 A3)))) (tptp.groups3674199335183972705nteger G (tptp.inf_in1364745209274528805nteger A3 B3))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.groups3455450783089532116nteger G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (= (tptp.aa_set871585252387937313nteger _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_set871585252387937313nteger _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3))) (tptp.aa_set871585252387937313nteger _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat B3) A3)))) (tptp.aa_set871585252387937313nteger _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3)))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G tptp.fun_int_assn)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (= (tptp.groups7882442080178216443t_assn G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups7882442080178216443t_assn G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3))) (tptp.groups7882442080178216443t_assn G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int B3) A3)))) (tptp.groups7882442080178216443t_assn G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Co4490034186337852034r_assn)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (= (tptp.groups1304777262505850412r_assn G (tptp.sup_su848401254843788991nteger A3 B3)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups1304777262505850412r_assn G (tptp.minus_2355218937544613996nteger A3 B3))) (tptp.groups1304777262505850412r_assn G (tptp.minus_2355218937544613996nteger B3 A3)))) (tptp.groups1304777262505850412r_assn G (tptp.inf_in1364745209274528805nteger A3 B3))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G tptp.fun_nat_assn)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (= (tptp.groups6906906614972039071t_assn G (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups6906906614972039071t_assn G (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3))) (tptp.groups6906906614972039071t_assn G (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat B3) A3)))) (tptp.groups6906906614972039071t_assn G (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (= (tptp.groups1072433553688619179nt_rat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.groups1072433553688619179nt_rat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3))) (tptp.groups1072433553688619179nt_rat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int B3) A3)))) (tptp.groups1072433553688619179nt_rat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (= (tptp.groups2555765274223993564er_rat G (tptp.sup_su848401254843788991nteger A3 B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.groups2555765274223993564er_rat G (tptp.minus_2355218937544613996nteger A3 B3))) (tptp.groups2555765274223993564er_rat G (tptp.minus_2355218937544613996nteger B3 A3)))) (tptp.groups2555765274223993564er_rat G (tptp.inf_in1364745209274528805nteger A3 B3))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups73079841787564623at_rat G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (= (tptp.aa_set_nat_rat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_set_nat_rat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3))) (tptp.aa_set_nat_rat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat B3) A3)))) (tptp.aa_set_nat_rat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3)))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (= (tptp.groups1707563613775114915nt_nat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.groups1707563613775114915nt_nat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3))) (tptp.groups1707563613775114915nt_nat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int B3) A3)))) (tptp.groups1707563613775114915nt_nat G (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))))))) (forall ((Z tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_rat tptp.numeral_numeral_rat _let_1))) (let ((_let_3 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_3) N2))) (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_2) Z)) _let_4) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_3) _let_4))) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat Z) N2))) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Z) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat tptp.one_one_rat) _let_2))) N2)))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_natural tptp.semiri3763490453095760265atural N2))) (= (tptp.groups6325495683096345652atural tptp.semiri3763490453095760265atural (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N2)) (tptp.divide5121882707175180666atural (tptp.times_2397367101498566445atural _let_1 (tptp.plus_p4538020629002901425atural _let_1 tptp.one_one_Code_natural)) (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) (= (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) (= (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (F tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (= (tptp.groups4541462559716669496nt_nat F (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.groups4541462559716669496nt_nat F A3)) (tptp.groups4541462559716669496nt_nat F B3))) (tptp.groups4541462559716669496nt_nat F (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (F tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (= (tptp.groups7237345082560585321er_nat F (tptp.sup_su848401254843788991nteger A3 B3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.groups7237345082560585321er_nat F A3)) (tptp.groups7237345082560585321er_nat F B3))) (tptp.groups7237345082560585321er_nat F (tptp.inf_in1364745209274528805nteger A3 B3))))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (F tptp.fun_Pr2602117396471556196at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat A3)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat B3)) (= (tptp.groups977919841031483927at_nat F (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat A3) B3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.groups977919841031483927at_nat F A3)) (tptp.groups977919841031483927at_nat F B3))) (tptp.groups977919841031483927at_nat F (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3))))))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (F tptp.fun_Pr2871540613828922186at_nat)) (=> (tptp.finite4392333629123659920at_nat A3) (=> (tptp.finite4392333629123659920at_nat B3) (= (tptp.groups1900718384385340925at_nat F (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3) B3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.groups1900718384385340925at_nat F A3)) (tptp.groups1900718384385340925at_nat F B3))) (tptp.groups1900718384385340925at_nat F (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat A3) B3))))))) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (F tptp.fun_Pr7574179848310716106at_nat)) (=> (tptp.finite1918287321285529104at_nat A3) (=> (tptp.finite1918287321285529104at_nat B3) (= (tptp.groups7059897769266147197at_nat F (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3) B3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.groups7059897769266147197at_nat F A3)) (tptp.groups7059897769266147197at_nat F B3))) (tptp.groups7059897769266147197at_nat F (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat A3) B3))))))) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (F tptp.fun_Pr1253225528153422666at_nat)) (=> (tptp.finite4343798906461161616at_nat A3) (=> (tptp.finite4343798906461161616at_nat B3) (= (tptp.groups3860910324918113789at_nat F (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3) B3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.groups3860910324918113789at_nat F A3)) (tptp.groups3860910324918113789at_nat F B3))) (tptp.groups3860910324918113789at_nat F (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat A3) B3))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (F tptp.fun_nat_nat)) (let ((_let_1 (tptp.groups3542108847815614940at_nat F))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (= (tptp.aa_set_nat_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_set_nat_nat _let_1 A3)) (tptp.aa_set_nat_nat _let_1 B3))) (tptp.aa_set_nat_nat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3)))))))) (forall ((G tptp.fun_nat_nat) (N2 tptp.nat) (M tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat N2) M)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_nat3783148529270815480at_nat (tptp.aTP_Lamm_jz G) N2) M)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc N2)) M)))) (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)) N2) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_nat3783148529270815480at_nat (tptp.aTP_Lamm_acj A) B) N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((G tptp.fun_nat_nat) (N2 tptp.nat) (M tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat G) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat N2) M)) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_nat3783148529270815480at_nat (tptp.aTP_Lamm_jz G) N2) M)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc N2)) M)))) (forall ((G tptp.fun_nat_int) (N2 tptp.nat) (M tptp.nat)) (= (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int G) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat N2) M)) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_nat_fun_nat_int (tptp.aa_nat1293065384339088724at_int (tptp.aTP_Lamm_nr G) N2) M)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc N2)) M)))) (forall ((R3 tptp.rat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc M))) (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_ack R3)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat _let_1)) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_rat (tptp.gbinomial_rat R3) _let_1))))) (forall ((A tptp.rat) (N2 tptp.nat)) (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat A) N2) (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat (tptp.aTP_Lamm_ok A)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger A) N2) (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger (tptp.aTP_Lamm_ol A)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)))) (forall ((A tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat A) N2) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_om A)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)))) (forall ((A tptp.int) (N2 tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int A) N2) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_int_fun_nat_int tptp.aTP_Lamm_on A)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)))) (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat)))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N2) _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_1 _let_2)) (tptp.aa_nat_nat _let_1 K))))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N2) K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat K)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K))))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat K)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N2) K))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N2)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K)))))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (= (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat tptp.suc) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat _let_1) N2)))) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat _let_1)))))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (= (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat tptp.suc) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat _let_1) N2)))) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int _let_1)))))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (= (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger N2) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat tptp.suc) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat _let_1) N2)))) (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger _let_1)))))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (= (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat tptp.suc) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat _let_1) N2)))) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat _let_1)))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_rat tptp.numeral_numeral_rat _let_1))) (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_2) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M))) tptp.one_one_rat))) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M)) (tptp.aa_nat_rat (tptp.power_power_rat _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) M)))))) (forall ((B3 tptp.set_bool) (A3 tptp.set_bool) (B tptp.bool) (F tptp.fun_bo7282069421189217543nteger)) (=> (tptp.finite_finite_bool B3) (=> (tptp.ord_less_eq_set_bool A3 B3) (=> (tptp.pp (tptp.member_bool B (tptp.minus_minus_set_bool B3 A3))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_bool_Code_integer F B))) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 B3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_bool_Code_integer F X3))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.groups1682264926906508858nteger F A3)) (tptp.groups1682264926906508858nteger F B3))))))))) (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B tptp.code_integer) (F tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) B3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer B) (tptp.minus_2355218937544613996nteger B3 A3))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger F B))) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) B3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger F X3))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.groups879477027807139574nteger F A3)) (tptp.groups879477027807139574nteger F B3))))))))) (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (B tptp.nat) (F tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.groups7501900531339628137nteger F))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) B3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat B3) A3))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer F B))) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) B3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer F X3))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_set871585252387937313nteger _let_1 A3)) (tptp.aa_set871585252387937313nteger _let_1 B3)))))))))) (forall ((B3 tptp.set_bool) (A3 tptp.set_bool) (B tptp.bool) (F tptp.fun_bool_rat)) (=> (tptp.finite_finite_bool B3) (=> (tptp.ord_less_eq_set_bool A3 B3) (=> (tptp.pp (tptp.member_bool B (tptp.minus_minus_set_bool B3 A3))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_bool_rat F B))) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 B3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_bool_rat F X3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups5133371213642249141ol_rat F A3)) (tptp.groups5133371213642249141ol_rat F B3))))))))) (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B tptp.code_integer) (F tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) B3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer B) (tptp.minus_2355218937544613996nteger B3 A3))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_Code_integer_rat F B))) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) B3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_Code_integer_rat F X3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups6602215022474089585er_rat F A3)) (tptp.groups6602215022474089585er_rat F B3))))))))) (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (B tptp.nat) (F tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups2906978787729119204at_rat F))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) B3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat B3) A3))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_nat_rat F B))) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) B3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat F X3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_set_nat_rat _let_1 A3)) (tptp.aa_set_nat_rat _let_1 B3)))))))))) (forall ((B3 tptp.set_bool) (A3 tptp.set_bool) (B tptp.bool) (F tptp.fun_bool_nat)) (=> (tptp.finite_finite_bool B3) (=> (tptp.ord_less_eq_set_bool A3 B3) (=> (tptp.pp (tptp.member_bool B (tptp.minus_minus_set_bool B3 A3))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_bool_nat F B))) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 B3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_bool_nat F X3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.groups5768501273728744877ol_nat F A3)) (tptp.groups5768501273728744877ol_nat F B3))))))))) (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B tptp.code_integer) (F tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) B3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer B) (tptp.minus_2355218937544613996nteger B3 A3))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_Code_integer_nat F B))) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) B3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_Code_integer_nat F X3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.groups7237345082560585321er_nat F A3)) (tptp.groups7237345082560585321er_nat F B3))))))))) (forall ((B3 tptp.set_bool) (A3 tptp.set_bool) (B tptp.bool) (F tptp.fun_bool_int)) (=> (tptp.finite_finite_bool B3) (=> (tptp.ord_less_eq_set_bool A3 B3) (=> (tptp.pp (tptp.member_bool B (tptp.minus_minus_set_bool B3 A3))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_bool_int F B))) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 B3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_bool_int F X3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.groups5766010803219694601ol_int F A3)) (tptp.groups5766010803219694601ol_int F B3))))))))) (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B tptp.code_integer) (F tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) B3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer B) (tptp.minus_2355218937544613996nteger B3 A3))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_Code_integer_int F B))) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) B3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_Code_integer_int F X3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.groups7234854612051535045er_int F A3)) (tptp.groups7234854612051535045er_int F B3))))))))) (forall ((B3 tptp.set_bool) (A3 tptp.set_bool) (F tptp.fun_bo7282069421189217543nteger)) (=> (tptp.finite_finite_bool B3) (=> (tptp.ord_less_eq_set_bool A3 B3) (=> (forall ((B4 tptp.bool)) (=> (tptp.pp (tptp.member_bool B4 (tptp.minus_minus_set_bool B3 A3))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (tptp.aa_bool_Code_integer F B4))))) (=> (forall ((A4 tptp.bool)) (=> (tptp.pp (tptp.member_bool A4 A3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_bool_Code_integer F A4))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.groups7272450149305381519nteger F A3)) (tptp.groups7272450149305381519nteger F B3)))))))) (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (F tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) B3)) (=> (forall ((B4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer B4) (tptp.minus_2355218937544613996nteger B3 A3))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger F B4))))) (=> (forall ((A4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A4) A3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger F A4))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.groups3674199335183972705nteger F A3)) (tptp.groups3674199335183972705nteger F B3)))))))) (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (F tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.groups3455450783089532116nteger F))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) B3)) (=> (forall ((B4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B4) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat B3) A3))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (tptp.aa_nat_Code_integer F B4))))) (=> (forall ((A4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A4) A3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer F A4))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_set871585252387937313nteger _let_1 A3)) (tptp.aa_set871585252387937313nteger _let_1 B3))))))))) (forall ((B3 tptp.set_bool) (A3 tptp.set_bool) (F tptp.fun_bool_rat)) (=> (tptp.finite_finite_bool B3) (=> (tptp.ord_less_eq_set_bool A3 B3) (=> (forall ((B4 tptp.bool)) (=> (tptp.pp (tptp.member_bool B4 (tptp.minus_minus_set_bool B3 A3))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_bool_rat F B4))))) (=> (forall ((A4 tptp.bool)) (=> (tptp.pp (tptp.member_bool A4 A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_bool_rat F A4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups1259819201609700362ol_rat F A3)) (tptp.groups1259819201609700362ol_rat F B3)))))))) (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (F tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) B3)) (=> (forall ((B4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer B4) (tptp.minus_2355218937544613996nteger B3 A3))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_Code_integer_rat F B4))))) (=> (forall ((A4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A4) A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_Code_integer_rat F A4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups2555765274223993564er_rat F A3)) (tptp.groups2555765274223993564er_rat F B3)))))))) (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (F tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups73079841787564623at_rat F))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) B3)) (=> (forall ((B4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B4) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat B3) A3))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_nat_rat F B4))))) (=> (forall ((A4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A4) A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat F A4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_set_nat_rat _let_1 A3)) (tptp.aa_set_nat_rat _let_1 B3))))))))) (forall ((B3 tptp.set_bool) (A3 tptp.set_bool) (F tptp.fun_bool_int)) (=> (tptp.finite_finite_bool B3) (=> (tptp.ord_less_eq_set_bool A3 B3) (=> (forall ((B4 tptp.bool)) (=> (tptp.pp (tptp.member_bool B4 (tptp.minus_minus_set_bool B3 A3))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) (tptp.aa_bool_int F B4))))) (=> (forall ((A4 tptp.bool)) (=> (tptp.pp (tptp.member_bool A4 A3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_bool_int F A4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.groups1892458791187145822ol_int F A3)) (tptp.groups1892458791187145822ol_int F B3)))))))) (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (F tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) B3)) (=> (forall ((B4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer B4) (tptp.minus_2355218937544613996nteger B3 A3))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) (tptp.aa_Code_integer_int F B4))))) (=> (forall ((A4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A4) A3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_Code_integer_int F A4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.groups3188404863801439024er_int F A3)) (tptp.groups3188404863801439024er_int F B3)))))))) (forall ((B3 tptp.set_int) (A3 tptp.set_int) (F tptp.fun_int_Code_integer)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (=> (forall ((B4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int B4) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int B3) A3))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (tptp.aa_int_Code_integer F B4))))) (=> (forall ((A4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A4) A3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_int_Code_integer F A4))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.groups3827104343326376752nteger F A3)) (tptp.groups3827104343326376752nteger F B3)))))))) (forall ((B3 tptp.set_int) (A3 tptp.set_int) (F tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (=> (forall ((B4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int B4) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int B3) A3))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_int_rat F B4))))) (=> (forall ((A4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A4) A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_int_rat F A4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups1072433553688619179nt_rat F A3)) (tptp.groups1072433553688619179nt_rat F B3)))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (F tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3))) (not (= (tptp.aa_int_rat F X3) tptp.zero_zero_rat)))) (= (tptp.groups1072433553688619179nt_rat F (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int A3) B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.groups1072433553688619179nt_rat F A3)) (tptp.groups1072433553688619179nt_rat F B3))) (tptp.groups1072433553688619179nt_rat F (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) B3)))))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (F tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) (tptp.inf_in1364745209274528805nteger A3 B3))) (not (= (tptp.aa_Code_integer_rat F X3) tptp.zero_zero_rat)))) (= (tptp.groups2555765274223993564er_rat F (tptp.sup_su848401254843788991nteger A3 B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.groups2555765274223993564er_rat F A3)) (tptp.groups2555765274223993564er_rat F B3))) (tptp.groups2555765274223993564er_rat F (tptp.inf_in1364745209274528805nteger A3 B3)))))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (F tptp.fun_Pr8317260874932935276at_rat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat A3)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat B3)) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat X3) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3))) (not (= (tptp.aa_Pro3608043709957902237at_rat F X3) tptp.zero_zero_rat)))) (= (tptp.groups3442636767675653108at_rat F (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat A3) B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.groups3442636767675653108at_rat F A3)) (tptp.groups3442636767675653108at_rat F B3))) (tptp.groups3442636767675653108at_rat F (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat A3) B3)))))))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (F tptp.fun_Pr8586684092290301266at_rat)) (=> (tptp.finite4392333629123659920at_nat A3) (=> (tptp.finite4392333629123659920at_nat B3) (=> (forall ((X3 tptp.produc859450856879609959at_nat)) (=> (tptp.member8206827879206165904at_nat X3 (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat A3) B3)) (not (= (tptp.aa_Pro7042314473122848387at_rat F X3) tptp.zero_zero_rat)))) (= (tptp.groups7136053025338371162at_rat F (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3) B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.groups7136053025338371162at_rat F A3)) (tptp.groups7136053025338371162at_rat F B3))) (tptp.groups7136053025338371162at_rat F (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.inf_in4302113700860409141at_nat A3) B3)))))))) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (F tptp.fun_Pr4065951289917319378at_rat)) (=> (tptp.finite1918287321285529104at_nat A3) (=> (tptp.finite1918287321285529104at_nat B3) (=> (forall ((X3 tptp.produc4166570645942440679at_nat)) (=> (tptp.member6689249552917799696at_nat X3 (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat A3) B3)) (not (= (tptp.aa_Pro6772482835110228483at_rat F X3) tptp.zero_zero_rat)))) (= (tptp.groups5938585286922990810at_rat F (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3) B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.groups5938585286922990810at_rat F A3)) (tptp.groups5938585286922990810at_rat F B3))) (tptp.groups5938585286922990810at_rat F (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.inf_in1697001100524423349at_nat A3) B3)))))))) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (F tptp.fun_Pr6968369006614801746at_rat)) (=> (tptp.finite4343798906461161616at_nat A3) (=> (tptp.finite4343798906461161616at_nat B3) (=> (forall ((X3 tptp.produc3843707927480180839at_nat)) (=> (tptp.member8757157785044589968at_nat X3 (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat A3) B3)) (not (= (tptp.aa_Pro5677984708781969027at_rat F X3) tptp.zero_zero_rat)))) (= (tptp.groups8874911130973611098at_rat F (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3) B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.groups8874911130973611098at_rat F A3)) (tptp.groups8874911130973611098at_rat F B3))) (tptp.groups8874911130973611098at_rat F (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.inf_in7913087082777306421at_nat A3) B3)))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (F tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups73079841787564623at_rat F))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3))) (not (= (tptp.aa_nat_rat F X3) tptp.zero_zero_rat)))) (= (tptp.aa_set_nat_rat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_set_nat_rat _let_1 A3)) (tptp.aa_set_nat_rat _let_1 B3))) (tptp.aa_set_nat_rat _let_1 (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) B3))))))))) (forall ((A tptp.rat) (M tptp.nat)) (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_ack A)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) tptp.one_one_rat)) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_rat (tptp.gbinomial_rat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) tptp.one_one_nat))))) (forall ((A tptp.rat) (B tptp.rat) (N2 tptp.nat)) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B)) N2) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aTP_Lamm_acl A) B) N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) N2) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aa_nat_fun_nat_int (tptp.aa_int431785320988601264at_int (tptp.aTP_Lamm_acm A) B) N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((A tptp.code_integer) (B tptp.code_integer) (N2 tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) B)) N2) (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger (tptp.aa_nat2010205248571845816nteger (tptp.aa_Cod3140087502949435154nteger (tptp.aTP_Lamm_acn A) B) N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)) N2) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_nat3783148529270815480at_nat (tptp.aTP_Lamm_acj A) B) N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((A tptp.rat) (B tptp.rat) (N2 tptp.nat)) (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat A) B)) N2) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aTP_Lamm_aco A) B) N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) N2) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aa_nat_fun_nat_int (tptp.aa_int431785320988601264at_int (tptp.aTP_Lamm_acp A) B) N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((A tptp.code_integer) (B tptp.code_integer) (N2 tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger A) B)) N2) (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger (tptp.aa_nat2010205248571845816nteger (tptp.aa_Cod3140087502949435154nteger (tptp.aTP_Lamm_acq A) B) N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((A tptp.rat) (K tptp.nat)) (= (tptp.aa_nat_rat (tptp.gbinomial_rat A) K) (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat (tptp.aa_nat_fun_nat_rat (tptp.aTP_Lamm_acr A) K)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K)))) (forall ((A tptp.rat) (K tptp.nat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.gbinomial_rat A) K)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat K)) (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat (tptp.aTP_Lamm_md A)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K)))) (forall ((K tptp.nat) (A tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat K)) (tptp.aa_nat_rat (tptp.gbinomial_rat A) K)) (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat (tptp.aTP_Lamm_md A)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K)))) (forall ((K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int K) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)))) (forall ((K tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int K) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.pp (tptp.aa_int_bool _let_1 K))))) (forall ((L tptp.num) (R3 tptp.nat) (Q5 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Q5))) (let ((_let_2 (tptp.aa_Pro262675715343573244at_nat (tptp.unique5026877609467782581ep_nat L) (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat Q5) R3)))) (let ((_let_3 (tptp.aa_num_nat tptp.numeral_numeral_nat L))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_3) R3)))) (and (=> _let_4 (= _let_2 (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat R3) _let_3)))) (=> (not _let_4) (= _let_2 (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat _let_1) R3))))))))) (forall ((L tptp.num) (R3 tptp.int) (Q5 tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) Q5))) (let ((_let_2 (tptp.aa_Pro6970504127699319548nt_int (tptp.unique5024387138958732305ep_int L) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q5) R3)))) (let ((_let_3 (tptp.aa_num_int tptp.numeral_numeral_int L))) (let ((_let_4 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_3) R3)))) (and (=> _let_4 (= _let_2 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int R3) _let_3)))) (=> (not _let_4) (= _let_2 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int _let_1) R3))))))))) (forall ((L tptp.num) (R3 tptp.code_integer) (Q5 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) Q5))) (let ((_let_2 (tptp.unique4921790084139445826nteger L (tptp.produc1086072967326762835nteger Q5 R3)))) (let ((_let_3 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger L))) (let ((_let_4 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger _let_3) R3)))) (and (=> _let_4 (= _let_2 (tptp.produc1086072967326762835nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger R3) _let_3)))) (=> (not _let_4) (= _let_2 (tptp.produc1086072967326762835nteger _let_1 R3))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat _let_1 M))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) _let_2)) (tptp.aa_nat_nat _let_1 N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M)))) _let_2)))))) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_int _let_1 M))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) _let_2)) (tptp.aa_nat_int _let_1 N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M)))) _let_2)))))) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_Code_integer _let_1 M))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) _let_2)) (tptp.aa_nat_Code_integer _let_1 N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) (tptp.aa_nat_Code_integer _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M)))) _let_2)))))) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.code_natural)) (let ((_let_1 (tptp.power_7079662738309270450atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_Code_natural _let_1 M))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.modulo8411746178871703098atural (tptp.times_2397367101498566445atural A _let_2) (tptp.aa_nat_Code_natural _let_1 N2)) (tptp.times_2397367101498566445atural (tptp.modulo8411746178871703098atural A (tptp.aa_nat_Code_natural _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M))) _let_2)))))) (forall ((P tptp.fun_nat_bool) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat)) (=> (forall ((N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P N5)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N5)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N5)))))) (=> (forall ((N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P N5)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N5)))))) (tptp.pp (tptp.aa_nat_bool P N2)))))) (forall ((K tptp.nat)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_df K))))) (forall ((P tptp.fun_Pr803113274115125473t_bool) (Q tptp.fun_Pr803113274115125473t_bool)) (=> (or (tptp.finite2998713641127702882nt_int (tptp.collec213857154873943460nt_int P)) (tptp.finite2998713641127702882nt_int (tptp.collec213857154873943460nt_int Q))) (tptp.finite2998713641127702882nt_int (tptp.collec213857154873943460nt_int (tptp.aa_fun8917503761599146496t_bool (tptp.aTP_Lamm_bp P) Q))))) (forall ((P tptp.fun_list_nat_bool) (Q tptp.fun_list_nat_bool)) (=> (or (tptp.finite8100373058378681591st_nat (tptp.collect_list_nat P)) (tptp.finite8100373058378681591st_nat (tptp.collect_list_nat Q))) (tptp.finite8100373058378681591st_nat (tptp.collect_list_nat (tptp.aa_fun6009467934925565500t_bool (tptp.aTP_Lamm_bq P) Q))))) (forall ((P tptp.fun_set_nat_bool) (Q tptp.fun_set_nat_bool)) (=> (or (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat (tptp.collect_set_nat P))) (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat (tptp.collect_set_nat Q)))) (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat (tptp.collect_set_nat (tptp.aa_fun3565389549526402364t_bool (tptp.aTP_Lamm_br P) Q)))))) (forall ((P tptp.fun_nat_bool) (Q tptp.fun_nat_bool)) (=> (or (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat P))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat Q)))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_bt P) Q)))))) (forall ((P tptp.fun_int_bool) (Q tptp.fun_int_bool)) (=> (or (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int P))) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int Q)))) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun5146555767781538748t_bool (tptp.aTP_Lamm_bs P) Q)))))) (forall ((P tptp.fun_Co8822979462182099027r_bool) (Q tptp.fun_Co8822979462182099027r_bool)) (=> (or (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.collect_Code_integer P))) (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.collect_Code_integer Q)))) (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.collect_Code_integer (tptp.aa_fun8875953811088571772r_bool (tptp.aTP_Lamm_acs P) Q)))))) (forall ((P tptp.fun_Pr7757163693017731481t_bool) (Q tptp.fun_Pr7757163693017731481t_bool)) (=> (or (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat (tptp.collec3392354462482085612at_nat P))) (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat (tptp.collec3392354462482085612at_nat Q)))) (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat (tptp.collec3392354462482085612at_nat (tptp.aa_fun830836278467416944t_bool (tptp.aTP_Lamm_bu P) Q)))))) (forall ((P tptp.fun_Pr803113274115125473t_bool) (Q tptp.fun_Pr803113274115125473t_bool)) (= (tptp.finite2998713641127702882nt_int (tptp.collec213857154873943460nt_int (tptp.aa_fun8917503761599146496t_bool (tptp.aTP_Lamm_cf P) Q))) (and (tptp.finite2998713641127702882nt_int (tptp.collec213857154873943460nt_int P)) (tptp.finite2998713641127702882nt_int (tptp.collec213857154873943460nt_int Q))))) (forall ((P tptp.fun_list_nat_bool) (Q tptp.fun_list_nat_bool)) (= (tptp.finite8100373058378681591st_nat (tptp.collect_list_nat (tptp.aa_fun6009467934925565500t_bool (tptp.aTP_Lamm_cg P) Q))) (and (tptp.finite8100373058378681591st_nat (tptp.collect_list_nat P)) (tptp.finite8100373058378681591st_nat (tptp.collect_list_nat Q))))) (forall ((P tptp.fun_set_nat_bool) (Q tptp.fun_set_nat_bool)) (= (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat (tptp.collect_set_nat (tptp.aa_fun3565389549526402364t_bool (tptp.aTP_Lamm_ch P) Q)))) (and (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat (tptp.collect_set_nat P))) (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat (tptp.collect_set_nat Q)))))) (forall ((P tptp.fun_nat_bool) (Q tptp.fun_nat_bool)) (= (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_cm P) Q)))) (and (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat P))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat Q)))))) (forall ((P tptp.fun_int_bool) (Q tptp.fun_int_bool)) (= (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun5146555767781538748t_bool (tptp.aTP_Lamm_ci P) Q)))) (and (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int P))) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int Q)))))) (forall ((P tptp.fun_Co8822979462182099027r_bool) (Q tptp.fun_Co8822979462182099027r_bool)) (= (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.collect_Code_integer (tptp.aa_fun8875953811088571772r_bool (tptp.aTP_Lamm_act P) Q)))) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.collect_Code_integer P))) (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.collect_Code_integer Q)))))) (forall ((P tptp.fun_Pr7757163693017731481t_bool) (Q tptp.fun_Pr7757163693017731481t_bool)) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat (tptp.collec3392354462482085612at_nat (tptp.aa_fun830836278467416944t_bool (tptp.aTP_Lamm_acu P) Q)))) (and (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat (tptp.collec3392354462482085612at_nat P))) (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat (tptp.collec3392354462482085612at_nat Q)))))) (forall ((A tptp.int) (B tptp.int)) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_acv A) B))))) (forall ((A tptp.int) (B tptp.int)) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_acw A) B))))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2) N2)) (forall ((F3 tptp.set_int) (G2 tptp.set_int)) (=> (or (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int F3)) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int G2))) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int F3) G2))))) (forall ((F3 tptp.set_Code_integer) (G2 tptp.set_Code_integer)) (=> (or (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger F3)) (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger G2))) (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.inf_in1364745209274528805nteger F3 G2))))) (forall ((F3 tptp.set_nat) (G2 tptp.set_nat)) (=> (or (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat F3)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat G2))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat F3) G2))))) (forall ((F3 tptp.set_Pr1261947904930325089at_nat) (G2 tptp.set_Pr1261947904930325089at_nat)) (=> (or (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat F3)) (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat G2))) (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat F3) G2))))) (forall ((F3 tptp.set_int) (G2 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int F3) G2))) (and (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int F3)) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int G2))))) (forall ((F3 tptp.set_Code_integer) (G2 tptp.set_Code_integer)) (= (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.sup_su848401254843788991nteger F3 G2))) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger F3)) (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger G2))))) (forall ((F3 tptp.set_Pr1261947904930325089at_nat) (G2 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat F3) G2))) (and (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat F3)) (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat G2))))) (forall ((F3 tptp.set_Pr8693737435421807431at_nat) (G2 tptp.set_Pr8693737435421807431at_nat)) (= (tptp.finite4392333629123659920at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat F3) G2)) (and (tptp.finite4392333629123659920at_nat F3) (tptp.finite4392333629123659920at_nat G2)))) (forall ((F3 tptp.set_Pr8551490117392284871at_nat) (G2 tptp.set_Pr8551490117392284871at_nat)) (= (tptp.finite1918287321285529104at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat F3) G2)) (and (tptp.finite1918287321285529104at_nat F3) (tptp.finite1918287321285529104at_nat G2)))) (forall ((F3 tptp.set_Pr4329608150637261639at_nat) (G2 tptp.set_Pr4329608150637261639at_nat)) (= (tptp.finite4343798906461161616at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat F3) G2)) (and (tptp.finite4343798906461161616at_nat F3) (tptp.finite4343798906461161616at_nat G2)))) (forall ((F3 tptp.set_nat) (G2 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat F3) G2))) (and (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat F3)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat G2))))) (forall ((A tptp.int) (B tptp.int)) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_acx A) B))))) (forall ((A tptp.int) (B tptp.int)) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_acy A) B))))) (forall ((K tptp.nat)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_dg K))))) (forall ((A3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat (tptp.collect_set_nat (tptp.aa_set5116768664143533222t_bool tptp.aTP_Lamm_cz A3)))))) (forall ((A3 tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (tptp.finite6931041176100689706nteger (tptp.collec574505750873337192nteger (tptp.aTP_Lamm_acz A3))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat A3)) (tptp.finite9047747110432174090at_nat (tptp.collec5514110066124741708at_nat (tptp.aa_set7594618562247239262t_bool tptp.aTP_Lamm_cv A3))))) (forall ((A3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (tptp.finite6197958912794628473et_int (tptp.collect_set_int (tptp.aa_set7694327796961020398t_bool tptp.aTP_Lamm_dd A3))))) (forall ((M6 tptp.set_list_nat)) (=> (tptp.finite8100373058378681591st_nat M6) (exists ((N5 tptp.nat)) (forall ((X5 tptp.list_nat)) (=> (tptp.member_list_nat X5 M6) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_list_nat_nat tptp.size_size_list_nat X5)) N5))))))) (forall ((M6 tptp.set_list_bool)) (=> (tptp.finite7866827932528546246t_bool M6) (exists ((N5 tptp.nat)) (forall ((X5 tptp.list_bool)) (=> (tptp.member_list_bool X5 M6) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.size_size_list_bool X5)) N5))))))) (forall ((L tptp.int) (U tptp.int)) (= (tptp.image_int_int (tptp.aa_int_fun_int_int tptp.aTP_Lamm_ht L) (tptp.set_or4662586982721622107an_int tptp.zero_zero_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int U) L))) (tptp.set_or4662586982721622107an_int L U))) (forall ((P tptp.fun_Pr803113274115125473t_bool)) (=> (not (tptp.finite2998713641127702882nt_int (tptp.collec213857154873943460nt_int P))) (exists ((X_1 tptp.product_prod_int_int)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool P X_1))))) (forall ((P tptp.fun_list_nat_bool)) (=> (not (tptp.finite8100373058378681591st_nat (tptp.collect_list_nat P))) (exists ((X_1 tptp.list_nat)) (tptp.pp (tptp.aa_list_nat_bool P X_1))))) (forall ((P tptp.fun_set_nat_bool)) (=> (not (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat (tptp.collect_set_nat P)))) (exists ((X_1 tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool P X_1))))) (forall ((P tptp.fun_nat_bool)) (=> (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat P)))) (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool P X_1))))) (forall ((P tptp.fun_int_bool)) (=> (not (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int P)))) (exists ((X_1 tptp.int)) (tptp.pp (tptp.aa_int_bool P X_1))))) (forall ((P tptp.fun_Co8822979462182099027r_bool)) (=> (not (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.collect_Code_integer P)))) (exists ((X_1 tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool P X_1))))) (forall ((P tptp.fun_Pr7757163693017731481t_bool)) (=> (not (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat (tptp.collec3392354462482085612at_nat P)))) (exists ((X_1 tptp.product_prod_nat_nat)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool P X_1))))) (forall ((A3 tptp.set_bool) (B3 tptp.set_nat) (R tptp.fun_bo3288154511880838028t_bool)) (=> (not (tptp.finite_finite_bool A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 A3)) (exists ((Xa3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa3) B3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_bool_fun_nat_bool R X3) Xa3)))))) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) B3)) (not (tptp.finite_finite_bool (tptp.collect_bool (tptp.aa_nat_fun_bool_bool (tptp.aa_fun4163026448321506586l_bool (tptp.aTP_Lamm_rg A3) R) X3)))))))))) (forall ((A3 tptp.set_bool) (B3 tptp.set_int) (R tptp.fun_bo2827871560234191408t_bool)) (=> (not (tptp.finite_finite_bool A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 A3)) (exists ((Xa3 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa3) B3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_bool_fun_int_bool R X3) Xa3)))))) (exists ((X3 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) B3)) (not (tptp.finite_finite_bool (tptp.collect_bool (tptp.aa_int_fun_bool_bool (tptp.aa_fun6035399485891414554l_bool (tptp.aTP_Lamm_rv A3) R) X3)))))))))) (forall ((A3 tptp.set_bool) (B3 tptp.set_Code_integer) (R tptp.fun_bo284609390884453567r_bool)) (=> (not (tptp.finite_finite_bool A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 A3)) (exists ((Xa3 tptp.code_integer)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Xa3) B3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_boo5858427943822696632r_bool R X3) Xa3)))))) (exists ((X3 tptp.code_integer)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) B3)) (not (tptp.finite_finite_bool (tptp.collect_bool (tptp.aa_Cod8494480694608518558l_bool (tptp.aa_fun9176172261886745818l_bool (tptp.aTP_Lamm_ada A3) R) X3)))))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (R tptp.fun_nat_fun_nat_bool)) (=> (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (exists ((Xa3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa3) B3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R X3) Xa3)))))) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) B3)) (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aa_fun3051233943552222972t_bool (tptp.aTP_Lamm_sv A3) R) X3))))))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_int) (R tptp.fun_nat_fun_int_bool)) (=> (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (exists ((Xa3 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa3) B3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_nat_fun_int_bool R X3) Xa3)))))) (exists ((X3 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) B3)) (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_int_fun_nat_bool (tptp.aa_fun8184653438340336124t_bool (tptp.aTP_Lamm_rz A3) R) X3))))))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_Code_integer) (R tptp.fun_na7774394808840722396r_bool)) (=> (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (exists ((Xa3 tptp.code_integer)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Xa3) B3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_nat6120813132205607877r_bool R X3) Xa3)))))) (exists ((X3 tptp.code_integer)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) B3)) (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_Cod2498268374540730821t_bool (tptp.aa_fun6816041618782723900t_bool (tptp.aTP_Lamm_sr A3) R) X3))))))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_nat) (R tptp.fun_int_fun_nat_bool)) (=> (not (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (exists ((Xa3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa3) B3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool R X3) Xa3)))))) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) B3)) (not (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int 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tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) A3)) (exists ((Xa3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa3) B3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_Cod2498268374540730821t_bool R X3) Xa3)))))) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) B3)) (not (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.collect_Code_integer (tptp.aa_nat6120813132205607877r_bool (tptp.aa_fun8839232882156773436r_bool (tptp.aTP_Lamm_rq A3) R) X3))))))))))) (forall ((A3 tptp.set_bool) (A tptp.bool)) (=> (tptp.finite_finite_bool A3) (=> (tptp.pp (tptp.member_bool A A3)) (exists ((X3 tptp.bool)) (and (tptp.pp (tptp.member_bool X3 A3)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.ord_less_eq_bool A) X3)) (forall ((Xa3 tptp.bool)) (=> (tptp.pp (tptp.member_bool Xa3 A3)) (=> (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.ord_less_eq_bool X3) Xa3)) (= (tptp.pp X3) (tptp.pp Xa3)))))))))) (forall ((A3 tptp.set_set_nat) (A tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat A3)) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat A) A3)) (exists ((X3 tptp.set_nat)) (and (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat X3) A3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A) X3)) (forall ((Xa3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat Xa3) A3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat X3) Xa3)) (= X3 Xa3))))))))) (forall ((A3 tptp.set_Code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A) A3)) (exists ((X3 tptp.code_integer)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) A3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) X3)) (forall ((Xa3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Xa3) A3)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger X3) Xa3)) (= X3 Xa3))))))))) (forall ((A3 tptp.set_set_int) (A tptp.set_int)) (=> (tptp.finite6197958912794628473et_int A3) (=> (tptp.member_set_int A A3) (exists ((X3 tptp.set_int)) (and (tptp.member_set_int X3 A3) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A) X3)) (forall ((Xa3 tptp.set_int)) (=> (tptp.member_set_int Xa3 A3) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X3) Xa3)) (= X3 Xa3))))))))) (forall ((A3 tptp.set_rat) (A tptp.rat)) (=> (tptp.finite_finite_rat A3) (=> (tptp.member_rat A A3) (exists ((X3 tptp.rat)) (and (tptp.member_rat X3 A3) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) X3)) (forall ((Xa3 tptp.rat)) (=> (tptp.member_rat Xa3 A3) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Xa3)) (= X3 Xa3))))))))) (forall ((A3 tptp.set_num) (A tptp.num)) (=> (tptp.finite_finite_num A3) (=> (tptp.member_num A A3) (exists ((X3 tptp.num)) (and (tptp.member_num X3 A3) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) X3)) (forall ((Xa3 tptp.num)) (=> (tptp.member_num Xa3 A3) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Xa3)) (= X3 Xa3))))))))) (forall ((A3 tptp.set_nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A) A3)) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) X3)) (forall ((Xa3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa3) A3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) Xa3)) (= X3 Xa3))))))))) (forall ((A3 tptp.set_int) (A tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A) A3)) (exists ((X3 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) X3)) (forall ((Xa3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa3) A3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X3) Xa3)) (= X3 Xa3))))))))) (forall ((A3 tptp.set_bool) (A tptp.bool)) (=> (tptp.finite_finite_bool A3) (=> (tptp.pp (tptp.member_bool A A3)) (exists ((X3 tptp.bool)) (and (tptp.pp (tptp.member_bool X3 A3)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.ord_less_eq_bool X3) A)) (forall ((Xa3 tptp.bool)) (=> (tptp.pp (tptp.member_bool Xa3 A3)) (=> (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.ord_less_eq_bool Xa3) X3)) (= (tptp.pp X3) (tptp.pp Xa3)))))))))) (forall ((A3 tptp.set_set_nat) (A tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat A3)) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat A) A3)) (exists ((X3 tptp.set_nat)) (and (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat X3) A3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat X3) A)) (forall ((Xa3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat Xa3) A3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat Xa3) X3)) (= X3 Xa3))))))))) (forall ((A3 tptp.set_Code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A) A3)) (exists ((X3 tptp.code_integer)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) A3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger X3) A)) (forall ((Xa3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Xa3) A3)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger Xa3) X3)) (= X3 Xa3))))))))) (forall ((A3 tptp.set_set_int) (A tptp.set_int)) (=> (tptp.finite6197958912794628473et_int A3) (=> (tptp.member_set_int A A3) (exists ((X3 tptp.set_int)) (and (tptp.member_set_int X3 A3) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X3) A)) (forall ((Xa3 tptp.set_int)) (=> (tptp.member_set_int Xa3 A3) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int Xa3) X3)) (= X3 Xa3))))))))) (forall ((A3 tptp.set_rat) (A tptp.rat)) (=> (tptp.finite_finite_rat A3) (=> (tptp.member_rat A A3) (exists ((X3 tptp.rat)) (and (tptp.member_rat X3 A3) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) A)) (forall ((Xa3 tptp.rat)) (=> (tptp.member_rat Xa3 A3) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Xa3) X3)) (= X3 Xa3))))))))) (forall ((A3 tptp.set_num) (A tptp.num)) (=> (tptp.finite_finite_num A3) (=> (tptp.member_num A A3) (exists ((X3 tptp.num)) (and (tptp.member_num X3 A3) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) A)) (forall ((Xa3 tptp.num)) (=> (tptp.member_num Xa3 A3) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Xa3) X3)) (= X3 Xa3))))))))) (forall ((A3 tptp.set_nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A) A3)) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) A)) (forall ((Xa3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa3) A3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Xa3) X3)) (= X3 Xa3))))))))) (forall ((A3 tptp.set_int) (A tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A) A3)) (exists ((X3 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X3) A)) (forall ((Xa3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa3) A3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Xa3) X3)) (= X3 Xa3))))))))) (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger tptp.bot_bo3990330152332043303nteger)) (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat tptp.bot_bo2099793752762293965at_nat)) (tptp.finite_finite_bool tptp.bot_bot_set_bool) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat tptp.bot_bot_set_nat)) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int tptp.bot_bot_set_int)) (forall ((S tptp.set_Code_integer)) (=> (not (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S))) (not (= S tptp.bot_bo3990330152332043303nteger)))) (forall ((S tptp.set_Pr1261947904930325089at_nat)) (=> (not (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat S))) (not (= S tptp.bot_bo2099793752762293965at_nat)))) (forall ((S tptp.set_bool)) (=> (not (tptp.finite_finite_bool S)) (not (= S tptp.bot_bot_set_bool)))) (forall ((S tptp.set_nat)) (=> (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S))) (not (= S tptp.bot_bot_set_nat)))) (forall ((S tptp.set_int)) (=> (not (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S))) (not (= S tptp.bot_bot_set_int)))) (forall ((F tptp.fun_nat_set_nat) (A3 tptp.set_nat) (P tptp.fun_set_set_nat_bool)) (= (forall ((B6 tptp.set_set_nat)) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat B6) (tptp.image_nat_set_nat F A3))) (tptp.pp (tptp.aa_set_set_nat_bool P B6)))) (forall ((B6 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B6) A3)) (tptp.pp (tptp.aa_set_set_nat_bool P (tptp.image_nat_set_nat F B6))))))) (forall ((F tptp.fun_nat_nat) (A3 tptp.set_nat) (P tptp.fun_set_nat_bool)) (= (forall ((B6 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B6) (tptp.image_nat_nat F A3))) (tptp.pp (tptp.aa_set_nat_bool P B6)))) (forall ((B6 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B6) A3)) (tptp.pp (tptp.aa_set_nat_bool P (tptp.image_nat_nat F B6))))))) (forall ((F tptp.fun_int_nat) (A3 tptp.set_int) (P tptp.fun_set_nat_bool)) (= (forall ((B6 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B6) (tptp.image_int_nat F A3))) (tptp.pp (tptp.aa_set_nat_bool P B6)))) (forall ((B6 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B6) A3)) (tptp.pp (tptp.aa_set_nat_bool P (tptp.image_int_nat F B6))))))) (forall ((F tptp.fun_nat_int) (A3 tptp.set_nat) (P tptp.fun_set_int_bool)) (= (forall ((B6 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B6) (tptp.image_nat_int F A3))) (tptp.pp (tptp.aa_set_int_bool P B6)))) (forall ((B6 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B6) A3)) (tptp.pp (tptp.aa_set_int_bool P (tptp.image_nat_int F B6))))))) (forall ((F tptp.fun_int_int) (A3 tptp.set_int) (P tptp.fun_set_int_bool)) (= (forall ((B6 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B6) (tptp.image_int_int F A3))) (tptp.pp (tptp.aa_set_int_bool P B6)))) (forall ((B6 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B6) A3)) (tptp.pp (tptp.aa_set_int_bool P (tptp.image_int_int F B6))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) B3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) B3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A3) B3)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat B3)) (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat A3))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3))))) (forall ((S tptp.set_nat) (T tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat S) T)) (=> (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S))) (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)))))) (forall ((S tptp.set_Code_integer) (T tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger S) T)) (=> (not (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S))) (not (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)))))) (forall ((S tptp.set_Pr1261947904930325089at_nat) (T tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat S) T)) (=> (not (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat S))) (not (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat T)))))) (forall ((S tptp.set_int) (T tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int S) T)) (=> (not (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S))) (not (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T)))))) (forall ((B3 tptp.set_nat) (A3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) B3)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3))))) (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) B3)) (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3))))) (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat B3)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A3) B3)) (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat A3))))) (forall ((B3 tptp.set_int) (A3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3))))) (forall ((F3 tptp.set_int) (G2 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int F3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int G2)) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int F3) G2)))))) (forall ((F3 tptp.set_Code_integer) (G2 tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger F3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger G2)) (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.sup_su848401254843788991nteger F3 G2)))))) (forall ((F3 tptp.set_Pr1261947904930325089at_nat) (G2 tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat F3)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat G2)) (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat F3) G2)))))) (forall ((F3 tptp.set_Pr8693737435421807431at_nat) (G2 tptp.set_Pr8693737435421807431at_nat)) (=> (tptp.finite4392333629123659920at_nat F3) (=> (tptp.finite4392333629123659920at_nat G2) (tptp.finite4392333629123659920at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat F3) G2))))) (forall ((F3 tptp.set_Pr8551490117392284871at_nat) (G2 tptp.set_Pr8551490117392284871at_nat)) (=> (tptp.finite1918287321285529104at_nat F3) (=> (tptp.finite1918287321285529104at_nat G2) (tptp.finite1918287321285529104at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat F3) G2))))) (forall ((F3 tptp.set_Pr4329608150637261639at_nat) (G2 tptp.set_Pr4329608150637261639at_nat)) (=> (tptp.finite4343798906461161616at_nat F3) (=> (tptp.finite4343798906461161616at_nat G2) (tptp.finite4343798906461161616at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat F3) G2))))) (forall ((F3 tptp.set_nat) (G2 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat F3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat G2)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat F3) G2)))))) (forall ((S tptp.set_int) (T tptp.set_int)) (=> (not (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S))) (not (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int S) T)))))) (forall ((S tptp.set_Code_integer) (T tptp.set_Code_integer)) (=> (not (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S))) (not (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.sup_su848401254843788991nteger S T)))))) (forall ((S tptp.set_Pr1261947904930325089at_nat) (T tptp.set_Pr1261947904930325089at_nat)) (=> (not (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat S))) (not (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat S) T)))))) (forall ((S tptp.set_Pr8693737435421807431at_nat) (T tptp.set_Pr8693737435421807431at_nat)) (=> (not (tptp.finite4392333629123659920at_nat S)) (not (tptp.finite4392333629123659920at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat S) T))))) (forall ((S tptp.set_Pr8551490117392284871at_nat) (T tptp.set_Pr8551490117392284871at_nat)) (=> (not (tptp.finite1918287321285529104at_nat S)) (not (tptp.finite1918287321285529104at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat S) T))))) (forall ((S tptp.set_Pr4329608150637261639at_nat) (T tptp.set_Pr4329608150637261639at_nat)) (=> (not (tptp.finite4343798906461161616at_nat S)) (not (tptp.finite4343798906461161616at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat S) T))))) (forall ((S tptp.set_nat) (T tptp.set_nat)) (=> (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S))) (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat S) T)))))) (forall ((S tptp.set_int) (T tptp.set_int)) (= (not (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int S) T)))) (or (not (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S))) (not (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T)))))) (forall ((S tptp.set_Code_integer) (T tptp.set_Code_integer)) (= (not (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.sup_su848401254843788991nteger S T)))) (or (not (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S))) (not (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)))))) (forall ((S tptp.set_Pr1261947904930325089at_nat) (T tptp.set_Pr1261947904930325089at_nat)) (= (not (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.sup_su6327502436637775413at_nat S) T)))) (or (not (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat S))) (not (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat T)))))) (forall ((S tptp.set_Pr8693737435421807431at_nat) (T tptp.set_Pr8693737435421807431at_nat)) (= (not (tptp.finite4392333629123659920at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat S) T))) (or (not (tptp.finite4392333629123659920at_nat S)) (not (tptp.finite4392333629123659920at_nat T))))) (forall ((S tptp.set_Pr8551490117392284871at_nat) (T tptp.set_Pr8551490117392284871at_nat)) (= (not (tptp.finite1918287321285529104at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat S) T))) (or (not (tptp.finite1918287321285529104at_nat S)) (not (tptp.finite1918287321285529104at_nat T))))) (forall ((S tptp.set_Pr4329608150637261639at_nat) (T tptp.set_Pr4329608150637261639at_nat)) (= (not (tptp.finite4343798906461161616at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat S) T))) (or (not (tptp.finite4343798906461161616at_nat S)) (not (tptp.finite4343798906461161616at_nat T))))) (forall ((S tptp.set_nat) (T tptp.set_nat)) (= (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat S) T)))) (or (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S))) (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)))))) (forall ((A3 tptp.set_nat) (P tptp.fun_set_nat_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (forall ((A6 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A6)) (=> (forall ((B7 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat B7) A6)) (tptp.pp (tptp.aa_set_nat_bool P B7)))) (tptp.pp (tptp.aa_set_nat_bool P A6))))) (tptp.pp (tptp.aa_set_nat_bool P A3))))) (forall ((A3 tptp.set_int) (P tptp.fun_set_int_bool)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (forall ((A6 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A6)) (=> (forall ((B7 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int B7) A6)) (tptp.pp (tptp.aa_set_int_bool P B7)))) (tptp.pp (tptp.aa_set_int_bool P A6))))) (tptp.pp (tptp.aa_set_int_bool P A3))))) (forall ((A3 tptp.set_Code_integer) (P tptp.fun_se2712834123562403997r_bool)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (forall ((A6 tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A6)) (=> (forall ((B7 tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le1307284697595431911nteger B7) A6)) (tptp.pp (tptp.aa_set1374477347934578310r_bool P B7)))) (tptp.pp (tptp.aa_set1374477347934578310r_bool P A6))))) (tptp.pp (tptp.aa_set1374477347934578310r_bool P A3))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (P tptp.fun_se8074476271188067385t_bool)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat A3)) (=> (forall ((A6 tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat A6)) (=> (forall ((B7 tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le7866589430770878221at_nat B7) A6)) (tptp.pp (tptp.aa_set3135850010578026034t_bool P B7)))) (tptp.pp (tptp.aa_set3135850010578026034t_bool P A6))))) (tptp.pp (tptp.aa_set3135850010578026034t_bool P A3))))) (forall ((A3 tptp.set_bool) (F tptp.fun_bool_nat)) (=> (not (tptp.finite_finite_bool A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.image_bool_nat F A3))) (exists ((X3 tptp.bool)) (and (tptp.pp (tptp.member_bool X3 A3)) (not (tptp.finite_finite_bool (tptp.collect_bool (tptp.aa_boo8970175072276269406l_bool (tptp.aa_fun5754907045972229615l_bool (tptp.aTP_Lamm_add A3) F) X3))))))))) (forall ((A3 tptp.set_bool) (F tptp.fun_bool_int)) (=> (not (tptp.finite_finite_bool A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.image_bool_int F A3))) (exists ((X3 tptp.bool)) (and (tptp.pp (tptp.member_bool X3 A3)) (not (tptp.finite_finite_bool (tptp.collect_bool (tptp.aa_boo8970175072276269406l_bool (tptp.aa_fun4343082806956354195l_bool (tptp.aTP_Lamm_ade A3) F) X3))))))))) (forall ((A3 tptp.set_bool) (F tptp.fun_bo7282069421189217543nteger)) (=> (not (tptp.finite_finite_bool A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.image_2396201541268454703nteger F A3))) (exists ((X3 tptp.bool)) (and (tptp.pp (tptp.member_bool X3 A3)) (not (tptp.finite_finite_bool (tptp.collect_bool (tptp.aa_boo8970175072276269406l_bool (tptp.aa_fun7305734610747869602l_bool (tptp.aTP_Lamm_adf A3) F) X3))))))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_nat)) (=> (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.image_nat_nat F A3))) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aa_fun3777555276967886990t_bool (tptp.aTP_Lamm_adg A3) F) X3)))))))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_int)) (=> (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.image_nat_int F A3))) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aa_fun2605284095902351154t_bool (tptp.aTP_Lamm_adh A3) F) X3)))))))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_Code_integer)) (=> (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.image_1215581382706833972nteger F A3))) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aa_fun2111297154760714689t_bool (tptp.aTP_Lamm_adi A3) F) X3)))))))))) (forall ((A3 tptp.set_int) (F tptp.fun_int_nat)) (=> (not (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.image_int_nat F A3))) (exists ((X3 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (not (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_int_fun_int_bool (tptp.aa_fun2912556895731619962t_bool (tptp.aTP_Lamm_adj A3) F) X3)))))))))) (forall ((A3 tptp.set_int) (F tptp.fun_int_int)) (=> (not (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.image_int_int F A3))) (exists ((X3 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (not (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_int_fun_int_bool (tptp.aa_fun1740285714666084126t_bool (tptp.aTP_Lamm_adk A3) F) X3)))))))))) (forall ((A3 tptp.set_int) (F tptp.fun_int_Code_integer)) (=> (not (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.image_1587234942943678608nteger F A3))) (exists ((X3 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (not (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_int_fun_int_bool (tptp.aa_fun8056663032588759469t_bool (tptp.aTP_Lamm_adl A3) F) X3)))))))))) (forall ((A3 tptp.set_Code_integer) (F tptp.fun_Code_integer_nat)) (=> (not (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.image_951025933927791156er_nat F A3))) (exists ((X3 tptp.code_integer)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) A3)) (not (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.collect_Code_integer (tptp.aa_Cod7250484176784686200r_bool (tptp.aa_fun3949617354051801383r_bool (tptp.aTP_Lamm_adm A3) F) X3)))))))))) (forall ((A3 tptp.set_set_nat) (F tptp.fun_nat_set_nat) (N2 tptp.nat)) (=> (= A3 (tptp.image_nat_set_nat F (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_dg N2)))) (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat A3)))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_nat) (N2 tptp.nat)) (=> (= A3 (tptp.image_nat_nat F (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_dg N2)))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)))) (forall ((A3 tptp.set_int) (F tptp.fun_nat_int) (N2 tptp.nat)) (=> (= A3 (tptp.image_nat_int F (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_dg N2)))) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)))) (forall ((A3 tptp.set_Code_integer) (F tptp.fun_nat_Code_integer) (N2 tptp.nat)) (=> (= A3 (tptp.image_1215581382706833972nteger F (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_dg N2)))) (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (F tptp.fun_na1476630412504255114at_nat) (N2 tptp.nat)) (=> (= A3 (tptp.image_5846123807819985514at_nat F (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_dg N2)))) (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat A3)))) (forall ((A3 tptp.set_set_nat)) (= (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat A3)) (exists ((N tptp.nat) (F4 tptp.fun_nat_set_nat)) (= A3 (tptp.image_nat_set_nat F4 (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_dg N))))))) (forall ((A3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (exists ((N tptp.nat) (F4 tptp.fun_nat_nat)) (= A3 (tptp.image_nat_nat F4 (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_dg N))))))) (forall ((A3 tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (exists ((N tptp.nat) (F4 tptp.fun_nat_int)) (= A3 (tptp.image_nat_int F4 (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_dg N))))))) (forall ((A3 tptp.set_Code_integer)) (= (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (exists ((N tptp.nat) (F4 tptp.fun_nat_Code_integer)) (= A3 (tptp.image_1215581382706833972nteger F4 (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_dg N))))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat A3)) (exists ((N tptp.nat) (F4 tptp.fun_na1476630412504255114at_nat)) (= A3 (tptp.image_5846123807819985514at_nat F4 (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_dg N))))))) (forall ((A3 tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (not (= A3 tptp.bot_bo3990330152332043303nteger)) (exists ((X3 tptp.code_integer)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) A3)) (forall ((Xa3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Xa3) A3)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger Xa3) X3)) (= X3 Xa3))))))))) (forall ((A3 tptp.set_bool)) (=> (tptp.finite_finite_bool A3) (=> (not (= A3 tptp.bot_bot_set_bool)) (exists ((X3 tptp.bool)) (and (tptp.pp (tptp.member_bool X3 A3)) (forall ((Xa3 tptp.bool)) (=> (tptp.pp (tptp.member_bool Xa3 A3)) (=> (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.ord_less_eq_bool Xa3) X3)) (= (tptp.pp X3) (tptp.pp Xa3)))))))))) (forall ((A3 tptp.set_set_int)) (=> (tptp.finite6197958912794628473et_int A3) (=> (not (= A3 tptp.bot_bot_set_set_int)) (exists ((X3 tptp.set_int)) (and (tptp.member_set_int X3 A3) (forall ((Xa3 tptp.set_int)) (=> (tptp.member_set_int Xa3 A3) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int Xa3) X3)) (= X3 Xa3))))))))) (forall ((A3 tptp.set_rat)) (=> (tptp.finite_finite_rat A3) (=> (not (= A3 tptp.bot_bot_set_rat)) (exists ((X3 tptp.rat)) (and (tptp.member_rat X3 A3) (forall ((Xa3 tptp.rat)) (=> (tptp.member_rat Xa3 A3) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Xa3) X3)) (= X3 Xa3))))))))) (forall ((A3 tptp.set_num)) (=> (tptp.finite_finite_num A3) (=> (not (= A3 tptp.bot_bot_set_num)) (exists ((X3 tptp.num)) (and (tptp.member_num X3 A3) (forall ((Xa3 tptp.num)) (=> (tptp.member_num Xa3 A3) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Xa3) X3)) (= X3 Xa3))))))))) (forall ((A3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (not (= A3 tptp.bot_bot_set_nat)) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (forall ((Xa3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa3) A3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Xa3) X3)) (= X3 Xa3))))))))) (forall ((A3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (not (= A3 tptp.bot_bot_set_int)) (exists ((X3 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (forall ((Xa3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa3) A3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Xa3) X3)) (= X3 Xa3))))))))) (forall ((A3 tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (not (= A3 tptp.bot_bo3990330152332043303nteger)) (exists ((X3 tptp.code_integer)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) A3)) (forall ((Xa3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Xa3) A3)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger X3) Xa3)) (= X3 Xa3))))))))) (forall ((A3 tptp.set_bool)) (=> (tptp.finite_finite_bool A3) (=> (not (= A3 tptp.bot_bot_set_bool)) (exists ((X3 tptp.bool)) (and (tptp.pp (tptp.member_bool X3 A3)) (forall ((Xa3 tptp.bool)) (=> (tptp.pp (tptp.member_bool Xa3 A3)) (=> (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.ord_less_eq_bool X3) Xa3)) (= (tptp.pp X3) (tptp.pp Xa3)))))))))) (forall ((A3 tptp.set_set_int)) (=> (tptp.finite6197958912794628473et_int A3) (=> (not (= A3 tptp.bot_bot_set_set_int)) (exists ((X3 tptp.set_int)) (and (tptp.member_set_int X3 A3) (forall ((Xa3 tptp.set_int)) (=> (tptp.member_set_int Xa3 A3) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int X3) Xa3)) (= X3 Xa3))))))))) (forall ((A3 tptp.set_rat)) (=> (tptp.finite_finite_rat A3) (=> (not (= A3 tptp.bot_bot_set_rat)) (exists ((X3 tptp.rat)) (and (tptp.member_rat X3 A3) (forall ((Xa3 tptp.rat)) (=> (tptp.member_rat Xa3 A3) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Xa3)) (= X3 Xa3))))))))) (forall ((A3 tptp.set_num)) (=> (tptp.finite_finite_num A3) (=> (not (= A3 tptp.bot_bot_set_num)) (exists ((X3 tptp.num)) (and (tptp.member_num X3 A3) (forall ((Xa3 tptp.num)) (=> (tptp.member_num Xa3 A3) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Xa3)) (= X3 Xa3))))))))) (forall ((A3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (not (= A3 tptp.bot_bot_set_nat)) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (forall ((Xa3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa3) A3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) Xa3)) (= X3 Xa3))))))))) (forall ((A3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (not (= A3 tptp.bot_bot_set_int)) (exists ((X3 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (forall ((Xa3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa3) A3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X3) Xa3)) (= X3 Xa3))))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (F tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B3) (tptp.image_nat_nat F A3))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_Code_integer) (F tptp.fun_nat_Code_integer)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) (tptp.image_1215581382706833972nteger F A3))) (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3))))) (forall ((A3 tptp.set_int) (B3 tptp.set_nat) (F tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B3) (tptp.image_int_nat F A3))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3))))) (forall ((A3 tptp.set_int) (B3 tptp.set_Code_integer) (F tptp.fun_int_Code_integer)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) (tptp.image_1587234942943678608nteger F A3))) (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_nat) (F tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B3) (tptp.image_951025933927791156er_nat F A3))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (F tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) (tptp.image_4470545334726330049nteger F A3))) (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_int) (F tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) (tptp.image_nat_int F A3))) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int) (F tptp.fun_int_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) (tptp.image_int_int F A3))) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_int) (F tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) (tptp.image_948535463418740880er_int F A3))) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_set_nat) (F tptp.fun_nat_set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat B3) (tptp.image_nat_set_nat F A3))) (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat B3))))) (forall ((B3 tptp.set_nat) (F tptp.fun_nat_nat) (A3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B3) (tptp.image_nat_nat F A3))) (exists ((C5 tptp.set_nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat C5) A3)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat C5)) (= B3 (tptp.image_nat_nat F C5))))))) (forall ((B3 tptp.set_nat) (F tptp.fun_Code_integer_nat) (A3 tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B3) (tptp.image_951025933927791156er_nat F A3))) (exists ((C5 tptp.set_Code_integer)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger C5) A3)) (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger C5)) (= B3 (tptp.image_951025933927791156er_nat F C5))))))) (forall ((B3 tptp.set_Code_integer) (F tptp.fun_nat_Code_integer) (A3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) (tptp.image_1215581382706833972nteger F A3))) (exists ((C5 tptp.set_nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat C5) A3)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat C5)) (= B3 (tptp.image_1215581382706833972nteger F C5))))))) (forall ((B3 tptp.set_Code_integer) (F tptp.fun_Co8499238673658658103nteger) (A3 tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) (tptp.image_4470545334726330049nteger F A3))) (exists ((C5 tptp.set_Code_integer)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger C5) A3)) (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger C5)) (= B3 (tptp.image_4470545334726330049nteger F C5))))))) (forall ((B3 tptp.set_nat) (F tptp.fun_int_nat) (A3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B3) (tptp.image_int_nat F A3))) (exists ((C5 tptp.set_int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int C5) A3)) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int C5)) (= B3 (tptp.image_int_nat F C5))))))) (forall ((B3 tptp.set_Code_integer) (F tptp.fun_int_Code_integer) (A3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B3) (tptp.image_1587234942943678608nteger F A3))) (exists ((C5 tptp.set_int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int C5) A3)) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int C5)) (= B3 (tptp.image_1587234942943678608nteger F C5))))))) (forall ((B3 tptp.set_int) (F tptp.fun_nat_int) (A3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) (tptp.image_nat_int F A3))) (exists ((C5 tptp.set_nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat C5) A3)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat C5)) (= B3 (tptp.image_nat_int F C5))))))) (forall ((B3 tptp.set_int) (F tptp.fun_Code_integer_int) (A3 tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) (tptp.image_948535463418740880er_int F A3))) (exists ((C5 tptp.set_Code_integer)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger C5) A3)) (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger C5)) (= B3 (tptp.image_948535463418740880er_int F C5))))))) (forall ((B3 tptp.set_int) (F tptp.fun_int_int) (A3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B3) (tptp.image_int_int F A3))) (exists ((C5 tptp.set_int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int C5) A3)) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int C5)) (= B3 (tptp.image_int_int F C5))))))) (forall ((B3 tptp.set_set_nat) (F tptp.fun_nat_set_nat) (A3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat B3)) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat B3) (tptp.image_nat_set_nat F A3))) (exists ((C5 tptp.set_nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat C5) A3)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat C5)) (= B3 (tptp.image_nat_set_nat F C5))))))) (forall ((F tptp.fun_nat_nat) (A3 tptp.set_nat) (P tptp.fun_set_nat_bool)) (= (exists ((B6 tptp.set_nat)) (and (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B6)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B6) (tptp.image_nat_nat F A3))) (tptp.pp (tptp.aa_set_nat_bool P B6)))) (exists ((B6 tptp.set_nat)) (and (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B6)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B6) A3)) (tptp.pp (tptp.aa_set_nat_bool P (tptp.image_nat_nat F B6))))))) (forall ((F tptp.fun_Code_integer_nat) (A3 tptp.set_Code_integer) (P tptp.fun_set_nat_bool)) (= (exists ((B6 tptp.set_nat)) (and (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B6)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B6) (tptp.image_951025933927791156er_nat F A3))) (tptp.pp (tptp.aa_set_nat_bool P B6)))) (exists ((B6 tptp.set_Code_integer)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B6)) (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B6) A3)) (tptp.pp (tptp.aa_set_nat_bool P (tptp.image_951025933927791156er_nat F B6))))))) (forall ((F tptp.fun_nat_Code_integer) (A3 tptp.set_nat) (P tptp.fun_se2712834123562403997r_bool)) (= (exists ((B6 tptp.set_Code_integer)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B6)) (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B6) (tptp.image_1215581382706833972nteger F A3))) (tptp.pp (tptp.aa_set1374477347934578310r_bool P B6)))) (exists ((B6 tptp.set_nat)) (and (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B6)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B6) A3)) (tptp.pp (tptp.aa_set1374477347934578310r_bool P (tptp.image_1215581382706833972nteger F B6))))))) (forall ((F tptp.fun_Co8499238673658658103nteger) (A3 tptp.set_Code_integer) (P tptp.fun_se2712834123562403997r_bool)) (= (exists ((B6 tptp.set_Code_integer)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B6)) (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B6) (tptp.image_4470545334726330049nteger F A3))) (tptp.pp (tptp.aa_set1374477347934578310r_bool P B6)))) (exists ((B6 tptp.set_Code_integer)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B6)) (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B6) A3)) (tptp.pp (tptp.aa_set1374477347934578310r_bool P (tptp.image_4470545334726330049nteger F B6))))))) (forall ((F tptp.fun_int_nat) (A3 tptp.set_int) (P tptp.fun_set_nat_bool)) (= (exists ((B6 tptp.set_nat)) (and (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B6)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B6) (tptp.image_int_nat F A3))) (tptp.pp (tptp.aa_set_nat_bool P B6)))) (exists ((B6 tptp.set_int)) (and (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B6)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B6) A3)) (tptp.pp (tptp.aa_set_nat_bool P (tptp.image_int_nat F B6))))))) (forall ((F tptp.fun_int_Code_integer) (A3 tptp.set_int) (P tptp.fun_se2712834123562403997r_bool)) (= (exists ((B6 tptp.set_Code_integer)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B6)) (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B6) (tptp.image_1587234942943678608nteger F A3))) (tptp.pp (tptp.aa_set1374477347934578310r_bool P B6)))) (exists ((B6 tptp.set_int)) (and (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B6)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B6) A3)) (tptp.pp (tptp.aa_set1374477347934578310r_bool P (tptp.image_1587234942943678608nteger F B6))))))) (forall ((F tptp.fun_nat_int) (A3 tptp.set_nat) (P tptp.fun_set_int_bool)) (= (exists ((B6 tptp.set_int)) (and (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B6)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B6) (tptp.image_nat_int F A3))) (tptp.pp (tptp.aa_set_int_bool P B6)))) (exists ((B6 tptp.set_nat)) (and (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B6)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B6) A3)) (tptp.pp (tptp.aa_set_int_bool P (tptp.image_nat_int F B6))))))) (forall ((F tptp.fun_Code_integer_int) (A3 tptp.set_Code_integer) (P tptp.fun_set_int_bool)) (= (exists ((B6 tptp.set_int)) (and (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B6)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B6) (tptp.image_948535463418740880er_int F A3))) (tptp.pp (tptp.aa_set_int_bool P B6)))) (exists ((B6 tptp.set_Code_integer)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B6)) (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B6) A3)) (tptp.pp (tptp.aa_set_int_bool P (tptp.image_948535463418740880er_int F B6))))))) (forall ((F tptp.fun_int_int) (A3 tptp.set_int) (P tptp.fun_set_int_bool)) (= (exists ((B6 tptp.set_int)) (and (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B6)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B6) (tptp.image_int_int F A3))) (tptp.pp (tptp.aa_set_int_bool P B6)))) (exists ((B6 tptp.set_int)) (and (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B6)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B6) A3)) (tptp.pp (tptp.aa_set_int_bool P (tptp.image_int_int F B6))))))) (forall ((F tptp.fun_nat_set_nat) (A3 tptp.set_nat) (P tptp.fun_set_set_nat_bool)) (= (exists ((B6 tptp.set_set_nat)) (and (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat B6)) (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat B6) (tptp.image_nat_set_nat F A3))) (tptp.pp (tptp.aa_set_set_nat_bool P B6)))) (exists ((B6 tptp.set_nat)) (and (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B6)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B6) A3)) (tptp.pp (tptp.aa_set_set_nat_bool P (tptp.image_nat_set_nat F B6))))))) (forall ((F tptp.fun_nat_nat) (A3 tptp.set_nat) (P tptp.fun_set_nat_bool)) (= (forall ((B6 tptp.set_nat)) (=> (and (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B6)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B6) (tptp.image_nat_nat F A3)))) (tptp.pp (tptp.aa_set_nat_bool P B6)))) (forall ((B6 tptp.set_nat)) (=> (and (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B6)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B6) A3))) (tptp.pp (tptp.aa_set_nat_bool P (tptp.image_nat_nat F B6))))))) (forall ((F tptp.fun_Code_integer_nat) (A3 tptp.set_Code_integer) (P tptp.fun_set_nat_bool)) (= (forall ((B6 tptp.set_nat)) (=> (and (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B6)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B6) (tptp.image_951025933927791156er_nat F A3)))) (tptp.pp (tptp.aa_set_nat_bool P B6)))) (forall ((B6 tptp.set_Code_integer)) (=> (and (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B6)) (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B6) A3))) (tptp.pp (tptp.aa_set_nat_bool P (tptp.image_951025933927791156er_nat F B6))))))) (forall ((F tptp.fun_nat_Code_integer) (A3 tptp.set_nat) (P tptp.fun_se2712834123562403997r_bool)) (= (forall ((B6 tptp.set_Code_integer)) (=> (and (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B6)) (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B6) (tptp.image_1215581382706833972nteger F A3)))) (tptp.pp (tptp.aa_set1374477347934578310r_bool P B6)))) (forall ((B6 tptp.set_nat)) (=> (and (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B6)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B6) A3))) (tptp.pp (tptp.aa_set1374477347934578310r_bool P (tptp.image_1215581382706833972nteger F B6))))))) (forall ((F tptp.fun_Co8499238673658658103nteger) (A3 tptp.set_Code_integer) (P tptp.fun_se2712834123562403997r_bool)) (= (forall ((B6 tptp.set_Code_integer)) (=> (and (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B6)) (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B6) (tptp.image_4470545334726330049nteger F A3)))) (tptp.pp (tptp.aa_set1374477347934578310r_bool P B6)))) (forall ((B6 tptp.set_Code_integer)) (=> (and (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B6)) (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B6) A3))) (tptp.pp (tptp.aa_set1374477347934578310r_bool P (tptp.image_4470545334726330049nteger F B6))))))) (forall ((F tptp.fun_int_nat) (A3 tptp.set_int) (P tptp.fun_set_nat_bool)) (= (forall ((B6 tptp.set_nat)) (=> (and (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B6)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B6) (tptp.image_int_nat F A3)))) (tptp.pp (tptp.aa_set_nat_bool P B6)))) (forall ((B6 tptp.set_int)) (=> (and (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B6)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B6) A3))) (tptp.pp (tptp.aa_set_nat_bool P (tptp.image_int_nat F B6))))))) (forall ((F tptp.fun_int_Code_integer) (A3 tptp.set_int) (P tptp.fun_se2712834123562403997r_bool)) (= (forall ((B6 tptp.set_Code_integer)) (=> (and (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B6)) (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B6) (tptp.image_1587234942943678608nteger F A3)))) (tptp.pp (tptp.aa_set1374477347934578310r_bool P B6)))) (forall ((B6 tptp.set_int)) (=> (and (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B6)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B6) A3))) (tptp.pp (tptp.aa_set1374477347934578310r_bool P (tptp.image_1587234942943678608nteger F B6))))))) (forall ((F tptp.fun_nat_int) (A3 tptp.set_nat) (P tptp.fun_set_int_bool)) (= (forall ((B6 tptp.set_int)) (=> (and (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B6)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B6) (tptp.image_nat_int F A3)))) (tptp.pp (tptp.aa_set_int_bool P B6)))) (forall ((B6 tptp.set_nat)) (=> (and (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B6)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B6) A3))) (tptp.pp (tptp.aa_set_int_bool P (tptp.image_nat_int F B6))))))) (forall ((F tptp.fun_Code_integer_int) (A3 tptp.set_Code_integer) (P tptp.fun_set_int_bool)) (= (forall ((B6 tptp.set_int)) (=> (and (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B6)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B6) (tptp.image_948535463418740880er_int F A3)))) (tptp.pp (tptp.aa_set_int_bool P B6)))) (forall ((B6 tptp.set_Code_integer)) (=> (and (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B6)) (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B6) A3))) (tptp.pp (tptp.aa_set_int_bool P (tptp.image_948535463418740880er_int F B6))))))) (forall ((F tptp.fun_int_int) (A3 tptp.set_int) (P tptp.fun_set_int_bool)) (= (forall ((B6 tptp.set_int)) (=> (and (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B6)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B6) (tptp.image_int_int F A3)))) (tptp.pp (tptp.aa_set_int_bool P B6)))) (forall ((B6 tptp.set_int)) (=> (and (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B6)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B6) A3))) (tptp.pp (tptp.aa_set_int_bool P (tptp.image_int_int F B6))))))) (forall ((F tptp.fun_nat_set_nat) (A3 tptp.set_nat) (P tptp.fun_set_set_nat_bool)) (= (forall ((B6 tptp.set_set_nat)) (=> (and (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat B6)) (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat B6) (tptp.image_nat_set_nat F A3)))) (tptp.pp (tptp.aa_set_set_nat_bool P B6)))) (forall ((B6 tptp.set_nat)) (=> (and (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B6)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B6) A3))) (tptp.pp (tptp.aa_set_set_nat_bool P (tptp.image_nat_set_nat F B6))))))) (forall ((N2 tptp.nat)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) tptp.zero_zero_int)))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se7882103937844011126it_nat tptp.zero_zero_nat) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1)))))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.bit_se2793503036327961859nteger tptp.zero_zero_nat) A) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) _let_1)))))) (forall ((A tptp.code_natural)) (let ((_let_1 (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.bit_se1617098188084679374atural tptp.zero_zero_nat A) (tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural (tptp.times_2397367101498566445atural _let_1 (tptp.divide5121882707175180666atural A _let_1)))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se7879613467334960850it_int tptp.zero_zero_nat) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) _let_1)))))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se4205575877204974255it_nat tptp.zero_zero_nat) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1))))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.bit_se8260200283734997820nteger tptp.zero_zero_nat) A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) _let_1))))) (forall ((A tptp.code_natural)) (let ((_let_1 (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.bit_se7083795435491715335atural tptp.zero_zero_nat A) (tptp.times_2397367101498566445atural _let_1 (tptp.divide5121882707175180666atural A _let_1))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se4203085406695923979it_int tptp.zero_zero_nat) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) _let_1))))) (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se7882103937844011126it_nat (tptp.aa_nat_nat tptp.suc N2)) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se7882103937844011126it_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1))))))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.bit_se2793503036327961859nteger (tptp.aa_nat_nat tptp.suc N2)) A) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) _let_1)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.bit_se2793503036327961859nteger N2) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) _let_1))))))) (forall ((N2 tptp.nat) (A tptp.code_natural)) (let ((_let_1 (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.bit_se1617098188084679374atural (tptp.aa_nat_nat tptp.suc N2) A) (tptp.plus_p4538020629002901425atural (tptp.modulo8411746178871703098atural A _let_1) (tptp.times_2397367101498566445atural _let_1 (tptp.bit_se1617098188084679374atural N2 (tptp.divide5121882707175180666atural A _let_1))))))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se7879613467334960850it_int (tptp.aa_nat_nat tptp.suc N2)) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se7879613467334960850it_int N2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) _let_1))))))) (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2161824704523386999it_nat (tptp.aa_nat_nat tptp.suc N2)) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2161824704523386999it_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1))))))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.bit_se1345352211410354436nteger (tptp.aa_nat_nat tptp.suc N2)) A) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) _let_1)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.bit_se1345352211410354436nteger N2) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) _let_1))))))) (forall ((N2 tptp.nat) (A tptp.code_natural)) (let ((_let_1 (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.bit_se168947363167071951atural (tptp.aa_nat_nat tptp.suc N2) A) (tptp.plus_p4538020629002901425atural (tptp.modulo8411746178871703098atural A _let_1) (tptp.times_2397367101498566445atural _let_1 (tptp.bit_se168947363167071951atural N2 (tptp.divide5121882707175180666atural A _let_1))))))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2159334234014336723it_int (tptp.aa_nat_nat tptp.suc N2)) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2159334234014336723it_int N2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) _let_1))))))) (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se4205575877204974255it_nat (tptp.aa_nat_nat tptp.suc N2)) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se4205575877204974255it_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1))))))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.bit_se8260200283734997820nteger (tptp.aa_nat_nat tptp.suc N2)) A) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) _let_1)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.bit_se8260200283734997820nteger N2) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) _let_1))))))) (forall ((N2 tptp.nat) (A tptp.code_natural)) (let ((_let_1 (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.bit_se7083795435491715335atural (tptp.aa_nat_nat tptp.suc N2) A) (tptp.plus_p4538020629002901425atural (tptp.modulo8411746178871703098atural A _let_1) (tptp.times_2397367101498566445atural _let_1 (tptp.bit_se7083795435491715335atural N2 (tptp.divide5121882707175180666atural A _let_1))))))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se4203085406695923979it_int (tptp.aa_nat_nat tptp.suc N2)) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se4203085406695923979it_int N2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) _let_1))))))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) _let_1))) (let ((_let_3 (tptp.aa_Cod1783974652533396728nteger (tptp.bit_ri6519982836138164636nteger N2) A))) (let ((_let_4 (= N2 tptp.zero_zero_nat))) (and (=> _let_4 (= _let_3 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger _let_2))) (=> (not _let_4) (= _let_3 (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger _let_2) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.bit_ri6519982836138164636nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat)) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) _let_1)))))))))))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) _let_1))) (let ((_let_3 (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2) A))) (let ((_let_4 (= N2 tptp.zero_zero_nat))) (and (=> _let_4 (= _let_3 (tptp.aa_int_int tptp.uminus_uminus_int _let_2))) (=> (not _let_4) (= _let_3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) _let_1)))))))))))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se4203085406695923979it_int N2) K))) (tptp.pp (tptp.aa_int_bool _let_1 K))))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se7879613467334960850it_int N2) K))) (tptp.pp (tptp.aa_int_bool _let_1 K))))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2159334234014336723it_int N2) K))) (tptp.pp (tptp.aa_int_bool _let_1 K))))) (forall ((N2 tptp.nat) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se4203085406695923979it_int N2) K)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)))) (forall ((N2 tptp.nat) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se7879613467334960850it_int N2) K)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)))) (forall ((N2 tptp.nat) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2159334234014336723it_int N2) K)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)))) (forall ((N2 tptp.nat) (K tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se4203085406695923979it_int N2) K)) K))) (forall ((K tptp.int) (N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se7879613467334960850it_int N2) K)))) (forall ((N2 tptp.nat) (K tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2) K)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (forall ((K tptp.int) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2) K))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2))))) (forall ((N2 tptp.nat) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2) K)) K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) K)))) (forall ((N2 tptp.nat) (K tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2) K)))) (forall ((N2 tptp.nat) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2) K)) K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) K)))) (forall ((K tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int K))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2) K))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2))))))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int _let_1 N2)) K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int K) (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat tptp.suc N2)))))))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int _let_1)) K)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) _let_1)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2) K) K))))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (= (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2) K) K) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int _let_1)) K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) _let_1)))))) (forall ((K tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int _let_1 N2)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat tptp.suc N2)))) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2) K)))))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.bit_ri6519982836138164636nteger (tptp.aa_nat_nat tptp.suc N2)) A) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) _let_1)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.bit_ri6519982836138164636nteger N2) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) _let_1))))))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int (tptp.aa_nat_nat tptp.suc N2)) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) _let_1))))))) (forall ((X tptp.rat) (Y tptp.int)) (let ((_let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat tptp.one_one_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_int_rat tptp.ring_1_of_int_rat Y))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat X) _let_1)) _let_2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) _let_1))) (= (tptp.aa_rat_int tptp.archim7778729529865785530nd_rat X) Y)))))) (forall ((S tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (exists ((K3 tptp.int)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.image_int_int tptp.abs_abs_int S)) (tptp.set_ord_atMost_int K3)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_adn N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_nat_rat (tptp.power_power_rat _let_1) N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aa_nat_fun_nat_int tptp.aTP_Lamm_ado N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int _let_1) N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger (tptp.aTP_Lamm_adp N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger _let_1) N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_adq N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_nat_rat (tptp.power_power_rat _let_1) N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aa_nat_fun_nat_int tptp.aTP_Lamm_adr N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int _let_1) N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger (tptp.aTP_Lamm_ads N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger _let_1) N2))))) (forall ((X tptp.rat)) (let ((_let_1 (tptp.aa_rat_int tptp.archim7778729529865785530nd_rat X))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat tptp.one_one_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_rat_rat tptp.archimedean_frac_rat X))))) (and (=> _let_2 (= _let_1 (tptp.aa_rat_int tptp.archim2889992004027027881ng_rat X))) (=> (not _let_2) (= _let_1 (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X))))))) (forall ((S tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (exists ((K3 tptp.nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat S) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat K3)))))) (forall ((M tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M) tptp.one_one_nat)) (= M tptp.one_one_nat))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C))) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger _let_1 A)) (tptp.aa_Cod1783974652533396728nteger _let_1 B))) (or (= C tptp.zero_z3403309356797280102nteger) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) B)))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B))) (or (= C tptp.zero_zero_rat) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A) B)))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B))) (or (= C tptp.zero_zero_int) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B)))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C))) (or (= C tptp.zero_z3403309356797280102nteger) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) B))))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C))) (or (= C tptp.zero_zero_rat) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A) B))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C))) (or (= C tptp.zero_zero_int) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A))) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger _let_1 B)) (tptp.aa_Cod1783974652533396728nteger _let_1 C))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) C)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (=> (not (= A tptp.zero_zero_nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat _let_1 B)) (tptp.aa_nat_nat _let_1 C))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) C)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (=> (not (= A tptp.zero_zero_int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int _let_1 B)) (tptp.aa_int_int _let_1 C))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) C)))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) A)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) A))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) A))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) A)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) C))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger B) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) A)))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 B))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat B) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) A)))) (tptp.pp (tptp.aa_rat_bool _let_1 B))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) A)))) (tptp.pp (tptp.aa_nat_bool _let_1 B))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) A)))) (tptp.pp (tptp.aa_int_bool _let_1 B))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) A)) B))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 B))))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat C) A)) B))) (tptp.pp (tptp.aa_rat_bool _let_1 B))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) A)) B))) (tptp.pp (tptp.aa_nat_bool _let_1 B))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) A)) B))) (tptp.pp (tptp.aa_int_bool _let_1 B))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)) tptp.one_one_Code_integer))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B)) tptp.one_one_nat))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) tptp.one_one_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) tptp.one_one_int))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) A)) B))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) A)) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) B)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger B) A)) B))) (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural A) B)) (= (tptp.times_2397367101498566445atural A (tptp.divide5121882707175180666atural B A)) B))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) A)) A) B))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) A)) A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) B)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger B) A)) A) B))) (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural A) B)) (= (tptp.times_2397367101498566445atural (tptp.divide5121882707175180666atural B A) A) B))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M) _let_1)) (= M _let_1)))) (forall ((K tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) K))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) A)) A) B))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) tptp.one_one_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) A)) A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger B) A)) A) B))) (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural A) tptp.one_one_Code_natural)) (= (tptp.times_2397367101498566445atural (tptp.divide5121882707175180666atural B A) A) B))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.one_one_nat) A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) A)))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) tptp.one_one_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int tptp.one_one_int) A)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) A)) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger B) A)))) (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural A) tptp.one_one_Code_natural)) (= (tptp.times_2397367101498566445atural B (tptp.divide5121882707175180666atural tptp.one_one_Code_natural A)) (tptp.divide5121882707175180666atural B A)))) (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B))))) (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int B) N2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B))) (or (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 B)))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B))) (or (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 B)))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B))) (or (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)))))) (forall ((A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (tptp.dvd_dvd_Code_natural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_Code_natural_bool _let_1 (tptp.times_2397367101498566445atural A B))) (or (tptp.pp (tptp.aa_Code_natural_bool _let_1 A)) (tptp.pp (tptp.aa_Code_natural_bool _let_1 B)))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N2))) (and (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2))) (and (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2))) (and (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))))) (forall ((A tptp.code_natural) (N2 tptp.nat)) (let ((_let_1 (tptp.dvd_dvd_Code_natural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_Code_natural_bool _let_1 (tptp.aa_nat_Code_natural (tptp.power_7079662738309270450atural A) N2))) (and (tptp.pp (tptp.aa_Code_natural_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))))) (forall ((A tptp.code_integer) (W2 tptp.num)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat W2))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_2)))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) _let_2))) (or _let_3 (and (not _let_3) (tptp.pp (tptp.aa_Code_integer_bool _let_1 A))))))))) (forall ((A tptp.rat) (W2 tptp.num)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat W2))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_2)))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) _let_2))) (or _let_3 (and (not _let_3) (tptp.pp (tptp.aa_rat_bool _let_1 A))))))))) (forall ((A tptp.int) (W2 tptp.num)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat W2))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_2)))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) _let_2))) (or _let_3 (and (not _let_3) (tptp.pp (tptp.aa_int_bool _let_1 A))))))))) (forall ((A tptp.code_integer) (W2 tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W2))) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) _let_1)) tptp.zero_z3403309356797280102nteger)) (and (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger)))))) (forall ((A tptp.rat) (W2 tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W2))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat A) _let_1)) tptp.zero_zero_rat)) (and (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)))))) (forall ((A tptp.int) (W2 tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W2))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) _let_1)) tptp.zero_zero_int)) (and (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int)))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2)) tptp.zero_z3403309356797280102nteger)) (and (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))) (forall ((A tptp.rat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N2)) tptp.zero_zero_rat)) (and (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat))))) (forall ((A tptp.int) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2)) tptp.zero_zero_int)) (and (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2))) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2))))))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1))) tptp.one_one_nat) A)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) _let_1))) tptp.one_one_int) A)))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) _let_1))) tptp.one_one_Code_integer) A)))) (forall ((A tptp.code_natural)) (let ((_let_1 (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (not (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural _let_1) A))) (= (tptp.plus_p4538020629002901425atural (tptp.times_2397367101498566445atural _let_1 (tptp.divide5121882707175180666atural A _let_1)) tptp.one_one_Code_natural) A)))) (forall ((A tptp.code_integer) (W2 tptp.num)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat W2))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_2)))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) _let_2))) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_z3403309356797280102nteger))) (and (not _let_3) (tptp.pp (tptp.aa_Code_integer_bool _let_1 A))))))))) (forall ((A tptp.rat) (W2 tptp.num)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat W2))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_2)))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) _let_2))) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_rat))) (and (not _let_3) (tptp.pp (tptp.aa_rat_bool _let_1 A))))))))) (forall ((A tptp.int) (W2 tptp.num)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat W2))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_2)))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) _let_2))) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_int))) (and (not _let_3) (tptp.pp (tptp.aa_int_bool _let_1 A))))))))) (forall ((A tptp.code_integer) (W2 tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W2))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1)))) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) _let_1)) tptp.zero_z3403309356797280102nteger)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) _let_1)) (or (and (not _let_2) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger))) (and _let_2 (= A tptp.zero_z3403309356797280102nteger)))))))) (forall ((A tptp.rat) (W2 tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W2))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat A) _let_1)) tptp.zero_zero_rat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) _let_1)) (or (and (not _let_2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat))) (and _let_2 (= A tptp.zero_zero_rat)))))))) (forall ((A tptp.int) (W2 tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W2))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1)))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) _let_1)) tptp.zero_zero_int)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) _let_1)) (or (and (not _let_2) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int))) (and _let_2 (= A tptp.zero_zero_int)))))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) A)) _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_2))))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int _let_1) N2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) A)) _let_2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) _let_2))))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger _let_1) N2))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) _let_2) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) _let_2))))))) (forall ((A tptp.code_natural) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_Code_natural (tptp.power_7079662738309270450atural _let_1) N2))) (=> (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural _let_1) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.divide5121882707175180666atural (tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural A) _let_2) (tptp.divide5121882707175180666atural A _let_2))))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) N2))) (let ((_let_3 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat _let_3 A)) _let_2) (tptp.aa_nat_nat _let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_2))))))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int _let_1) N2))) (let ((_let_3 (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int _let_3 A)) _let_2) (tptp.aa_int_int _let_3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) _let_2))))))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger _let_1) N2))) (let ((_let_3 (tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger _let_3 A)) _let_2) (tptp.aa_Cod1783974652533396728nteger _let_3 (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) _let_2))))))))) (forall ((A tptp.code_natural) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_Code_natural (tptp.power_7079662738309270450atural _let_1) N2))) (=> (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural _let_1) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.modulo8411746178871703098atural (tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural A) _let_2) (tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural (tptp.modulo8411746178871703098atural A _let_2)))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat N2) M)) (= M N2)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C))) (exists ((B8 tptp.nat) (C6 tptp.nat)) (and (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B8) C6)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B8) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C6) C)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C))) (exists ((B8 tptp.int) (C6 tptp.int)) (and (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B8) C6)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B8) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C6) C)))))) (forall ((P3 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat P3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B))) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= P3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat X3) Y3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat X3) A)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat Y3) B))))))))) (forall ((P3 tptp.int) (A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int P3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B))) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= P3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X3) Y3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int X3) A)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int Y3) B))))))))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) A)) (not (forall ((K2 tptp.code_integer)) (not (= A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) K2))))))) (forall ((B tptp.assn) (A tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.dvd_dvd_assn B) A)) (not (forall ((K2 tptp.assn)) (not (= A (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn B) K2))))))) (forall ((B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat B) A)) (not (forall ((K2 tptp.rat)) (not (= A (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) K2))))))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) A)) (not (forall ((K2 tptp.nat)) (not (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) K2))))))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) A)) (not (forall ((K2 tptp.int)) (not (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) K2))))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (K tptp.code_integer)) (=> (= A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) K)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) A)))) (forall ((A tptp.assn) (B tptp.assn) (K tptp.assn)) (=> (= A (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn B) K)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.dvd_dvd_assn B) A)))) (forall ((A tptp.rat) (B tptp.rat) (K tptp.rat)) (=> (= A (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) K)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat B) A)))) (forall ((A tptp.nat) (B tptp.nat) (K tptp.nat)) (=> (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) A)))) (forall ((A tptp.int) (B tptp.int) (K tptp.int)) (=> (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) A)))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) A)) (exists ((K3 tptp.code_integer)) (= A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) K3))))) (forall ((B tptp.assn) (A tptp.assn)) (= (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.dvd_dvd_assn B) A)) (exists ((K3 tptp.assn)) (= A (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn B) K3))))) (forall ((B tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat B) A)) (exists ((K3 tptp.rat)) (= A (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) K3))))) (forall ((B tptp.nat) (A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) A)) (exists ((K3 tptp.nat)) (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) K3))))) (forall ((B tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) A)) (exists ((K3 tptp.int)) (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) K3))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 C)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C)))))) (forall ((A tptp.assn) (C tptp.assn) (B tptp.assn)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.dvd_dvd_assn A))) (=> (tptp.pp (tptp.aa_assn_bool _let_1 C)) (tptp.pp (tptp.aa_assn_bool _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn B) C)))))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 C)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C)))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 C)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C)))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 C)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C)))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C)))))) (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (tptp.aa_ass5323576183532441186n_bool tptp.dvd_dvd_assn A))) (=> (tptp.pp (tptp.aa_assn_bool _let_1 B)) (tptp.pp (tptp.aa_assn_bool _let_1 (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn B) C)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) C)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C)))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) C)))) (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.dvd_dvd_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn A) B)) C)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.dvd_dvd_assn A) C)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A) C)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B)) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) C)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) C)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)))) (forall ((A tptp.assn) (B tptp.assn)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.dvd_dvd_assn A) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn A) B)))) (forall ((A tptp.rat) (B tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)))) (forall ((A tptp.nat) (B tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B)))) (forall ((A tptp.int) (B tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) D2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) D2)))))) (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn) (D2 tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.dvd_dvd_assn A) B)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.dvd_dvd_assn C) D2)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.dvd_dvd_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn A) C)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn B) D2)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat C) D2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) D2)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) D2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) D2)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) D2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) D2)))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) C)))) (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (=> (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.dvd_dvd_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn A) B)) C)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.dvd_dvd_assn B) C)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) B)) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat B) C)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B)) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) C)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) C)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) A)))) (forall ((A tptp.assn) (B tptp.assn)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.dvd_dvd_assn A) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn B) A)))) (forall ((A tptp.rat) (B tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat B) A)))) (forall ((A tptp.nat) (B tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) A)))) (forall ((A tptp.int) (B tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) A)))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat K))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 M)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 N2)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2))))))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_adt A))) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_adt B)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger (tptp.collect_Code_integer (tptp.aa_Cod7250484176784686200r_bool tptp.aTP_Lamm_adu A))) (tptp.collect_Code_integer (tptp.aa_Cod7250484176784686200r_bool tptp.aTP_Lamm_adu B)))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) B)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.collect_int (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_adv A))) (tptp.collect_int (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_adv B)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B)))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_adt A))) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_adt B)))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) A)))))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int (tptp.collect_int (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_adv A))) (tptp.collect_int (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_adv B)))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) A)))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le1307284697595431911nteger (tptp.collect_Code_integer (tptp.aa_Cod7250484176784686200r_bool tptp.aTP_Lamm_adu A))) (tptp.collect_Code_integer (tptp.aa_Cod7250484176784686200r_bool tptp.aTP_Lamm_adu B)))) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) B)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) A)))))) (forall ((D2 tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X5 tptp.code_integer)) (let ((_let_1 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer D2) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger X5) S2))))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger Z2) X5)) (= _let_1 _let_1)))))) (forall ((D2 tptp.rat) (S2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat D2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X5) S2))))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z2) X5)) (= _let_1 _let_1)))))) (forall ((D2 tptp.nat) (S2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat D2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X5) S2))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z2) X5)) (= _let_1 _let_1)))))) (forall ((D2 tptp.int) (S2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X5) S2))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z2) X5)) (= _let_1 _let_1)))))) (forall ((D2 tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X5 tptp.code_integer)) (let ((_let_1 (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer D2) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger X5) S2)))))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger Z2) X5)) (= _let_1 _let_1)))))) (forall ((D2 tptp.rat) (S2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat D2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X5) S2)))))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z2) X5)) (= _let_1 _let_1)))))) (forall ((D2 tptp.nat) (S2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat D2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X5) S2)))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z2) X5)) (= _let_1 _let_1)))))) (forall ((D2 tptp.int) (S2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X5) S2)))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z2) X5)) (= _let_1 _let_1)))))) (forall ((D2 tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X5 tptp.code_integer)) (let ((_let_1 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer D2) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger X5) S2))))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger X5) Z2)) (= _let_1 _let_1)))))) (forall ((D2 tptp.rat) (S2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat D2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X5) S2))))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X5) Z2)) (= _let_1 _let_1)))))) (forall ((D2 tptp.nat) (S2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat D2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X5) S2))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X5) Z2)) (= _let_1 _let_1)))))) (forall ((D2 tptp.int) (S2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X5) S2))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X5) Z2)) (= _let_1 _let_1)))))) (forall ((D2 tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X5 tptp.code_integer)) (let ((_let_1 (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer D2) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger X5) S2)))))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger X5) Z2)) (= _let_1 _let_1)))))) (forall ((D2 tptp.rat) (S2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat D2) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X5) S2)))))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X5) Z2)) (= _let_1 _let_1)))))) (forall ((D2 tptp.nat) (S2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat D2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X5) S2)))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X5) Z2)) (= _let_1 _let_1)))))) (forall ((D2 tptp.int) (S2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X5) S2)))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X5) Z2)) (= _let_1 _let_1)))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) A)) (= B C)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) A)) (= B C)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) tptp.one_one_int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) A)) (= B C)))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger _let_1 B) (tptp.aa_Cod1783974652533396728nteger _let_1 C)) (= B C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (= (= (tptp.aa_nat_nat _let_1 B) (tptp.aa_nat_nat _let_1 C)) (= B C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) tptp.one_one_int)) (= (= (tptp.aa_int_int _let_1 B) (tptp.aa_int_int _let_1 C)) (= B C))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B)) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) tptp.one_one_int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) C))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 C)))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) tptp.one_one_nat)) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C))) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) tptp.one_one_int)) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C))) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) C))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) tptp.one_one_nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B)) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) C))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) tptp.one_one_int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) C))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) B))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 C)))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) tptp.one_one_nat)) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) B))) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) tptp.one_one_int)) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B))) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)) tptp.one_one_Code_integer)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer))))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B)) tptp.one_one_nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) tptp.one_one_nat))))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) tptp.one_one_int)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) tptp.one_one_int))))) (forall ((B tptp.nat) (A tptp.nat) (D2 tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat D2) C)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat C) D2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) D2)))))) (forall ((B tptp.int) (A tptp.int) (D2 tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D2) C)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int C) D2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) D2)))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (D2 tptp.code_integer) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer D2) C)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) B)) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger C) D2)) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) D2)))))) (forall ((B tptp.code_natural) (A tptp.code_natural) (D2 tptp.code_natural) (C tptp.code_natural)) (=> (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural B) A)) (=> (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural D2) C)) (= (tptp.times_2397367101498566445atural (tptp.divide5121882707175180666atural A B) (tptp.divide5121882707175180666atural C D2)) (tptp.divide5121882707175180666atural (tptp.times_2397367101498566445atural A C) (tptp.times_2397367101498566445atural B D2)))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) C))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) C))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger B) C))))) (forall ((A tptp.code_natural) (C tptp.code_natural) (B tptp.code_natural)) (=> (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural (tptp.times_2397367101498566445atural A C)) B)) (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural A) (tptp.divide5121882707175180666atural B C))))) (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_2) A)) (= (tptp.aa_nat_nat _let_1 _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 B)) C)))))) (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.divide_divide_int A))) (let ((_let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_2) A)) (= (tptp.aa_int_int _let_1 _let_2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int _let_1 B)) C)))))) (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (tptp.divide6298287555418463151nteger A))) (let ((_let_2 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_2) A)) (= (tptp.aa_Cod1783974652533396728nteger _let_1 _let_2) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B)) C)))))) (forall ((B tptp.code_natural) (C tptp.code_natural) (A tptp.code_natural)) (let ((_let_1 (tptp.times_2397367101498566445atural B C))) (=> (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural _let_1) A)) (= (tptp.divide5121882707175180666atural A _let_1) (tptp.divide5121882707175180666atural (tptp.divide5121882707175180666atural A B) C))))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) A)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 B)) C)))))) (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.divide_divide_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) A)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int _let_1 B)) C)))))) (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (tptp.divide6298287555418463151nteger A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) A)) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger B) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B)) C)))))) (forall ((C tptp.code_natural) (B tptp.code_natural) (A tptp.code_natural)) (=> (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural C) B)) (=> (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural B) A)) (= (tptp.divide5121882707175180666atural A (tptp.divide5121882707175180666atural B C)) (tptp.times_2397367101498566445atural (tptp.divide5121882707175180666atural A B) C))))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) B)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 B)) C))))) (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) B)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int _let_1 B)) C))))) (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) B)) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger B) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B)) C))))) (forall ((C tptp.code_natural) (B tptp.code_natural) (A tptp.code_natural)) (=> (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural C) B)) (= (tptp.times_2397367101498566445atural A (tptp.divide5121882707175180666atural B C)) (tptp.divide5121882707175180666atural (tptp.times_2397367101498566445atural A B) C)))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) C)) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) A)) C)))) (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) C)) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) A)) C)))) (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) B)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger B) C)) A) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) A)) C)))) (forall ((C tptp.code_natural) (B tptp.code_natural) (A tptp.code_natural)) (=> (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural C) B)) (= (tptp.times_2397367101498566445atural (tptp.divide5121882707175180666atural B C) A) (tptp.divide5121882707175180666atural (tptp.times_2397367101498566445atural B A) C)))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M) N2)) (tptp.pp (tptp.aa_nat_bool _let_1 M)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat N2) M)))))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer X) Y)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) N2)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Y) M)))))) (forall ((X tptp.nat) (Y tptp.nat) (N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat X) Y)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Y) M)))))) (forall ((X tptp.int) (Y tptp.int) (N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int X) Y)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int X) N2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Y) M)))))) (forall ((A tptp.code_integer) (N2 tptp.nat) (B tptp.code_integer) (M tptp.nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_nat_Code_integer _let_1 N2)) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_nat_Code_integer _let_1 M)) B)))))) (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat _let_1 N2)) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat _let_1 M)) B)))))) (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int) (M tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_nat_int _let_1 N2)) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_nat_int _let_1 M)) B)))))) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.power_8256067586552552935nteger A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_nat_Code_integer _let_1 M)) (tptp.aa_nat_Code_integer _let_1 N2)))))) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N2)))))) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_nat_int _let_1 M)) (tptp.aa_nat_int _let_1 N2)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M))) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)) (tptp.pp (tptp.aa_nat_bool _let_1 N2)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.pp (tptp.aa_nat_bool _let_1 N2)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M))))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat K))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (tptp.pp (tptp.aa_nat_bool _let_1 N2))))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat K))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (tptp.pp (tptp.aa_nat_bool _let_1 M))))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N2)) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int M))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger N2)) (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger M))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat M))))) (forall ((P tptp.fun_Co8822979462182099027r_bool) (L tptp.code_integer)) (= (exists ((X4 tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool P (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger L) X4)))) (exists ((X4 tptp.code_integer)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer L) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger X4) tptp.zero_z3403309356797280102nteger))) (tptp.pp (tptp.aa_Code_integer_bool P X4)))))) (forall ((P tptp.fun_rat_bool) (L tptp.rat)) (= (exists ((X4 tptp.rat)) (tptp.pp (tptp.aa_rat_bool P (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat L) X4)))) (exists ((X4 tptp.rat)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat L) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X4) tptp.zero_zero_rat))) (tptp.pp (tptp.aa_rat_bool P X4)))))) (forall ((P tptp.fun_nat_bool) (L tptp.nat)) (= (exists ((X4 tptp.nat)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat L) X4)))) (exists ((X4 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat L) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X4) tptp.zero_zero_nat))) (tptp.pp (tptp.aa_nat_bool P X4)))))) (forall ((P tptp.fun_int_bool) (L tptp.int)) (= (exists ((X4 tptp.int)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int L) X4)))) (exists ((X4 tptp.int)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int L) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X4) tptp.zero_zero_int))) (tptp.pp (tptp.aa_int_bool P X4)))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer)) (not (=> (not (= A tptp.zero_z3403309356797280102nteger)) (forall ((C2 tptp.code_integer)) (not (= B (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C2)))))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((C2 tptp.nat)) (not (= B (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C2)))))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) tptp.one_one_int)) (not (=> (not (= A tptp.zero_zero_int)) (forall ((C2 tptp.int)) (not (= B (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C2)))))))) (forall ((D2 tptp.code_integer) (D3 tptp.code_integer) (T5 tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer D2) D3)) (forall ((X5 tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer D2))) (= (not (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger X5) T5)))) (not (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger X5) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger K4) D3))) T5))))))))) (forall ((D2 tptp.rat) (D3 tptp.rat) (T5 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat D2) D3)) (forall ((X5 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat D2))) (= (not (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X5) T5)))) (not (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat X5) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat K4) D3))) T5))))))))) (forall ((D2 tptp.int) (D3 tptp.int) (T5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D2) D3)) (forall ((X5 tptp.int) (K4 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D2))) (= (not (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X5) T5)))) (not (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X5) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K4) D3))) T5))))))))) (forall ((D2 tptp.code_integer) (D3 tptp.code_integer) (T5 tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer D2) D3)) (forall ((X5 tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer D2))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger X5) T5))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger X5) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger K4) D3))) T5)))))))) (forall ((D2 tptp.rat) (D3 tptp.rat) (T5 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat D2) D3)) (forall ((X5 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat D2))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X5) T5))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat X5) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat K4) D3))) T5)))))))) (forall ((D2 tptp.int) (D3 tptp.int) (T5 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D2) D3)) (forall ((X5 tptp.int) (K4 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D2))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X5) T5))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X5) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K4) D3))) T5)))))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= C tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) D2)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat D2) C)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) D2)))))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= C tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) D2)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int D2) C)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) D2)))))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) D2)) (= (= (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger B) A) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger D2) C)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) D2)))))))) (forall ((A tptp.code_natural) (C tptp.code_natural) (B tptp.code_natural) (D2 tptp.code_natural)) (=> (not (= A tptp.zero_z2226904508553997617atural)) (=> (not (= C tptp.zero_z2226904508553997617atural)) (=> (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural A) B)) (=> (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural C) D2)) (= (= (tptp.divide5121882707175180666atural B A) (tptp.divide5121882707175180666atural D2 C)) (= (tptp.times_2397367101498566445atural B C) (tptp.times_2397367101498566445atural A D2)))))))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) B)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) C))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) B)))))) (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (not (= C tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) B)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) C))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) B)))))) (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) B)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger B) C))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) B)))))) (forall ((C tptp.code_natural) (B tptp.code_natural) (A tptp.code_natural)) (=> (not (= C tptp.zero_z2226904508553997617atural)) (=> (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural C) B)) (= (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural A) (tptp.divide5121882707175180666atural B C))) (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural (tptp.times_2397367101498566445atural A C)) B)))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) A)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B)) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) B))))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) A)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B))))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) A)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) B)) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) B))))))) (forall ((B tptp.code_natural) (A tptp.code_natural) (C tptp.code_natural)) (=> (not (= B tptp.zero_z2226904508553997617atural)) (=> (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural B) A)) (= (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural (tptp.divide5121882707175180666atural A B)) C)) (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural A) (tptp.times_2397367101498566445atural C B))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) A) C) (= B (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) A)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) A) C) (= B (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) A)))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) B)) (= (= (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger B) A) C) (= B (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) A)))))) (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (=> (not (= A tptp.zero_z2226904508553997617atural)) (=> (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural A) B)) (= (= (tptp.divide5121882707175180666atural B A) C) (= B (tptp.times_2397367101498566445atural C A)))))) (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) tptp.one_one_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) tptp.one_one_nat)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 B)) C)))))) (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.divide_divide_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) tptp.one_one_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) tptp.one_one_int)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int _let_1 B)) C)))))) (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (tptp.divide6298287555418463151nteger A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer)) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B)) C)))))) (forall ((B tptp.code_natural) (C tptp.code_natural) (A tptp.code_natural)) (=> (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural)) (=> (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural C) tptp.one_one_Code_natural)) (= (tptp.divide5121882707175180666atural A (tptp.times_2397367101498566445atural B C)) (tptp.divide5121882707175180666atural (tptp.divide5121882707175180666atural A B) C))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) tptp.one_one_nat)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 B)) C))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) tptp.one_one_int)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int _let_1 B)) C))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer)) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger B) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B)) C))))) (forall ((C tptp.code_natural) (A tptp.code_natural) (B tptp.code_natural)) (=> (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural C) tptp.one_one_Code_natural)) (= (tptp.times_2397367101498566445atural A (tptp.divide5121882707175180666atural B C)) (tptp.divide5121882707175180666atural (tptp.times_2397367101498566445atural A B) C)))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) tptp.one_one_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B)) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) B)))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) tptp.one_one_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) B)))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) B)) C) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) B)))) (forall ((B tptp.code_natural) (A tptp.code_natural) (C tptp.code_natural)) (=> (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural)) (= (tptp.times_2397367101498566445atural (tptp.divide5121882707175180666atural A B) C) (tptp.divide5121882707175180666atural (tptp.times_2397367101498566445atural A C) B)))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) tptp.one_one_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) A)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 B)) C)))))) (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.divide_divide_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) tptp.one_one_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) A)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int _let_1 B)) C)))))) (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (tptp.divide6298287555418463151nteger A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) A)) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B)) C)))))) (forall ((C tptp.code_natural) (B tptp.code_natural) (A tptp.code_natural)) (=> (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural C) tptp.one_one_Code_natural)) (=> (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural B) A)) (= (tptp.divide5121882707175180666atural A (tptp.times_2397367101498566445atural B C)) (tptp.divide5121882707175180666atural (tptp.divide5121882707175180666atural A B) C))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) tptp.one_one_nat)) (= (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat C) B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B) C)))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) tptp.one_one_int)) (= (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int C) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B) C)))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)) (= (= A (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger C) B)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B) C)))) (forall ((B tptp.code_natural) (A tptp.code_natural) (C tptp.code_natural)) (=> (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural)) (= (= A (tptp.divide5121882707175180666atural C B)) (= (tptp.times_2397367101498566445atural A B) C)))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) tptp.one_one_nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B) C) (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) B))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) tptp.one_one_int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B) C) (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)) (= (= (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) B) C) (= A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) B))))) (forall ((B tptp.code_natural) (A tptp.code_natural) (C tptp.code_natural)) (=> (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural)) (= (= (tptp.divide5121882707175180666atural A B) C) (= A (tptp.times_2397367101498566445atural C B))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim7778729529865785530nd_rat X)) (tptp.aa_rat_int tptp.archim7778729529865785530nd_rat Y))))) (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (F tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) B3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.groups3190895334310489300er_nat F A3)) (tptp.groups3190895334310489300er_nat F B3)))))) (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (F tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) B3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.groups3188404863801439024er_int F A3)) (tptp.groups3188404863801439024er_int F B3)))))) (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (F tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.groups3455450783089532116nteger F))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) B3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_set871585252387937313nteger _let_1 A3)) (tptp.aa_set871585252387937313nteger _let_1 B3))))))) (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (F tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) B3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.groups3674199335183972705nteger F A3)) (tptp.groups3674199335183972705nteger F B3)))))) (forall ((B3 tptp.set_int) (A3 tptp.set_int) (F tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.groups1707563613775114915nt_nat F A3)) (tptp.groups1707563613775114915nt_nat F B3)))))) (forall ((B3 tptp.set_int) (A3 tptp.set_int) (F tptp.fun_int_Code_integer)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.groups3827104343326376752nteger F A3)) (tptp.groups3827104343326376752nteger F B3)))))) (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (F tptp.fun_nat_nat)) (let ((_let_1 (tptp.groups708209901874060359at_nat F))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) B3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_set_nat_nat _let_1 A3)) (tptp.aa_set_nat_nat _let_1 B3))))))) (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (F tptp.fun_nat_int)) (let ((_let_1 (tptp.groups705719431365010083at_int F))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) B3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_set_nat_int _let_1 A3)) (tptp.aa_set_nat_int _let_1 B3))))))) (forall ((B3 tptp.set_int) (A3 tptp.set_int) (F tptp.fun_int_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.groups1705073143266064639nt_int F A3)) (tptp.groups1705073143266064639nt_int F B3)))))) (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (F tptp.fun_Pr2602117396471556196at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat B3)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A3) B3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.groups4077766827762148844at_nat F A3)) (tptp.groups4077766827762148844at_nat F B3)))))) (forall ((B3 tptp.set_bool) (A3 tptp.set_bool) (F tptp.fun_bool_nat) (G tptp.fun_bool_nat)) (=> (tptp.finite_finite_bool B3) (=> (tptp.ord_less_eq_set_bool A3 B3) (=> (forall ((A4 tptp.bool)) (=> (tptp.pp (tptp.member_bool A4 A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_bool_nat F A4)) (tptp.aa_bool_nat G A4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.groups1894949261696196098ol_nat F A3)) (tptp.groups1894949261696196098ol_nat G B3))))))) (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (F tptp.fun_Code_integer_nat) (G tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) B3)) (=> (forall ((A4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A4) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_Code_integer_nat F A4)) (tptp.aa_Code_integer_nat G A4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.groups3190895334310489300er_nat F A3)) (tptp.groups3190895334310489300er_nat G B3))))))) (forall ((B3 tptp.set_bool) (A3 tptp.set_bool) (F tptp.fun_bool_int) (G tptp.fun_bool_int)) (=> (tptp.finite_finite_bool B3) (=> (tptp.ord_less_eq_set_bool A3 B3) (=> (forall ((A4 tptp.bool)) (=> (tptp.pp (tptp.member_bool A4 A3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_bool_int F A4)) (tptp.aa_bool_int G A4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.groups1892458791187145822ol_int F A3)) (tptp.groups1892458791187145822ol_int G B3))))))) (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (F tptp.fun_Code_integer_int) (G tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) B3)) (=> (forall ((A4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A4) A3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_Code_integer_int F A4)) (tptp.aa_Code_integer_int G A4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.groups3188404863801439024er_int F A3)) (tptp.groups3188404863801439024er_int G B3))))))) (forall ((B3 tptp.set_bool) (A3 tptp.set_bool) (F tptp.fun_bo7282069421189217543nteger) (G tptp.fun_bo7282069421189217543nteger)) (=> (tptp.finite_finite_bool B3) (=> (tptp.ord_less_eq_set_bool A3 B3) (=> (forall ((A4 tptp.bool)) (=> (tptp.pp (tptp.member_bool A4 A3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_bool_Code_integer F A4)) (tptp.aa_bool_Code_integer G A4))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.groups7272450149305381519nteger F A3)) (tptp.groups7272450149305381519nteger G B3))))))) (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (F tptp.fun_nat_Code_integer) (G tptp.fun_nat_Code_integer)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) B3)) (=> (forall ((A4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A4) A3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_nat_Code_integer F A4)) (tptp.aa_nat_Code_integer G A4))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger F) A3)) (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger G) B3))))))) (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (F tptp.fun_Co8499238673658658103nteger) (G tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) B3)) (=> (forall ((A4 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer A4) A3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger F A4)) (tptp.aa_Cod1783974652533396728nteger G A4))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.groups3674199335183972705nteger F A3)) (tptp.groups3674199335183972705nteger G B3))))))) (forall ((B3 tptp.set_int) (A3 tptp.set_int) (F tptp.fun_int_nat) (G tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (=> (forall ((A4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A4) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_int_nat F A4)) (tptp.aa_int_nat G A4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.groups1707563613775114915nt_nat F A3)) (tptp.groups1707563613775114915nt_nat G B3))))))) (forall ((B3 tptp.set_int) (A3 tptp.set_int) (F tptp.fun_int_Code_integer) (G tptp.fun_int_Code_integer)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (=> (forall ((A4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A4) A3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_int_Code_integer F A4)) (tptp.aa_int_Code_integer G A4))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.groups3827104343326376752nteger F A3)) (tptp.groups3827104343326376752nteger G B3))))))) (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (F tptp.fun_nat_nat) (G tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) B3)) (=> (forall ((A4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A4) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat F A4)) (tptp.aa_nat_nat G A4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat F) A3)) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat G) B3))))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat K) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M) N2)))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M) N2)))))) (forall ((K tptp.nat) (N2 tptp.nat)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger K)) (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger N2))) (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) N2))))) (forall ((K tptp.nat) (N2 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat K)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N2))) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) N2))))) (forall ((K tptp.nat) (N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int K)) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N2))) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) N2))))) (forall ((K tptp.nat) (N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat K)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2))) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N2))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat N2) M))))) (forall ((N2 tptp.nat) (M tptp.nat) (Q5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) Q5) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N2) Q5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat Q5) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)))))) (forall ((X tptp.rat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X)) (tptp.aa_rat_int tptp.archim7778729529865785530nd_rat X)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2)))))) (forall ((M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_adt M)))))) (tptp.pp (tptp.aa_nat_bool (tptp.ordering_top_nat tptp.dvd_dvd_nat tptp.aTP_Lamm_adw) tptp.zero_zero_nat)) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) tptp.one_one_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.one_one_nat) B))))) (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) tptp.one_one_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) A)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int tptp.one_one_int) B))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) A)) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) B))))) (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (not (= A tptp.zero_z2226904508553997617atural)) (=> (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural)) (= (tptp.divide5121882707175180666atural A (tptp.times_2397367101498566445atural B A)) (tptp.divide5121882707175180666atural tptp.one_one_Code_natural B))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) tptp.one_one_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.one_one_nat) B))))) (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) tptp.one_one_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int tptp.one_one_int) B))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) B))))) (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (not (= A tptp.zero_z2226904508553997617atural)) (=> (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural)) (= (tptp.divide5121882707175180666atural A (tptp.times_2397367101498566445atural A B)) (tptp.divide5121882707175180666atural tptp.one_one_Code_natural B))))) (forall ((A tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((B4 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.one_one_nat))) (=> (not (= B4 tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B4) tptp.one_one_nat)) (=> (= (tptp.aa_nat_nat _let_1 A) B4) (=> (= (tptp.aa_nat_nat _let_1 B4) A) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B4) tptp.one_one_nat) (not (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat C) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) B4)))))))))))))) (forall ((A tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) tptp.one_one_int)) (not (=> (not (= A tptp.zero_zero_int)) (forall ((B4 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.divide_divide_int tptp.one_one_int))) (=> (not (= B4 tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B4) tptp.one_one_int)) (=> (= (tptp.aa_int_int _let_1 A) B4) (=> (= (tptp.aa_int_int _let_1 B4) A) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B4) tptp.one_one_int) (not (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int C) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B4)))))))))))))) (forall ((A tptp.code_integer) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer)) (not (=> (not (= A tptp.zero_z3403309356797280102nteger)) (forall ((B4 tptp.code_integer)) (let ((_let_1 (tptp.divide6298287555418463151nteger tptp.one_one_Code_integer))) (=> (not (= B4 tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B4) tptp.one_one_Code_integer)) (=> (= (tptp.aa_Cod1783974652533396728nteger _let_1 A) B4) (=> (= (tptp.aa_Cod1783974652533396728nteger _let_1 B4) A) (=> (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B4) tptp.one_one_Code_integer) (not (= (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger C) A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) B4)))))))))))))) (forall ((A tptp.code_natural) (C tptp.code_natural)) (=> (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural A) tptp.one_one_Code_natural)) (not (=> (not (= A tptp.zero_z2226904508553997617atural)) (forall ((B4 tptp.code_natural)) (=> (not (= B4 tptp.zero_z2226904508553997617atural)) (=> (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural B4) tptp.one_one_Code_natural)) (=> (= (tptp.divide5121882707175180666atural tptp.one_one_Code_natural A) B4) (=> (= (tptp.divide5121882707175180666atural tptp.one_one_Code_natural B4) A) (=> (= (tptp.times_2397367101498566445atural A B4) tptp.one_one_Code_natural) (not (= (tptp.divide5121882707175180666atural C A) (tptp.times_2397367101498566445atural C B4))))))))))))) (forall ((A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) A)) (not (forall ((B4 tptp.nat)) (not (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) B4))))))) (forall ((A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) A)) (not (forall ((B4 tptp.int)) (not (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) B4))))))) (forall ((A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) A)) (not (forall ((B4 tptp.code_integer)) (not (= A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) B4))))))) (forall ((A tptp.code_natural)) (=> (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one))) A)) (not (forall ((B4 tptp.code_natural)) (not (= A (tptp.times_2397367101498566445atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)) B4))))))) (forall ((X tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger X))) (=> (not (= X tptp.zero_z3403309356797280102nteger)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_nat_Code_integer _let_1 M)) (tptp.aa_nat_Code_integer _let_1 N2))) (or (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer X) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2))))))) (forall ((X tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X))) (=> (not (= X tptp.zero_zero_nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N2))) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat X) tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2))))))) (forall ((X tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int X))) (=> (not (= X tptp.zero_zero_int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_nat_int _let_1 M)) (tptp.aa_nat_int _let_1 N2))) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int X) tptp.one_one_int)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2))))))) (forall ((N2 tptp.nat) (X tptp.code_integer)) (=> (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= X tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer X) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) N2))))) (forall ((N2 tptp.nat) (X tptp.rat)) (=> (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= X tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat X) (tptp.aa_nat_rat (tptp.power_power_rat X) N2))))) (forall ((N2 tptp.nat) (X tptp.nat)) (=> (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= X tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) N2))))) (forall ((N2 tptp.nat) (X tptp.int)) (=> (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= X tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int X) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int X) N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N2)) M)) (= N2 tptp.one_one_nat)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) M)) M)) (= N2 tptp.one_one_nat)))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger K)) (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K)))) (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger N2))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat K)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K)))) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N2))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int K)) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K)))) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N2))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat K)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K)))) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2))))) (forall ((Q5 tptp.nat) (N2 tptp.nat) (R3 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat R3) M))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M))) (let ((_let_3 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Q5))) (=> (tptp.pp (tptp.aa_nat_bool _let_3 N2)) (=> (tptp.pp (tptp.aa_nat_bool _let_3 _let_1)) (= (tptp.pp (tptp.aa_nat_bool _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) Q5))) (tptp.pp (tptp.aa_nat_bool _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat _let_1) Q5))))))))))) (forall ((R3 tptp.nat) (N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat R3) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat R3) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) R3))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N2) R3))))) (forall ((I2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat I2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat) I2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1)) A)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) _let_1)) A)))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) _let_1)) A)))) (forall ((A tptp.code_natural)) (let ((_let_1 (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural _let_1) A)) (= (tptp.times_2397367101498566445atural _let_1 (tptp.divide5121882707175180666atural A _let_1)) A)))) (forall ((N2 tptp.nat) (A tptp.rat) (B tptp.rat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N2)) (tptp.aa_nat_rat (tptp.power_power_rat B) N2)))))) (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int B) N2)))))) (forall ((N2 tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) K)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat _let_1 M)) (tptp.aa_nat_nat _let_1 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))))) (forall ((A3 tptp.set_int) (F tptp.fun_int_nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.groups4541462559716669496nt_nat F A3)) B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.groups4541462559716669496nt_nat (tptp.aa_nat_fun_int_nat (tptp.aTP_Lamm_adx F) B) (tptp.aa_set_int_set_int _let_1 (tptp.collect_int (tptp.aa_nat_fun_int_bool (tptp.aTP_Lamm_ady F) B))))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.groups4541462559716669496nt_nat F (tptp.aa_set_int_set_int _let_1 (tptp.collect_int (tptp.aa_nat_fun_int_bool (tptp.aTP_Lamm_adz F) B))))) B)))))) (forall ((A3 tptp.set_Code_integer) (F tptp.fun_Code_integer_nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.groups7237345082560585321er_nat F A3)) B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.groups7237345082560585321er_nat (tptp.aa_nat5852537043073606456er_nat (tptp.aTP_Lamm_aea F) B) (tptp.inf_in1364745209274528805nteger A3 (tptp.collect_Code_integer (tptp.aa_nat6120813132205607877r_bool (tptp.aTP_Lamm_aeb F) B))))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.groups7237345082560585321er_nat F (tptp.inf_in1364745209274528805nteger A3 (tptp.collect_Code_integer (tptp.aa_nat6120813132205607877r_bool (tptp.aTP_Lamm_aec F) B))))) B))))) (forall ((A3 tptp.set_Code_integer) (F tptp.fun_Code_integer_int) (B tptp.int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.groups7234854612051535045er_int F A3)) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups7234854612051535045er_int (tptp.aa_int1390634949194299888er_int (tptp.aTP_Lamm_aed F) B) (tptp.inf_in1364745209274528805nteger A3 (tptp.collect_Code_integer (tptp.aa_int3865899974016033897r_bool (tptp.aTP_Lamm_aee F) B))))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.groups7234854612051535045er_int F (tptp.inf_in1364745209274528805nteger A3 (tptp.collect_Code_integer (tptp.aa_int3865899974016033897r_bool (tptp.aTP_Lamm_aef F) B))))) B))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_int) (B tptp.int)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3))) (let ((_let_2 (tptp.groups3539618377306564664at_int F))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_set_nat_int _let_2 A3)) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_aeg F) B)) (tptp.aa_set_nat_set_nat _let_1 (tptp.collect_nat (tptp.aa_int_fun_nat_bool (tptp.aTP_Lamm_aeh F) B))))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_set_nat_int _let_2 (tptp.aa_set_nat_set_nat _let_1 (tptp.collect_nat (tptp.aa_int_fun_nat_bool (tptp.aTP_Lamm_aei F) B))))) B))))))) (forall ((A3 tptp.set_int) (F tptp.fun_int_Code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.groups7873554091576472773nteger F A3)) B) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.groups7873554091576472773nteger (tptp.aa_Cod1949805079358391713nteger (tptp.aTP_Lamm_aej F) B) (tptp.aa_set_int_set_int _let_1 (tptp.collect_int (tptp.aa_Cod8597349444926882409t_bool (tptp.aTP_Lamm_aek F) B))))) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.groups7873554091576472773nteger F (tptp.aa_set_int_set_int _let_1 (tptp.collect_int (tptp.aa_Cod8597349444926882409t_bool (tptp.aTP_Lamm_ael F) B))))) B)))))) (forall ((A3 tptp.set_Code_integer) (F tptp.fun_Co8499238673658658103nteger) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.groups879477027807139574nteger F A3)) B) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.groups879477027807139574nteger (tptp.aa_Cod4161879620478718930nteger (tptp.aTP_Lamm_aem F) B) (tptp.inf_in1364745209274528805nteger A3 (tptp.collect_Code_integer (tptp.aa_Cod7250484176784686200r_bool (tptp.aTP_Lamm_aen F) B))))) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.groups879477027807139574nteger F (tptp.inf_in1364745209274528805nteger A3 (tptp.collect_Code_integer (tptp.aa_Cod7250484176784686200r_bool (tptp.aTP_Lamm_aeo F) B))))) B))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_Code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3))) (let ((_let_2 (tptp.groups7501900531339628137nteger F))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_set871585252387937313nteger _let_2 A3)) B) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger (tptp.aa_Cod1578151519121547077nteger (tptp.aTP_Lamm_aep F) B)) (tptp.aa_set_nat_set_nat _let_1 (tptp.collect_nat (tptp.aa_Cod2498268374540730821t_bool (tptp.aTP_Lamm_aeq F) B))))) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_set871585252387937313nteger _let_2 (tptp.aa_set_nat_set_nat _let_1 (tptp.collect_nat (tptp.aa_Cod2498268374540730821t_bool (tptp.aTP_Lamm_aer F) B))))) B))))))) (forall ((A3 tptp.set_int) (F tptp.fun_int_Code_natural) (B tptp.code_natural)) (let ((_let_1 (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.divide5121882707175180666atural (tptp.groups6697149243333190288atural F A3) B) (tptp.plus_p4538020629002901425atural (tptp.groups6697149243333190288atural (tptp.aa_Cod5692187177200718263atural (tptp.aTP_Lamm_aes F) B) (tptp.aa_set_int_set_int _let_1 (tptp.collect_int (tptp.aa_Cod6239439722579490142t_bool (tptp.aTP_Lamm_aet F) B)))) (tptp.divide5121882707175180666atural (tptp.groups6697149243333190288atural F (tptp.aa_set_int_set_int _let_1 (tptp.collect_int (tptp.aa_Cod6239439722579490142t_bool (tptp.aTP_Lamm_aeu F) B)))) B)))))) (forall ((A3 tptp.set_Code_integer) (F tptp.fun_Co3734316457315071362atural) (B tptp.code_natural)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.divide5121882707175180666atural (tptp.groups8926444216418632897atural F A3) B) (tptp.plus_p4538020629002901425atural (tptp.groups8926444216418632897atural (tptp.aa_Cod1476545362447692776atural (tptp.aTP_Lamm_aev F) B) (tptp.inf_in1364745209274528805nteger A3 (tptp.collect_Code_integer (tptp.aa_Cod8557728523445623661r_bool (tptp.aTP_Lamm_aew F) B)))) (tptp.divide5121882707175180666atural (tptp.groups8926444216418632897atural F (tptp.inf_in1364745209274528805nteger A3 (tptp.collect_Code_integer (tptp.aa_Cod8557728523445623661r_bool (tptp.aTP_Lamm_aex F) B)))) B))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_Code_natural) (B tptp.code_natural)) (let ((_let_1 (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.divide5121882707175180666atural (tptp.groups6325495683096345652atural F A3) B) (tptp.plus_p4538020629002901425atural (tptp.groups6325495683096345652atural (tptp.aa_Cod5320533616963873627atural (tptp.aTP_Lamm_aey F) B) (tptp.aa_set_nat_set_nat _let_1 (tptp.collect_nat (tptp.aa_Cod140358652193338554t_bool (tptp.aTP_Lamm_aez F) B)))) (tptp.divide5121882707175180666atural (tptp.groups6325495683096345652atural F (tptp.aa_set_nat_set_nat _let_1 (tptp.collect_nat (tptp.aa_Cod140358652193338554t_bool (tptp.aTP_Lamm_afa F) B)))) B)))))) (forall ((Z tptp.rat) (M tptp.int)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat Z))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat _let_1 (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_rat_int tptp.archim7778729529865785530nd_rat Z))))) (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat _let_1 (tptp.aa_int_rat tptp.ring_1_of_int_rat M))))))) (forall ((A tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) A))) (not (forall ((B4 tptp.nat)) (not (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) B4)) tptp.one_one_nat))))))) (forall ((A tptp.int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) A))) (not (forall ((B4 tptp.int)) (not (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) B4)) tptp.one_one_int))))))) (forall ((A tptp.code_integer)) (=> (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) A))) (not (forall ((B4 tptp.code_integer)) (not (= A (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) B4)) tptp.one_one_Code_integer))))))) (forall ((A tptp.code_natural)) (=> (not (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one))) A))) (not (forall ((B4 tptp.code_natural)) (not (= A (tptp.plus_p4538020629002901425atural (tptp.times_2397367101498566445atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)) B4) tptp.one_one_Code_natural))))))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2))))) (forall ((N2 tptp.nat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat (tptp.power_power_rat A) N2))))) (forall ((N2 tptp.nat) (A tptp.int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2))))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)))))) (forall ((N2 tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N2))) (tptp.pp (tptp.aa_rat_bool _let_1 A)))))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2))) (tptp.pp (tptp.aa_int_bool _let_1 A)))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2))) (or _let_2 (and (not _let_2) (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)))))))) (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N2))) (or _let_2 (and (not _let_2) (tptp.pp (tptp.aa_rat_bool _let_1 A)))))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2))) (or _let_2 (and (not _let_2) (tptp.pp (tptp.aa_int_bool _let_1 A)))))))) (forall ((N2 tptp.nat) (A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer A)) (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer B))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger B) N2)))))) (forall ((N2 tptp.nat) (A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N2)) (tptp.aa_nat_rat (tptp.power_power_rat B) N2)))))) (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int A)) (tptp.aa_int_int tptp.abs_abs_int B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int B) N2)))))) (forall ((A3 tptp.set_set_nat) (R tptp.fun_se707272970763642173t_bool)) (=> (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat A3)) (=> (forall ((X3 tptp.set_nat)) (not (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool R X3) X3)))) (=> (forall ((X3 tptp.set_nat) (Y3 tptp.set_nat) (Z2 tptp.set_nat)) (let ((_let_1 (tptp.aa_set5116768664143533222t_bool R X3))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 Y3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool R Y3) Z2)) (tptp.pp (tptp.aa_set_nat_bool _let_1 Z2)))))) (=> (forall ((X3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat X3) A3)) (exists ((Y4 tptp.set_nat)) (and (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat Y4) A3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool R X3) Y4)))))) (= A3 tptp.bot_bot_set_set_nat)))))) (forall ((A3 tptp.set_Code_integer) (R tptp.fun_Co8310303586393106575r_bool)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (forall ((X3 tptp.code_integer)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool R X3) X3)))) (=> (forall ((X3 tptp.code_integer) (Y3 tptp.code_integer) (Z2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool R X3))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 Y3)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool R Y3) Z2)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 Z2)))))) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) A3)) (exists ((Y4 tptp.code_integer)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Y4) A3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool R X3) Y4)))))) (= A3 tptp.bot_bo3990330152332043303nteger)))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (R tptp.fun_Pr248683899324676269t_bool)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat A3)) (=> (forall ((X3 tptp.product_prod_nat_nat)) (not (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool R X3) X3)))) (=> (forall ((X3 tptp.product_prod_nat_nat) (Y3 tptp.product_prod_nat_nat) (Z2 tptp.product_prod_nat_nat)) (let ((_let_1 (tptp.aa_Pro595088089689268830t_bool R X3))) (=> (tptp.pp (tptp.aa_Pro2232559814647311250t_bool _let_1 Y3)) (=> (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool R Y3) Z2)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool _let_1 Z2)))))) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat X3) A3)) (exists ((Y4 tptp.product_prod_nat_nat)) (and (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat Y4) A3)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool R X3) Y4)))))) (= A3 tptp.bot_bo2099793752762293965at_nat)))))) (forall ((A3 tptp.set_bool) (R tptp.fun_bo1841576699660343469l_bool)) (=> (tptp.finite_finite_bool A3) (=> (forall ((X3 tptp.bool)) (not (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool R X3) X3)))) (=> (forall ((X3 tptp.bool) (Y3 tptp.bool) (Z2 tptp.bool)) (let ((_let_1 (tptp.aa_boo8970175072276269406l_bool R X3))) (=> (tptp.pp (tptp.aa_bool_bool _let_1 Y3)) (=> (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool R Y3) Z2)) (tptp.pp (tptp.aa_bool_bool _let_1 Z2)))))) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 A3)) (exists ((Y4 tptp.bool)) (and (tptp.pp (tptp.member_bool Y4 A3)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool R X3) Y4)))))) (= A3 tptp.bot_bot_set_bool)))))) (forall ((A3 tptp.set_nat) (R tptp.fun_nat_fun_nat_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (forall ((X3 tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R X3) X3)))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool R X3))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 Y3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R Y3) Z2)) (tptp.pp (tptp.aa_nat_bool _let_1 Z2)))))) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A3)) (exists ((Y4 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Y4) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R X3) Y4)))))) (= A3 tptp.bot_bot_set_nat)))))) (forall ((A3 tptp.set_int) (R tptp.fun_int_fun_int_bool)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (forall ((X3 tptp.int)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool R X3) X3)))) (=> (forall ((X3 tptp.int) (Y3 tptp.int) (Z2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool R X3))) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool R Y3) Z2)) (tptp.pp (tptp.aa_int_bool _let_1 Z2)))))) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) A3)) (exists ((Y4 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Y4) A3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool R X3) Y4)))))) (= A3 tptp.bot_bot_set_int)))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2))) (or (= N2 tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_z3403309356797280102nteger))) (and (not _let_2) (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)))))))) (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N2))) (or (= N2 tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_rat))) (and (not _let_2) (tptp.pp (tptp.aa_rat_bool _let_1 A)))))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2))) (or (= N2 tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_int))) (and (not _let_2) (tptp.pp (tptp.aa_int_bool _let_1 A)))))))) (forall ((K tptp.nat) (S tptp.set_nat)) (=> (forall ((M5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K) M5)) (exists ((N8 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M5) N8)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N8) S)))))) (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S))))) (forall ((S tptp.set_nat)) (= (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S))) (forall ((M3 tptp.nat)) (exists ((N tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M3) N)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N) S))))))) (forall ((S tptp.set_nat)) (= (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S))) (forall ((M3 tptp.nat)) (exists ((N tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M3) N)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N) S))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_2 M)) tptp.one_one_nat)) (tptp.aa_nat_nat _let_2 N2)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_fun_nat_int tptp.power_power_int _let_1))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int _let_2 M)) tptp.one_one_int)) (tptp.aa_nat_int _let_2 N2)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_8256067586552552935nteger _let_1))) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_nat_Code_integer _let_2 M)) tptp.one_one_Code_integer)) (tptp.aa_nat_Code_integer _let_2 N2)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_7079662738309270450atural _let_1))) (= (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural _let_1) (tptp.divide5121882707175180666atural (tptp.minus_7197305767214868737atural (tptp.aa_nat_Code_natural _let_2 M) tptp.one_one_Code_natural) (tptp.aa_nat_Code_natural _let_2 N2)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2)) tptp.zero_z3403309356797280102nteger)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (or (and (not _let_1) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger))) (and _let_1 (= A tptp.zero_z3403309356797280102nteger))))))) (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N2)) tptp.zero_zero_rat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (or (and (not _let_1) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat))) (and _let_1 (= A tptp.zero_zero_rat))))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2)) tptp.zero_zero_int)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (or (and (not _let_1) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int))) (and _let_1 (= A tptp.zero_zero_int))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1))) (let ((_let_3 (tptp.aa_nat_nat _let_2 N2))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_2 M)) tptp.one_one_nat)) _let_3))) (or (= _let_3 tptp.zero_zero_nat) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_fun_nat_int tptp.power_power_int _let_1))) (let ((_let_3 (tptp.aa_nat_int _let_2 N2))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int _let_2 M)) tptp.one_one_int)) _let_3))) (or (= _let_3 tptp.zero_zero_int) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_8256067586552552935nteger _let_1))) (let ((_let_3 (tptp.aa_nat_Code_integer _let_2 N2))) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_nat_Code_integer _let_2 M)) tptp.one_one_Code_integer)) _let_3))) (or (= _let_3 tptp.zero_z3403309356797280102nteger) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_7079662738309270450atural _let_1))) (let ((_let_3 (tptp.aa_nat_Code_natural _let_2 N2))) (= (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural _let_1) (tptp.divide5121882707175180666atural (tptp.minus_7197305767214868737atural (tptp.aa_nat_Code_natural _let_2 M) tptp.one_one_Code_natural) _let_3))) (or (= _let_3 tptp.zero_z2226904508553997617atural) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))))))) (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1))) (let ((_let_3 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1))) (let ((_let_4 (tptp.aa_nat_nat _let_2 N2))) (= (tptp.pp (tptp.aa_nat_bool _let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) (tptp.aa_nat_nat _let_2 M))) _let_4))) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)) (= _let_4 tptp.zero_zero_nat) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (tptp.pp (tptp.aa_nat_bool _let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M))))))))))))) (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_fun_nat_int tptp.power_power_int _let_1))) (let ((_let_3 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1))) (let ((_let_4 (tptp.aa_nat_int _let_2 N2))) (= (tptp.pp (tptp.aa_int_bool _let_3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) (tptp.aa_nat_int _let_2 M))) _let_4))) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)) (= _let_4 tptp.zero_zero_int) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (tptp.pp (tptp.aa_int_bool _let_3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) (tptp.aa_nat_int _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M))))))))))))) (forall ((A tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_8256067586552552935nteger _let_1))) (let ((_let_3 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1))) (let ((_let_4 (tptp.aa_nat_Code_integer _let_2 N2))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_3 (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) (tptp.aa_nat_Code_integer _let_2 M))) _let_4))) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)) (= _let_4 tptp.zero_z3403309356797280102nteger) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (tptp.pp (tptp.aa_Code_integer_bool _let_3 (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) (tptp.aa_nat_Code_integer _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M))))))))))))) (forall ((A tptp.code_natural) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_7079662738309270450atural _let_1))) (let ((_let_3 (tptp.dvd_dvd_Code_natural _let_1))) (let ((_let_4 (tptp.aa_nat_Code_natural _let_2 N2))) (= (tptp.pp (tptp.aa_Code_natural_bool _let_3 (tptp.divide5121882707175180666atural (tptp.times_2397367101498566445atural A (tptp.aa_nat_Code_natural _let_2 M)) _let_4))) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)) (= _let_4 tptp.zero_z2226904508553997617atural) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (tptp.pp (tptp.aa_Code_natural_bool _let_3 (tptp.divide5121882707175180666atural A (tptp.aa_nat_Code_natural _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M))))))))))))) (forall ((X tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_rat_int tptp.archim7778729529865785530nd_rat X))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat tptp.one_one_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (forall ((X tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat tptp.one_one_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_rat_int tptp.archim7778729529865785530nd_rat X))))) (forall ((X tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat X) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat tptp.one_one_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_rat_int tptp.archim7778729529865785530nd_rat X))))) (forall ((S tptp.set_int)) (= (not (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S))) (forall ((M3 tptp.int)) (exists ((N tptp.int)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int M3) (tptp.aa_int_int tptp.abs_abs_int N))) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int N) S))))))) (forall ((S tptp.set_int)) (= (not (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S))) (forall ((M3 tptp.int)) (exists ((N tptp.int)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int M3) (tptp.aa_int_int tptp.abs_abs_int N))) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int N) S))))))) (forall ((X tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_rat_int tptp.archim7778729529865785530nd_rat X))) X))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat tptp.one_one_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((X tptp.rat) (N2 tptp.int)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat X) (tptp.aa_int_rat tptp.ring_1_of_int_rat N2)))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat tptp.one_one_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_rat_int tptp.archim7778729529865785530nd_rat X) N2))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.member8277197624267554838et_nat (tptp.produc4532415448927165861et_nat A3 B3) tptp.finite_psubset_nat) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat A3) B3)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (tptp.member2572552093476627150et_int (tptp.produc6363374080413544029et_int A3 B3) tptp.finite_psubset_int) (and (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int A3) B3)) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer)) (= (tptp.member4307123515891402160nteger (tptp.produc7443773368509356479nteger A3 B3) tptp.finite2416775604798480986nteger) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le1307284697595431911nteger A3) B3)) (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.member8757157785044589968at_nat (tptp.produc2922128104949294807at_nat A3 B3) tptp.finite469560695537375940at_nat) (and (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le7866589430770878221at_nat A3) B3)) (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat B3))))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.bit_se1345352211410354436nteger tptp.zero_zero_nat) A) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) _let_1)))))) (forall ((A tptp.code_natural)) (let ((_let_1 (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.bit_se168947363167071951atural tptp.zero_zero_nat A) (tptp.plus_p4538020629002901425atural (tptp.zero_n8403883297036319079atural (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural _let_1) A)) (tptp.times_2397367101498566445atural _let_1 (tptp.divide5121882707175180666atural A _let_1)))))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2161824704523386999it_nat tptp.zero_zero_nat) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1)))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2159334234014336723it_int tptp.zero_zero_nat) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) _let_1)))))) (forall ((X tptp.nat)) (= (tptp.aa_nat_set_nat tptp.nat_set_decode X) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_afb X)))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_Cod1783974652533396728nteger (tptp.bit_se1745604003318907178nteger N2) A))) (let ((_let_3 (= N2 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.bit_se1745604003318907178nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat)) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) _let_1))) _let_1)) (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) _let_1))))))))) (forall ((N2 tptp.nat) (A tptp.code_natural)) (let ((_let_1 (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.bit_se569199155075624693atural N2 A))) (let ((_let_3 (= N2 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_z2226904508553997617atural)) (=> (not _let_3) (= _let_2 (tptp.plus_p4538020629002901425atural (tptp.times_2397367101498566445atural (tptp.bit_se569199155075624693atural (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat) (tptp.divide5121882707175180666atural A _let_1)) _let_1) (tptp.modulo8411746178871703098atural A _let_1))))))))) (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N2) A))) (let ((_let_3 (= N2 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1))) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_1))))))))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) A))) (let ((_let_3 (= N2 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) _let_1))) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) _let_1))))))))) (forall ((L tptp.num) (Qr tptp.product_prod_nat_nat)) (= (tptp.aa_Pro262675715343573244at_nat (tptp.unique5026877609467782581ep_nat L) Qr) (tptp.aa_Pro262675715343573244at_nat (tptp.produc2626176000494625587at_nat (tptp.aTP_Lamm_afc L)) Qr))) (forall ((L tptp.num) (Qr tptp.product_prod_int_int)) (= (tptp.aa_Pro6970504127699319548nt_int (tptp.unique5024387138958732305ep_int L) Qr) (tptp.aa_Pro6970504127699319548nt_int (tptp.aa_fun8026974734089330650nt_int tptp.produc4245557441103728435nt_int (tptp.aTP_Lamm_afd L)) Qr))) (forall ((L tptp.num) (Qr tptp.produc8923325533196201883nteger)) (= (tptp.unique4921790084139445826nteger L Qr) (tptp.produc6916734918728496179nteger (tptp.aTP_Lamm_afe L) Qr))) (forall ((N2 tptp.nat)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((N2 tptp.nat)) (= (tptp.modulo8411746178871703098atural tptp.one_one_Code_natural (tptp.aa_nat_Code_natural (tptp.power_7079662738309270450atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) (tptp.zero_n8403883297036319079atural (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat tptp.one_one_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((N2 tptp.nat)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int tptp.one_one_int) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((P tptp.bool) (Q tptp.bool)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_bool_rat tptp.zero_n2052037380579107095ol_rat P)) (tptp.aa_bool_rat tptp.zero_n2052037380579107095ol_rat Q))) (=> (tptp.pp P) (tptp.pp Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat P)) (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat Q))) (=> (tptp.pp P) (tptp.pp Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P)) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int Q))) (=> (tptp.pp P) (tptp.pp Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_bool_rat tptp.zero_n2052037380579107095ol_rat P)) (tptp.aa_bool_rat tptp.zero_n2052037380579107095ol_rat Q))) (and (not (tptp.pp P)) (tptp.pp Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat P)) (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat Q))) (and (not (tptp.pp P)) (tptp.pp Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P)) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int Q))) (and (not (tptp.pp P)) (tptp.pp Q)))) (forall ((P tptp.bool)) (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat P)) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger P))) (forall ((P tptp.bool)) (let ((_let_1 (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat P))) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat _let_1) _let_1))) (forall ((P tptp.bool)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat P)) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P))) (forall ((A tptp.nat) (B tptp.nat) (A3 tptp.set_Pr1261947904930325089at_nat) (F tptp.fun_nat_fun_nat_bool)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat A) B)) A3)) (tptp.pp (tptp.member_bool (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool F A) B) (tptp.image_2883496220479709787t_bool (tptp.produc8955392012077580105t_bool F) A3))))) (forall ((A tptp.nat) (B tptp.nat) (A3 tptp.set_Pr1261947904930325089at_nat) (F tptp.fun_nat_fun_nat_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat A) B)) A3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat F A) B)) (tptp.image_2486076414777270412at_nat (tptp.produc6842872674320459806at_nat F) A3))))) (forall ((A tptp.nat) (B tptp.nat) (A3 tptp.set_Pr1261947904930325089at_nat) (F tptp.fun_nat_fun_nat_int)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat A) B)) A3)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int F A) B)) (tptp.image_2483585944268220136at_int (tptp.produc6840382203811409530at_int F) A3))))) (forall ((A tptp.int) (B tptp.int) (A3 tptp.set_Pr958786334691620121nt_int) (F tptp.fun_int_fun_int_bool)) (=> (tptp.member5262025264175285858nt_int (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) B) A3) (tptp.pp (tptp.member_bool (tptp.aa_int_bool (tptp.aa_int_fun_int_bool F A) B) (tptp.image_5152817838431879587t_bool (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool F) A3))))) (forall ((A tptp.int) (B tptp.int) (A3 tptp.set_Pr958786334691620121nt_int) (F tptp.fun_int_fun_int_int)) (=> (tptp.member5262025264175285858nt_int (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) B) A3) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int (tptp.aa_int_int (tptp.aa_int_fun_int_int F A) B)) (tptp.image_5042161079198086560nt_int (tptp.aa_fun914008879417524284nt_int tptp.produc8211389475949308722nt_int F) A3))))) (forall ((A tptp.nat) (B tptp.nat) (A3 tptp.set_Pr1261947904930325089at_nat) (F tptp.fun_na6128946301132549280et_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat A) B)) A3)) (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat F A) B)) (tptp.image_15824709712370754et_nat (tptp.produc6189476227299908564et_nat F) A3))))) (forall ((A tptp.nat) (B tptp.nat) (A3 tptp.set_Pr1261947904930325089at_nat) (F tptp.fun_na4138050610385705875at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat A) B)) A3)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat F A) B)) (tptp.image_5168914502847457605at_nat (tptp.produc2626176000494625587at_nat F) A3))))) (forall ((A tptp.int) (B tptp.int) (A3 tptp.set_Pr958786334691620121nt_int) (F tptp.fun_in1696471567231710611nt_int)) (=> (tptp.member5262025264175285858nt_int (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) B) A3) (tptp.member5262025264175285858nt_int (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int F A) B) (tptp.image_2653370878348428101nt_int (tptp.aa_fun8026974734089330650nt_int tptp.produc4245557441103728435nt_int F) A3)))) (forall ((A tptp.a) (B tptp.produc6653097349344004940it_nat) (A3 tptp.set_Pr7098220151150636591it_nat) (F tptp.fun_a_4602865052023851497t_bool)) (=> (tptp.member4554412811331277712it_nat (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat A) B) A3) (tptp.pp (tptp.member_bool (tptp.aa_Pro3182513528956304653t_bool (tptp.aa_a_f736957945511644770t_bool F A) B) (tptp.image_2085947142583304215t_bool (tptp.produc62718094566300407t_bool F) A3))))) (forall ((A tptp.a) (B tptp.produc6653097349344004940it_nat) (A3 tptp.set_Pr7098220151150636591it_nat) (F tptp.fun_a_5416464254913058730at_nat)) (=> (tptp.member4554412811331277712it_nat (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat A) B) A3) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat (tptp.aa_Pro3734910839824185690at_nat (tptp.aa_a_f8203466477562882395at_nat F A) B)) (tptp.image_1030127162643715024at_nat (tptp.produc7727125748877983984at_nat F) A3))))) (forall ((F tptp.fun_na1668100129766719005at_nat) (A tptp.nat) (B tptp.nat)) (= (tptp.aa_Pro8023792847356852296at_nat (tptp.aa_fun6875833325056119164at_nat tptp.produc4528391901023682385at_nat F) (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat A) B)) (tptp.aa_nat7997280740862404369at_nat (tptp.aa_nat5682243440470347102at_nat F A) B))) (forall ((F tptp.fun_na4786964484885125043t_bool) (A tptp.nat) (B tptp.nat)) (= (tptp.aa_Pro595088089689268830t_bool (tptp.aa_fun174371099813217148t_bool tptp.produc5023667602222594023t_bool F) (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat A) B)) (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool F A) B))) (forall ((F tptp.fun_in1696471567231710611nt_int) (A tptp.int) (B tptp.int)) (= (tptp.aa_Pro6970504127699319548nt_int (tptp.aa_fun8026974734089330650nt_int tptp.produc4245557441103728435nt_int F) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) B)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int F A) B))) (forall ((F tptp.fun_int_fun_int_bool) (A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool F) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool F A) B)))) (forall ((F tptp.fun_int_fun_int_int) (A tptp.int) (B tptp.int)) (= (tptp.aa_Pro6799258434465214121nt_int (tptp.aa_fun914008879417524284nt_int tptp.produc8211389475949308722nt_int F) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int F A) B))) (forall ((F tptp.fun_na1668100129766719005at_nat)) (= (tptp.produc4701859392678344816at_nat (tptp.aa_fun6875833325056119164at_nat tptp.produc4528391901023682385at_nat F)) F)) (forall ((F tptp.fun_na4786964484885125043t_bool)) (= (tptp.produc2783699230612031110t_bool (tptp.aa_fun174371099813217148t_bool tptp.produc5023667602222594023t_bool F)) F)) (forall ((F tptp.fun_in1696471567231710611nt_int)) (= (tptp.produc8249235968001453780nt_int (tptp.aa_fun8026974734089330650nt_int tptp.produc4245557441103728435nt_int F)) F)) (forall ((F tptp.fun_int_fun_int_bool)) (= (tptp.produc8844785472727440050t_bool (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool F)) F)) (forall ((F tptp.fun_int_fun_int_int)) (= (tptp.produc1016772743285680337nt_int (tptp.aa_fun914008879417524284nt_int tptp.produc8211389475949308722nt_int F)) F)) (forall ((F tptp.fun_Pr2477239776880934807at_nat)) (= (tptp.aa_fun6875833325056119164at_nat tptp.produc4528391901023682385at_nat (tptp.produc4701859392678344816at_nat F)) F)) (forall ((F tptp.fun_Pr248683899324676269t_bool)) (= (tptp.aa_fun174371099813217148t_bool tptp.produc5023667602222594023t_bool (tptp.produc2783699230612031110t_bool F)) F)) (forall ((F tptp.fun_Pr2478283820680522243nt_int)) (= (tptp.aa_fun8026974734089330650nt_int tptp.produc4245557441103728435nt_int (tptp.produc8249235968001453780nt_int F)) F)) (forall ((F tptp.fun_Pr803113274115125473t_bool)) (= (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool (tptp.produc8844785472727440050t_bool F)) F)) (forall ((F tptp.fun_Pr982841511892225912nt_int)) (= (tptp.aa_fun914008879417524284nt_int tptp.produc8211389475949308722nt_int (tptp.produc1016772743285680337nt_int F)) F)) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((P tptp.bool)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger P))) (tptp.pp P))) (forall ((P tptp.bool)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_bool_rat tptp.zero_n2052037380579107095ol_rat P))) (tptp.pp P))) (forall ((P tptp.bool)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat P))) (tptp.pp P))) (forall ((P tptp.bool)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P))) (tptp.pp P))) (forall ((P tptp.bool)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer)) (not (tptp.pp P)))) (forall ((P tptp.bool)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_bool_rat tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat)) (not (tptp.pp P)))) (forall ((P tptp.bool)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat)) (not (tptp.pp P)))) (forall ((P tptp.bool)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int)) (not (tptp.pp P)))) (= (tptp.aa_nat_set_nat tptp.nat_set_decode tptp.zero_zero_nat) tptp.bot_bot_set_nat) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer A))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) _let_1) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_bool_bool tptp.fNot (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer A) tptp.zero_z3403309356797280102nteger)))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.sgn_sgn_rat A))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat _let_1) _let_1) (tptp.aa_bool_rat tptp.zero_n2052037380579107095ol_rat (tptp.aa_bool_bool tptp.fNot (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.fequal_rat A) tptp.zero_zero_rat)))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.sgn_sgn_int A))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) _let_1) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int A) tptp.zero_zero_int)))))) (forall ((N2 tptp.nat)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.bit_se1745604003318907178nteger N2) tptp.one_one_Code_integer) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N2) tptp.one_one_nat) (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((N2 tptp.nat)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) tptp.one_one_int) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((N2 tptp.nat)) (= (tptp.aa_rat_rat tptp.sgn_sgn_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2)) (tptp.aa_bool_rat tptp.zero_n2052037380579107095ol_rat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((N2 tptp.nat)) (= (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2)) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((N2 tptp.nat)) (= (tptp.aa_int_int tptp.sgn_sgn_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((A3 tptp.set_int) (F tptp.fun_int_Code_integer) (P tptp.fun_int_bool)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups7873554091576472773nteger (tptp.aa_fun5397227419668681614nteger (tptp.aTP_Lamm_aff F) P) A3) (tptp.groups7873554091576472773nteger F (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) (tptp.collect_int P)))))) (forall ((A3 tptp.set_Code_integer) (F tptp.fun_Co8499238673658658103nteger) (P tptp.fun_Co8822979462182099027r_bool)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups879477027807139574nteger (tptp.aa_fun526110101794841038nteger (tptp.aTP_Lamm_afg F) P) A3) (tptp.groups879477027807139574nteger F (tptp.inf_in1364745209274528805nteger A3 (tptp.collect_Code_integer P)))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_Code_integer) (P tptp.fun_nat_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger (tptp.aa_fun42370497693836430nteger (tptp.aTP_Lamm_afh F) P)) A3) (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger F) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) (tptp.collect_nat P)))))) (forall ((A3 tptp.set_int) (F tptp.fun_int_rat) (P tptp.fun_int_bool)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups3906332499630173760nt_rat (tptp.aa_fun4400602662665189257nt_rat (tptp.aTP_Lamm_afi F) P) A3) (tptp.groups3906332499630173760nt_rat F (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) (tptp.collect_int P)))))) (forall ((A3 tptp.set_Code_integer) (F tptp.fun_Code_integer_rat) (P tptp.fun_Co8822979462182099027r_bool)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups6602215022474089585er_rat (tptp.aa_fun4600455420518417865er_rat (tptp.aTP_Lamm_afj F) P) A3) (tptp.groups6602215022474089585er_rat F (tptp.inf_in1364745209274528805nteger A3 (tptp.collect_Code_integer P)))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_rat) (P tptp.fun_nat_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aa_fun5656162108953708681at_rat (tptp.aTP_Lamm_afk F) P)) A3) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat F) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) (tptp.collect_nat P)))))) (forall ((A3 tptp.set_int) (F tptp.fun_int_nat) (P tptp.fun_int_bool)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups4541462559716669496nt_nat (tptp.aa_fun7908831221058585985nt_nat (tptp.aTP_Lamm_afl F) P) A3) (tptp.groups4541462559716669496nt_nat F (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) (tptp.collect_int P)))))) (forall ((A3 tptp.set_Code_integer) (F tptp.fun_Code_integer_nat) (P tptp.fun_Co8822979462182099027r_bool)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups7237345082560585321er_nat (tptp.aa_fun8108683978911814593er_nat (tptp.aTP_Lamm_afm F) P) A3) (tptp.groups7237345082560585321er_nat F (tptp.inf_in1364745209274528805nteger A3 (tptp.collect_Code_integer P)))))) (forall ((A3 tptp.set_Code_integer) (F tptp.fun_Code_integer_int) (P tptp.fun_Co8822979462182099027r_bool)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups7234854612051535045er_int (tptp.aa_fun3930832959402617885er_int (tptp.aTP_Lamm_afn F) P) A3) (tptp.groups7234854612051535045er_int F (tptp.inf_in1364745209274528805nteger A3 (tptp.collect_Code_integer P)))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_int) (P tptp.fun_nat_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aa_fun4986539647837908701at_int (tptp.aTP_Lamm_afo F) P)) A3) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int F) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) (tptp.collect_nat P)))))) (forall ((A3 tptp.set_int) (P tptp.fun_int_bool) (F tptp.fun_int_Code_integer)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups7873554091576472773nteger (tptp.aa_fun5304498221708291146nteger (tptp.aTP_Lamm_afp P) F) A3) (tptp.groups7873554091576472773nteger F (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) (tptp.collect_int P)))))) (forall ((A3 tptp.set_Code_integer) (P tptp.fun_Co8822979462182099027r_bool) (F tptp.fun_Co8499238673658658103nteger)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups879477027807139574nteger (tptp.aa_fun4435975922079263404nteger (tptp.aTP_Lamm_afq P) F) A3) (tptp.groups879477027807139574nteger F (tptp.inf_in1364745209274528805nteger A3 (tptp.collect_Code_integer P)))))) (forall ((A3 tptp.set_nat) (P tptp.fun_nat_bool) (F tptp.fun_nat_Code_integer)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger (tptp.aa_fun589076786913273746nteger (tptp.aTP_Lamm_afr P) F)) A3) (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger F) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) (tptp.collect_nat P)))))) (forall ((A3 tptp.set_int) (P tptp.fun_int_bool) (F tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups3906332499630173760nt_rat (tptp.aa_fun1481061427733998144nt_rat (tptp.aTP_Lamm_afs P) F) A3) (tptp.groups3906332499630173760nt_rat F (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) (tptp.collect_int P)))))) (forall ((A3 tptp.set_Code_integer) (P tptp.fun_Co8822979462182099027r_bool) (F tptp.fun_Code_integer_rat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups6602215022474089585er_rat (tptp.aa_fun8169474305930283170er_rat (tptp.aTP_Lamm_aft P) F) A3) (tptp.groups6602215022474089585er_rat F (tptp.inf_in1364745209274528805nteger A3 (tptp.collect_Code_integer P)))))) (forall ((A3 tptp.set_nat) (P tptp.fun_nat_bool) (F tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_afu P) F)) A3) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat F) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) (tptp.collect_nat P)))))) (forall ((A3 tptp.set_int) (P tptp.fun_int_bool) (F tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.groups4541462559716669496nt_nat (tptp.aa_fun6506752150744536624nt_nat (tptp.aTP_Lamm_afv P) F) A3) (tptp.groups4541462559716669496nt_nat F (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) (tptp.collect_int P)))))) (forall ((A3 tptp.set_Code_integer) (P tptp.fun_Co8822979462182099027r_bool) (F tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups7237345082560585321er_nat (tptp.aa_fun3076867170244285586er_nat (tptp.aTP_Lamm_afw P) F) A3) (tptp.groups7237345082560585321er_nat F (tptp.inf_in1364745209274528805nteger A3 (tptp.collect_Code_integer P)))))) (forall ((A3 tptp.set_Code_integer) (P tptp.fun_Co8822979462182099027r_bool) (F tptp.fun_Code_integer_int)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.groups7234854612051535045er_int (tptp.aa_fun3291479149765983562er_int (tptp.aTP_Lamm_afx P) F) A3) (tptp.groups7234854612051535045er_int F (tptp.inf_in1364745209274528805nteger A3 (tptp.collect_Code_integer P)))))) (forall ((A3 tptp.set_nat) (P tptp.fun_nat_bool) (F tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aa_fun5565043122120104496at_int (tptp.aTP_Lamm_afy P) F)) A3) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int F) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) (tptp.collect_nat P)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.bit_se1745604003318907178nteger M) _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M))) _let_1)))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_natural (tptp.power_7079662738309270450atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (= (tptp.bit_se569199155075624693atural M _let_1) (tptp.times_2397367101498566445atural (tptp.zero_n8403883297036319079atural (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)) _let_1)))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat M) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M))) _let_1)))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int M) _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M))) _let_1)))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger _let_1))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.bit_se1745604003318907178nteger N2) _let_2) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N2))) _let_2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural _let_1))) (= (tptp.bit_se569199155075624693atural N2 _let_2) (tptp.times_2397367101498566445atural (tptp.zero_n8403883297036319079atural (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N2)) _let_2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N2) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) N2))) _let_1)))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int _let_1))) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) _let_2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N2))) _let_2))))) (forall ((F tptp.fun_na1668100129766719005at_nat) (X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (tptp.aa_Pro262675715343573244at_nat (tptp.aa_Pro8023792847356852296at_nat (tptp.aa_fun6875833325056119164at_nat tptp.produc4528391901023682385at_nat F) X) Y) (tptp.aa_Pro262675715343573244at_nat (tptp.produc2626176000494625587at_nat (tptp.aa_Pro6895555690143131534at_nat (tptp.aTP_Lamm_afz F) Y)) X))) (forall ((F tptp.fun_na4786964484885125043t_bool) (X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool (tptp.aa_fun174371099813217148t_bool tptp.produc5023667602222594023t_bool F) X) Y)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.produc8955392012077580105t_bool (tptp.aa_Pro3143461022101918244t_bool (tptp.aTP_Lamm_aga F) Y)) X)))) (forall ((F tptp.fun_na1668100129766719005at_nat) (X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (tptp.aa_Pro262675715343573244at_nat (tptp.aa_Pro8023792847356852296at_nat (tptp.aa_fun6875833325056119164at_nat tptp.produc4528391901023682385at_nat F) X) Y) (tptp.aa_Pro262675715343573244at_nat (tptp.produc2626176000494625587at_nat (tptp.aa_Pro6895555690143131534at_nat (tptp.aTP_Lamm_afz F) Y)) X))) (forall ((F tptp.fun_na4786964484885125043t_bool) (X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool (tptp.aa_fun174371099813217148t_bool tptp.produc5023667602222594023t_bool F) X) Y)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.produc8955392012077580105t_bool (tptp.aa_Pro3143461022101918244t_bool (tptp.aTP_Lamm_aga F) Y)) X)))) (forall ((H tptp.fun_bool_bool) (F tptp.fun_int_fun_int_bool) (Prod tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_bool_bool H (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool F) Prod))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool (tptp.aa_fun8168818243683596540t_bool (tptp.aTP_Lamm_agb H) F)) Prod)))) (forall ((H tptp.fun_bool_int) (F tptp.fun_int_fun_int_bool) (Prod tptp.product_prod_int_int)) (= (tptp.aa_bool_int H (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool F) Prod)) (tptp.aa_Pro6799258434465214121nt_int (tptp.aa_fun914008879417524284nt_int tptp.produc8211389475949308722nt_int (tptp.aa_fun5341983444565040691nt_int (tptp.aTP_Lamm_agc H) F)) Prod))) (forall ((H tptp.fun_int_bool) (F tptp.fun_int_fun_int_int) (Prod tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_int_bool H (tptp.aa_Pro6799258434465214121nt_int (tptp.aa_fun914008879417524284nt_int tptp.produc8211389475949308722nt_int F) Prod))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool (tptp.aa_fun980369494830392501t_bool (tptp.aTP_Lamm_agd H) F)) Prod)))) (forall ((H tptp.fun_int_int) (F tptp.fun_int_fun_int_int) (Prod tptp.product_prod_int_int)) (= (tptp.aa_int_int H (tptp.aa_Pro6799258434465214121nt_int (tptp.aa_fun914008879417524284nt_int tptp.produc8211389475949308722nt_int F) Prod)) (tptp.aa_Pro6799258434465214121nt_int (tptp.aa_fun914008879417524284nt_int tptp.produc8211389475949308722nt_int (tptp.aa_fun6119123525526402106nt_int (tptp.aTP_Lamm_age H) F)) Prod))) (forall ((H tptp.fun_Pr803113274115125473t_bool) (F tptp.fun_in1696471567231710611nt_int) (Prod tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool H (tptp.aa_Pro6970504127699319548nt_int (tptp.aa_fun8026974734089330650nt_int tptp.produc4245557441103728435nt_int F) Prod))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool (tptp.aa_fun395975271853239642t_bool (tptp.aTP_Lamm_agf H) F)) Prod)))) (forall ((H tptp.fun_Pr982841511892225912nt_int) (F tptp.fun_in1696471567231710611nt_int) (Prod tptp.product_prod_int_int)) (= (tptp.aa_Pro6799258434465214121nt_int H (tptp.aa_Pro6970504127699319548nt_int (tptp.aa_fun8026974734089330650nt_int tptp.produc4245557441103728435nt_int F) Prod)) (tptp.aa_Pro6799258434465214121nt_int (tptp.aa_fun914008879417524284nt_int tptp.produc8211389475949308722nt_int (tptp.aa_fun7461304428735181397nt_int (tptp.aTP_Lamm_agg H) F)) Prod))) (forall ((H tptp.fun_bo7720638723722887333nt_int) (F tptp.fun_int_fun_int_bool) (Prod tptp.product_prod_int_int)) (= (tptp.aa_boo6976928504896087454nt_int H (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool F) Prod)) (tptp.aa_Pro6970504127699319548nt_int (tptp.aa_fun8026974734089330650nt_int tptp.produc4245557441103728435nt_int (tptp.aa_fun9101259627203045662nt_int (tptp.aTP_Lamm_agh H) F)) Prod))) (forall ((H tptp.fun_in4211310926729683942nt_int) (F tptp.fun_int_fun_int_int) (Prod tptp.product_prod_int_int)) (= (tptp.aa_int7462565939943104719nt_int H (tptp.aa_Pro6799258434465214121nt_int (tptp.aa_fun914008879417524284nt_int tptp.produc8211389475949308722nt_int F) Prod)) (tptp.aa_Pro6970504127699319548nt_int (tptp.aa_fun8026974734089330650nt_int tptp.produc4245557441103728435nt_int (tptp.aa_fun1034830265760468567nt_int (tptp.aTP_Lamm_agi H) F)) Prod))) (forall ((H tptp.fun_Pr2478283820680522243nt_int) (F tptp.fun_in1696471567231710611nt_int) (Prod tptp.product_prod_int_int)) (= (tptp.aa_Pro6970504127699319548nt_int H (tptp.aa_Pro6970504127699319548nt_int (tptp.aa_fun8026974734089330650nt_int tptp.produc4245557441103728435nt_int F) Prod)) (tptp.aa_Pro6970504127699319548nt_int (tptp.aa_fun8026974734089330650nt_int tptp.produc4245557441103728435nt_int (tptp.aa_fun4152872853588681340nt_int (tptp.aTP_Lamm_agj H) F)) Prod))) (forall ((H tptp.fun_fu6897202038601531823t_bool) (F tptp.fun_na4786964484885125043t_bool) (Prod tptp.product_prod_nat_nat)) (= (tptp.aa_fun830836278467416944t_bool H (tptp.aa_Pro595088089689268830t_bool (tptp.aa_fun174371099813217148t_bool tptp.produc5023667602222594023t_bool F) Prod)) (tptp.aa_Pro595088089689268830t_bool (tptp.aa_fun174371099813217148t_bool tptp.produc5023667602222594023t_bool (tptp.aa_fun3491305611276047780t_bool (tptp.aTP_Lamm_agk H) F)) Prod))) (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat M))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N2))) (=> (= (tptp.aa_nat_nat _let_2 A) (tptp.aa_nat_nat _let_2 B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_nat_nat _let_1 A) (tptp.aa_nat_nat _let_1 B))))))) (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int M))) (let ((_let_2 (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2))) (=> (= (tptp.aa_int_int _let_2 A) (tptp.aa_int_int _let_2 B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_int_int _let_1 A) (tptp.aa_int_int _let_1 B))))))) (forall ((M tptp.nat) (N2 tptp.nat) (Q5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat M) Q5)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N2) Q5))))) (forall ((N2 tptp.nat) (M tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N2) M)) M))) (forall ((P tptp.bool) (Q tptp.bool)) (= (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fconj P) Q)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger P)) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (= (tptp.aa_bool_rat tptp.zero_n2052037380579107095ol_rat (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fconj P) Q)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_bool_rat tptp.zero_n2052037380579107095ol_rat P)) (tptp.aa_bool_rat tptp.zero_n2052037380579107095ol_rat Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (= (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fconj P) Q)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat P)) (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (= (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fconj P) Q)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P)) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int Q)))) (forall ((Q5 tptp.product_prod_nat_nat) (F tptp.fun_na1668100129766719005at_nat) (G tptp.fun_na1668100129766719005at_nat) (P3 tptp.product_prod_nat_nat)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat X3) Y3) Q5) (= (tptp.aa_nat7997280740862404369at_nat (tptp.aa_nat5682243440470347102at_nat F X3) Y3) (tptp.aa_nat7997280740862404369at_nat (tptp.aa_nat5682243440470347102at_nat G X3) Y3)))) (=> (= P3 Q5) (= (tptp.aa_Pro8023792847356852296at_nat (tptp.aa_fun6875833325056119164at_nat tptp.produc4528391901023682385at_nat F) P3) (tptp.aa_Pro8023792847356852296at_nat (tptp.aa_fun6875833325056119164at_nat tptp.produc4528391901023682385at_nat G) Q5))))) (forall ((Q5 tptp.product_prod_nat_nat) (F tptp.fun_na4786964484885125043t_bool) (G tptp.fun_na4786964484885125043t_bool) (P3 tptp.product_prod_nat_nat)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat X3) Y3) Q5) (= (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool F X3) Y3) (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool G X3) Y3)))) (=> (= P3 Q5) (= (tptp.aa_Pro595088089689268830t_bool (tptp.aa_fun174371099813217148t_bool tptp.produc5023667602222594023t_bool F) P3) (tptp.aa_Pro595088089689268830t_bool (tptp.aa_fun174371099813217148t_bool tptp.produc5023667602222594023t_bool G) Q5))))) (forall ((Q5 tptp.product_prod_int_int) (F tptp.fun_in1696471567231710611nt_int) (G tptp.fun_in1696471567231710611nt_int) (P3 tptp.product_prod_int_int)) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X3) Y3) Q5) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int F X3) Y3) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int G X3) Y3)))) (=> (= P3 Q5) (= (tptp.aa_Pro6970504127699319548nt_int (tptp.aa_fun8026974734089330650nt_int tptp.produc4245557441103728435nt_int F) P3) (tptp.aa_Pro6970504127699319548nt_int (tptp.aa_fun8026974734089330650nt_int tptp.produc4245557441103728435nt_int G) Q5))))) (forall ((Q5 tptp.product_prod_int_int) (F tptp.fun_int_fun_int_bool) (G tptp.fun_int_fun_int_bool) (P3 tptp.product_prod_int_int)) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X3) Y3) Q5) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool F X3) Y3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool G X3) Y3))))) (=> (= P3 Q5) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool F) P3)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool G) Q5)))))) (forall ((Q5 tptp.product_prod_int_int) (F tptp.fun_int_fun_int_int) (G tptp.fun_int_fun_int_int) (P3 tptp.product_prod_int_int)) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X3) Y3) Q5) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int F X3) Y3) (tptp.aa_int_int (tptp.aa_int_fun_int_int G X3) Y3)))) (=> (= P3 Q5) (= (tptp.aa_Pro6799258434465214121nt_int (tptp.aa_fun914008879417524284nt_int tptp.produc8211389475949308722nt_int F) P3) (tptp.aa_Pro6799258434465214121nt_int (tptp.aa_fun914008879417524284nt_int tptp.produc8211389475949308722nt_int G) Q5))))) (forall ((F tptp.fun_na1668100129766719005at_nat) (X1 tptp.nat) (X2 tptp.nat)) (= (tptp.aa_Pro8023792847356852296at_nat (tptp.aa_fun6875833325056119164at_nat tptp.produc4528391901023682385at_nat F) (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat X1) X2)) (tptp.aa_nat7997280740862404369at_nat (tptp.aa_nat5682243440470347102at_nat F X1) X2))) (forall ((F tptp.fun_na4786964484885125043t_bool) (X1 tptp.nat) (X2 tptp.nat)) (= (tptp.aa_Pro595088089689268830t_bool (tptp.aa_fun174371099813217148t_bool tptp.produc5023667602222594023t_bool F) (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat X1) X2)) (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool F X1) X2))) (forall ((F tptp.fun_in1696471567231710611nt_int) (X1 tptp.int) (X2 tptp.int)) (= (tptp.aa_Pro6970504127699319548nt_int (tptp.aa_fun8026974734089330650nt_int tptp.produc4245557441103728435nt_int F) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X1) X2)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int F X1) X2))) (forall ((F tptp.fun_int_fun_int_bool) (X1 tptp.int) (X2 tptp.int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool F) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X1) X2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool F X1) X2)))) (forall ((F tptp.fun_int_fun_int_int) (X1 tptp.int) (X2 tptp.int)) (= (tptp.aa_Pro6799258434465214121nt_int (tptp.aa_fun914008879417524284nt_int tptp.produc8211389475949308722nt_int F) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X1) X2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int F X1) X2))) (forall ((P3 tptp.produc6108883039684432031et_nat)) (= (tptp.produc7835526202635639141et_nat tptp.produc8148480564485311129et_nat P3) P3)) (forall ((P3 tptp.produc1542783094787327164et_nat)) (= (tptp.produc2839874632939241247et_nat tptp.produc3083477295402903094et_nat P3) P3)) (forall ((P3 tptp.produc4441460161354545860nt_int)) (= (tptp.produc7428976581010258791nt_int tptp.produc1560874099174258678nt_int P3) P3)) (forall ((P3 tptp.produc6768802789813714928nt_int)) (= (tptp.produc3712466714231214015nt_int tptp.produc4852315488734385442nt_int P3) P3)) (forall ((P3 tptp.produc3260487557148687353it_nat)) (= (tptp.produc2183267410226956569it_nat tptp.produc9178034014595674355it_nat P3) P3)) (forall ((P3 tptp.product_prod_int_int)) (= (tptp.aa_Pro6970504127699319548nt_int (tptp.aa_fun8026974734089330650nt_int tptp.produc4245557441103728435nt_int tptp.product_Pair_int_int) P3) P3)) (forall ((K tptp.int) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N2) (tptp.aa_int_nat tptp.nat2 K)) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) K))))) (forall ((K tptp.int) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N2) (tptp.aa_int_nat tptp.nat2 K))))) (forall ((F tptp.fun_na1668100129766719005at_nat) (G tptp.fun_Pr2477239776880934807at_nat)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (= (tptp.aa_nat7997280740862404369at_nat (tptp.aa_nat5682243440470347102at_nat F X3) Y3) (tptp.aa_Pro8023792847356852296at_nat G (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat X3) Y3)))) (= (tptp.aa_fun6875833325056119164at_nat tptp.produc4528391901023682385at_nat F) G))) (forall ((F tptp.fun_na4786964484885125043t_bool) (G tptp.fun_Pr248683899324676269t_bool)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (= (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool F X3) Y3) (tptp.aa_Pro595088089689268830t_bool G (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat X3) Y3)))) (= (tptp.aa_fun174371099813217148t_bool tptp.produc5023667602222594023t_bool F) G))) (forall ((F tptp.fun_in1696471567231710611nt_int) (G tptp.fun_Pr2478283820680522243nt_int)) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int F X3) Y3) (tptp.aa_Pro6970504127699319548nt_int G (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X3) Y3)))) (= (tptp.aa_fun8026974734089330650nt_int tptp.produc4245557441103728435nt_int F) G))) (forall ((F tptp.fun_int_fun_int_bool) (G tptp.fun_Pr803113274115125473t_bool)) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool F X3) Y3)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool G (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X3) Y3))))) (= (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool F) G))) (forall ((F tptp.fun_int_fun_int_int) (G tptp.fun_Pr982841511892225912nt_int)) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int F X3) Y3) (tptp.aa_Pro6799258434465214121nt_int G (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X3) Y3)))) (= (tptp.aa_fun914008879417524284nt_int tptp.produc8211389475949308722nt_int F) G))) (forall ((F tptp.fun_Pr2477239776880934807at_nat)) (= (tptp.aa_fun6875833325056119164at_nat tptp.produc4528391901023682385at_nat (tptp.aTP_Lamm_agl F)) F)) (forall ((F tptp.fun_Pr248683899324676269t_bool)) (= (tptp.aa_fun174371099813217148t_bool tptp.produc5023667602222594023t_bool (tptp.aTP_Lamm_agm F)) F)) (forall ((F tptp.fun_Pr2478283820680522243nt_int)) (= (tptp.aa_fun8026974734089330650nt_int tptp.produc4245557441103728435nt_int (tptp.aTP_Lamm_agn F)) F)) (forall ((F tptp.fun_Pr803113274115125473t_bool)) (= (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool (tptp.aTP_Lamm_ago F)) F)) (forall ((F tptp.fun_Pr982841511892225912nt_int)) (= (tptp.aa_fun914008879417524284nt_int tptp.produc8211389475949308722nt_int (tptp.aTP_Lamm_agp F)) F)) (forall ((Q tptp.fun_fu7919257609373989805t_bool) (P tptp.fun_na1668100129766719005at_nat) (Z tptp.product_prod_nat_nat)) (=> (tptp.pp (tptp.aa_fun4519828053337421206t_bool Q (tptp.aa_Pro8023792847356852296at_nat (tptp.aa_fun6875833325056119164at_nat tptp.produc4528391901023682385at_nat P) Z))) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= Z (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat X3) Y3)) (not (tptp.pp (tptp.aa_fun4519828053337421206t_bool Q (tptp.aa_nat7997280740862404369at_nat (tptp.aa_nat5682243440470347102at_nat P X3) Y3))))))))) (forall ((Q tptp.fun_fu5641360819561228055l_bool) (P tptp.fun_na4786964484885125043t_bool) (Z tptp.product_prod_nat_nat)) (=> (tptp.pp (tptp.aa_fun8663595511526100224l_bool Q (tptp.aa_Pro595088089689268830t_bool (tptp.aa_fun174371099813217148t_bool tptp.produc5023667602222594023t_bool P) Z))) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= Z (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat X3) Y3)) (not (tptp.pp (tptp.aa_fun8663595511526100224l_bool Q (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool P X3) Y3))))))))) (forall ((Q tptp.fun_Pr803113274115125473t_bool) (P tptp.fun_in1696471567231710611nt_int) (Z tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool Q (tptp.aa_Pro6970504127699319548nt_int (tptp.aa_fun8026974734089330650nt_int tptp.produc4245557441103728435nt_int P) Z))) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= Z (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X3) Y3)) (not (tptp.pp (tptp.aa_Pro4501881432599481050t_bool Q (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int P X3) Y3))))))))) (forall ((Q tptp.fun_bool_bool) (P tptp.fun_int_fun_int_bool) (Z tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_bool_bool Q (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool P) Z))) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= Z (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X3) Y3)) (not (tptp.pp (tptp.aa_bool_bool Q (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P X3) Y3))))))))) (forall ((Q tptp.fun_int_bool) (P tptp.fun_int_fun_int_int) (Z tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_int_bool Q (tptp.aa_Pro6799258434465214121nt_int (tptp.aa_fun914008879417524284nt_int tptp.produc8211389475949308722nt_int P) Z))) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= Z (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X3) Y3)) (not (tptp.pp (tptp.aa_int_bool Q (tptp.aa_int_int (tptp.aa_int_fun_int_int P X3) Y3))))))))) (forall ((P tptp.bool)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger P)))) (forall ((P tptp.bool)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_bool_rat tptp.zero_n2052037380579107095ol_rat P)))) (forall ((P tptp.bool)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat P)))) (forall ((P tptp.bool)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P)))) (forall ((P tptp.bool)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer))) (forall ((P tptp.bool)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_bool_rat tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat))) (forall ((P tptp.bool)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat))) (forall ((P tptp.bool)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int))) (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int M) K)) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) K))))) (forall ((N2 tptp.nat) (K tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) K)))) (forall ((N2 tptp.nat) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) K)) K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)))) (forall ((N2 tptp.nat) (K tptp.int)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) K)) tptp.zero_zero_int)))) (forall ((K tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int K))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) K))) (tptp.pp (tptp.aa_int_bool _let_1 tptp.zero_zero_int))))) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int M))) (let ((_let_2 (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int _let_2 A)) (tptp.aa_int_int (tptp.if_fun_int_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M) _let_2 _let_1) A))))) (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N2))) (let ((_let_2 (tptp.aa_nat_nat _let_1 A))) (let ((_let_3 (tptp.aa_nat_fun_nat_nat tptp.bit_se4205575877204974255it_nat M))) (let ((_let_4 (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat _let_3 A)))) (let ((_let_5 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (tptp.aa_nat_nat _let_3 _let_2)))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2))) (let ((_let_2 (tptp.aa_int_int _let_1 A))) (let ((_let_3 (tptp.aa_nat_fun_int_int tptp.bit_se4203085406695923979it_int M))) (let ((_let_4 (tptp.aa_int_int _let_1 (tptp.aa_int_int _let_3 A)))) (let ((_let_5 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (tptp.aa_int_int _let_3 _let_2)))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N2))) (let ((_let_2 (tptp.aa_nat_nat _let_1 A))) (let ((_let_3 (tptp.aa_nat_fun_nat_nat tptp.bit_se7882103937844011126it_nat M))) (let ((_let_4 (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat _let_3 A)))) (let ((_let_5 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (tptp.aa_nat_nat _let_3 _let_2)))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2))) (let ((_let_2 (tptp.aa_int_int _let_1 A))) (let ((_let_3 (tptp.aa_nat_fun_int_int tptp.bit_se7879613467334960850it_int M))) (let ((_let_4 (tptp.aa_int_int _let_1 (tptp.aa_int_int _let_3 A)))) (let ((_let_5 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (tptp.aa_int_int _let_3 _let_2)))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N2))) (let ((_let_2 (tptp.aa_nat_nat _let_1 A))) (let ((_let_3 (tptp.aa_nat_fun_nat_nat tptp.bit_se2161824704523386999it_nat M))) (let ((_let_4 (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat _let_3 A)))) (let ((_let_5 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (tptp.aa_nat_nat _let_3 _let_2)))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2))) (let ((_let_2 (tptp.aa_int_int _let_1 A))) (let ((_let_3 (tptp.aa_nat_fun_int_int tptp.bit_se2159334234014336723it_int M))) (let ((_let_4 (tptp.aa_int_int _let_1 (tptp.aa_int_int _let_3 A)))) (let ((_let_5 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (tptp.aa_int_int _let_3 _let_2)))))))))) (forall ((M tptp.int) (N2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 M)) (=> (tptp.pp (tptp.aa_int_bool _let_1 N2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int M) N2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int N2) M)) (= M N2))))))) (forall ((M tptp.int) (N2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) M)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int M) N2)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int N2) M)))))) (forall ((F tptp.fun_na1668100129766719005at_nat)) (= (tptp.uncurr9212869592684144700at_nat F) (tptp.aa_fun6875833325056119164at_nat tptp.produc4528391901023682385at_nat F))) (forall ((F tptp.fun_na4786964484885125043t_bool)) (= (tptp.uncurr5288680794045420626t_bool F) (tptp.aa_fun174371099813217148t_bool tptp.produc5023667602222594023t_bool F))) (forall ((F tptp.fun_in1696471567231710611nt_int)) (= (tptp.uncurr7650761721940715016nt_int F) (tptp.aa_fun8026974734089330650nt_int tptp.produc4245557441103728435nt_int F))) (forall ((F tptp.fun_int_fun_int_bool)) (= (tptp.uncurry_int_int_bool F) (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool F))) (forall ((F tptp.fun_int_fun_int_int)) (= (tptp.uncurry_int_int_int F) (tptp.aa_fun914008879417524284nt_int tptp.produc8211389475949308722nt_int F))) (= tptp.produc8104577556401574439at_nat tptp.produc4528391901023682385at_nat) (= tptp.produc4094335902574358973t_bool tptp.produc5023667602222594023t_bool) (= tptp.produc297006045350968285nt_int tptp.produc4245557441103728435nt_int) (= tptp.produc5452422923090572859t_bool tptp.produc8560705615207772305t_bool) (= tptp.produc7926200574084438792nt_int tptp.produc8211389475949308722nt_int) (forall ((I2 tptp.int)) (=> (not (= I2 tptp.zero_zero_int)) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int (tptp.collect_int (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_adv I2)))))) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int M))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) (tptp.aa_nat_nat tptp.suc N2))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2) A)) (tptp.aa_int_int _let_1 A))))) (forall ((Z tptp.int) (N2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int Z) N2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) N2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z) N2))))) (forall ((I2 tptp.int) (D2 tptp.int)) (=> (not (= I2 tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D2) I2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int D2)) (tptp.aa_int_int tptp.abs_abs_int I2)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_nat_set_nat tptp.nat_set_decode M)) (tptp.aa_nat_set_nat tptp.nat_set_decode N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int K) L))) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int L) K)) (and (= L tptp.zero_zero_int) (tptp.pp (tptp.aa_int_bool _let_1 K))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) L)))))) (forall ((N2 tptp.nat) (K tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.bit_se1745604003318907178nteger (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 K))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.bit_se1745604003318907178nteger N2) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger K))) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((N2 tptp.nat) (K tptp.num)) (= (tptp.bit_se569199155075624693atural (tptp.aa_nat_nat tptp.suc N2) (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 K))) (tptp.times_2397367101498566445atural (tptp.bit_se569199155075624693atural N2 (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural K)) (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((N2 tptp.nat) (K tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 K))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N2) (tptp.aa_num_nat tptp.numeral_numeral_nat K))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((N2 tptp.nat) (K tptp.num)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 K))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) (tptp.aa_num_int tptp.numeral_numeral_int K))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N2) M) M))) (forall ((N2 tptp.nat) (M tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N2) M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N2) M) M) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2))))) (forall ((N2 tptp.nat) (K tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) K)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N2) M)) M)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) M)))) (forall ((P tptp.fun_Co8822979462182099027r_bool) (A tptp.code_integer)) (=> (forall ((A4 tptp.code_integer)) (=> (= (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A4) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) A4) (tptp.pp (tptp.aa_Code_integer_bool P A4)))) (=> (forall ((A4 tptp.code_integer) (B4 tptp.bool)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger B4)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) A4)))) (=> (tptp.pp (tptp.aa_Code_integer_bool P A4)) (=> (= (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger _let_2) _let_1) A4) (tptp.pp (tptp.aa_Code_integer_bool P _let_2))))))) (tptp.pp (tptp.aa_Code_integer_bool P A))))) (forall ((P tptp.fun_Co7175331531449502024l_bool) (A tptp.code_natural)) (=> (forall ((A4 tptp.code_natural)) (=> (= (tptp.divide5121882707175180666atural A4 (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one))) A4) (tptp.pp (tptp.aa_Code_natural_bool P A4)))) (=> (forall ((A4 tptp.code_natural) (B4 tptp.bool)) (let ((_let_1 (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.plus_p4538020629002901425atural (tptp.zero_n8403883297036319079atural B4) (tptp.times_2397367101498566445atural _let_1 A4)))) (=> (tptp.pp (tptp.aa_Code_natural_bool P A4)) (=> (= (tptp.divide5121882707175180666atural _let_2 _let_1) A4) (tptp.pp (tptp.aa_Code_natural_bool P _let_2))))))) (tptp.pp (tptp.aa_Code_natural_bool P A))))) (forall ((P tptp.fun_nat_bool) (A tptp.nat)) (=> (forall ((A4 tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A4) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) A4) (tptp.pp (tptp.aa_nat_bool P A4)))) (=> (forall ((A4 tptp.nat) (B4 tptp.bool)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat B4)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) A4)))) (=> (tptp.pp (tptp.aa_nat_bool P A4)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_2) _let_1) A4) (tptp.pp (tptp.aa_nat_bool P _let_2))))))) (tptp.pp (tptp.aa_nat_bool P A))))) (forall ((P tptp.fun_int_bool) (A tptp.int)) (=> (forall ((A4 tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A4) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) A4) (tptp.pp (tptp.aa_int_bool P A4)))) (=> (forall ((A4 tptp.int) (B4 tptp.bool)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int B4)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) A4)))) (=> (tptp.pp (tptp.aa_int_bool P A4)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int _let_2) _let_1) A4) (tptp.pp (tptp.aa_int_bool P _let_2))))))) (tptp.pp (tptp.aa_int_bool P A))))) (forall ((K tptp.int) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) K))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2))))) (forall ((N2 tptp.nat) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) K)) K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) K)))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.divmod_nat M) N2))) (let ((_let_2 (or (= N2 tptp.zero_zero_nat) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2))))) (and (=> _let_2 (= _let_1 (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat tptp.zero_zero_nat) M))) (=> (not _let_2) (= _let_1 (tptp.aa_Pro262675715343573244at_nat (tptp.produc2626176000494625587at_nat tptp.aTP_Lamm_agq) (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.divmod_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) N2)))))))) (forall ((Z tptp.int) (M tptp.nat)) (let ((_let_1 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_int_nat tptp.nat2 Z)) M)) (and (=> _let_1 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int Z) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))) (forall ((N2 tptp.nat) (K tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) K) K) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))))) (forall ((K tptp.int) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) K) K)))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_Code_integer _let_1 M))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger _let_2) (tptp.aa_nat_Code_integer _let_1 N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2))) _let_2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_7079662738309270450atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_Code_natural _let_1 M))) (= (tptp.modulo8411746178871703098atural _let_2 (tptp.aa_nat_Code_natural _let_1 N2)) (tptp.times_2397367101498566445atural (tptp.zero_n8403883297036319079atural (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) _let_2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat _let_1 M))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat _let_2) (tptp.aa_nat_nat _let_1 N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2))) _let_2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_int _let_1 M))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int _let_2) (tptp.aa_nat_int _let_1 N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2))) _let_2))))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.bit_se1745604003318907178nteger (tptp.aa_nat_nat tptp.suc N2)) A) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.bit_se1745604003318907178nteger N2) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger A) _let_1))) _let_1)) (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger A) _let_1))))) (forall ((N2 tptp.nat) (A tptp.code_natural)) (let ((_let_1 (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.bit_se569199155075624693atural (tptp.aa_nat_nat tptp.suc N2) A) (tptp.plus_p4538020629002901425atural (tptp.times_2397367101498566445atural (tptp.bit_se569199155075624693atural N2 (tptp.divide5121882707175180666atural A _let_1)) _let_1) (tptp.modulo8411746178871703098atural A _let_1))))) (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat (tptp.aa_nat_nat tptp.suc N2)) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1))) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_1))))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int (tptp.aa_nat_nat tptp.suc N2)) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) _let_1))) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) _let_1))))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_1) K)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int K) _let_1))))))) (forall ((K tptp.int) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) K))))) (forall ((K tptp.int)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) (tptp.aa_int_nat tptp.nat2 K))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int _let_1)) K)))))) (forall ((L tptp.num) (Qr tptp.product_prod_nat_nat)) (= (tptp.aa_Pro262675715343573244at_nat (tptp.unique5026877609467782581ep_nat L) Qr) (tptp.aa_Pro262675715343573244at_nat (tptp.produc2626176000494625587at_nat (tptp.aTP_Lamm_afc L)) Qr))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_Code_integer _let_1 M))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger _let_2) (tptp.aa_nat_Code_integer _let_1 N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer _let_2) tptp.zero_z3403309356797280102nteger))) (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)))) (tptp.aa_nat_Code_integer _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_7079662738309270450atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_Code_natural _let_1 M))) (= (tptp.divide5121882707175180666atural _let_2 (tptp.aa_nat_Code_natural _let_1 N2)) (tptp.times_2397367101498566445atural (tptp.zero_n8403883297036319079atural (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_Code_natural_bool (tptp.fequal_Code_natural _let_2) tptp.zero_z2226904508553997617atural))) (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M))) (tptp.aa_nat_Code_natural _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat _let_1 M))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_2) (tptp.aa_nat_nat _let_1 N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat _let_2) tptp.zero_zero_nat))) (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)))) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_int _let_1 M))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int _let_2) (tptp.aa_nat_int _let_1 N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int _let_2) tptp.zero_zero_int))) (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)))) (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2))))))) (forall ((L tptp.num) (Qr tptp.product_prod_int_int)) (= (tptp.aa_Pro6970504127699319548nt_int (tptp.unique5024387138958732305ep_int L) Qr) (tptp.aa_Pro6970504127699319548nt_int (tptp.aa_fun8026974734089330650nt_int tptp.produc4245557441103728435nt_int (tptp.aTP_Lamm_afd L)) Qr))) (forall ((K tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) K)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) _let_1)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) (tptp.aa_int_int tptp.uminus_uminus_int K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int _let_1) K)))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int _let_1) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N2))) (tptp.aa_option_num_int (tptp.case_option_int_num tptp.zero_zero_int (tptp.aTP_Lamm_agr M)) (tptp.aa_num_option_num (tptp.bit_take_bit_num _let_1) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.unique5052692396658037445od_int (tptp.aa_num_num tptp.bit0 M) (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_Pro6970504127699319548nt_int (tptp.aa_fun8026974734089330650nt_int tptp.produc4245557441103728435nt_int tptp.aTP_Lamm_ags) (tptp.unique5052692396658037445od_int M N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.unique5055182867167087721od_nat (tptp.aa_num_num tptp.bit0 M) (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_Pro262675715343573244at_nat (tptp.produc2626176000494625587at_nat tptp.aTP_Lamm_agt) (tptp.unique5055182867167087721od_nat M N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.unique3479559517661332726nteger (tptp.aa_num_num tptp.bit0 M) (tptp.aa_num_num tptp.bit0 N2)) (tptp.produc6916734918728496179nteger tptp.aTP_Lamm_agu (tptp.unique3479559517661332726nteger M N2)))) (forall ((Q5 tptp.int) (R3 tptp.int)) (= (tptp.aa_Pro6799258434465214121nt_int tptp.adjust_div (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q5) R3)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Q5) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int R3) tptp.zero_zero_int)))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.unique5055182867167087721od_nat M N2))) (let ((_let_2 (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N2)))) (and (=> _let_2 (= _let_1 (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat tptp.zero_zero_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat M)))) (=> (not _let_2) (= _let_1 (tptp.aa_Pro262675715343573244at_nat (tptp.unique5026877609467782581ep_nat N2) (tptp.unique5055182867167087721od_nat M (tptp.aa_num_num tptp.bit0 N2))))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.unique5052692396658037445od_int M N2))) (let ((_let_2 (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N2)))) (and (=> _let_2 (= _let_1 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) (tptp.aa_num_int tptp.numeral_numeral_int M)))) (=> (not _let_2) (= _let_1 (tptp.aa_Pro6970504127699319548nt_int (tptp.unique5024387138958732305ep_int N2) (tptp.unique5052692396658037445od_int M (tptp.aa_num_num tptp.bit0 N2))))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.unique3479559517661332726nteger M N2))) (let ((_let_2 (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N2)))) (and (=> _let_2 (= _let_1 (tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)))) (=> (not _let_2) (= _let_1 (tptp.unique4921790084139445826nteger N2 (tptp.unique3479559517661332726nteger M (tptp.aa_num_num tptp.bit0 N2))))))))) (forall ((N2 tptp.num)) (= (tptp.unique5052692396658037445od_int tptp.one (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) (tptp.aa_num_int tptp.numeral_numeral_int tptp.one)))) (forall ((N2 tptp.num)) (= (tptp.unique5055182867167087721od_nat tptp.one (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat tptp.zero_zero_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one)))) (forall ((N2 tptp.num)) (= (tptp.unique3479559517661332726nteger tptp.one (tptp.aa_num_num tptp.bit0 N2)) (tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger tptp.one)))) (forall ((F tptp.fun_fu7398481913972163267t_bool) (A tptp.fun_Pr6001797050664311790t_bool) (B tptp.produc3658429121746597890et_nat)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.aa_fun6808777976510360636t_bool F A) B)) (tptp.pp (tptp.aa_Pro7454463142485379962t_bool (tptp.produc1182838020028369617t_bool F) (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat A) B))))) (forall ((F tptp.fun_fu5758690788630904038t_bool) (A tptp.fun_Pr6001797050664311790t_bool) (B tptp.produc6108883039684432031et_nat)) (=> (tptp.pp (tptp.aa_Pro7454463142485379962t_bool (tptp.aa_fun1003322038264691679t_bool F A) B)) (tptp.pp (tptp.aa_Pro6092667153363046813t_bool (tptp.produc4112941013039140468t_bool F) (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat A) B))))) (forall ((F tptp.fun_fu4196931294019812808t_bool) (A tptp.fun_Pr9164807099015279978e_term) (B tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun5300525129335604105t_bool F A) B)) (tptp.pp (tptp.aa_Pro5031108791230793749t_bool (tptp.produc625993674133193396t_bool F) (tptp.aa_Pro3513184699142849729nt_int (tptp.aa_fun1388719692539776744nt_int tptp.produc1560874099174258678nt_int A) B))))) (forall ((F tptp.fun_fu5117548769634986908t_bool) (A tptp.fun_in6429348457993719614e_term) (B tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun4446166836006121821t_bool F A) B)) (tptp.pp (tptp.aa_Pro7591400126937138665t_bool (tptp.produc6627716702706253960t_bool F) (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int A) B))))) (forall ((F tptp.fun_a_4602865052023851497t_bool) (A tptp.a) (B tptp.produc6653097349344004940it_nat)) (=> (tptp.pp (tptp.aa_Pro3182513528956304653t_bool (tptp.aa_a_f736957945511644770t_bool F A) B)) (tptp.pp (tptp.aa_Pro8278066377857552544t_bool (tptp.produc62718094566300407t_bool F) (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat A) B))))) (forall ((F tptp.fun_int_fun_int_bool) (A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool F A) B)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool F) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) B))))) (forall ((P3 tptp.produc6108883039684432031et_nat) (C tptp.fun_fu7398481913972163267t_bool)) (=> (forall ((A4 tptp.fun_Pr6001797050664311790t_bool) (B4 tptp.produc3658429121746597890et_nat)) (=> (= P3 (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat A4) B4)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.aa_fun6808777976510360636t_bool C A4) B4)))) (tptp.pp (tptp.aa_Pro7454463142485379962t_bool (tptp.produc1182838020028369617t_bool C) P3)))) (forall ((P3 tptp.produc1542783094787327164et_nat) (C tptp.fun_fu5758690788630904038t_bool)) (=> (forall ((A4 tptp.fun_Pr6001797050664311790t_bool) (B4 tptp.produc6108883039684432031et_nat)) (=> (= P3 (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat A4) B4)) (tptp.pp (tptp.aa_Pro7454463142485379962t_bool (tptp.aa_fun1003322038264691679t_bool C A4) B4)))) (tptp.pp (tptp.aa_Pro6092667153363046813t_bool (tptp.produc4112941013039140468t_bool C) P3)))) (forall ((P3 tptp.produc4441460161354545860nt_int) (C tptp.fun_fu4196931294019812808t_bool)) (=> (forall ((A4 tptp.fun_Pr9164807099015279978e_term) (B4 tptp.product_prod_int_int)) (=> (= P3 (tptp.aa_Pro3513184699142849729nt_int (tptp.aa_fun1388719692539776744nt_int tptp.produc1560874099174258678nt_int A4) B4)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun5300525129335604105t_bool C A4) B4)))) (tptp.pp (tptp.aa_Pro5031108791230793749t_bool (tptp.produc625993674133193396t_bool C) P3)))) (forall ((P3 tptp.produc6768802789813714928nt_int) (C tptp.fun_fu5117548769634986908t_bool)) (=> (forall ((A4 tptp.fun_in6429348457993719614e_term) (B4 tptp.product_prod_int_int)) (=> (= P3 (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int A4) B4)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun4446166836006121821t_bool C A4) B4)))) (tptp.pp (tptp.aa_Pro7591400126937138665t_bool (tptp.produc6627716702706253960t_bool C) P3)))) (forall ((P3 tptp.produc3260487557148687353it_nat) (C tptp.fun_a_4602865052023851497t_bool)) (=> (forall ((A4 tptp.a) (B4 tptp.produc6653097349344004940it_nat)) (=> (= P3 (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat A4) B4)) (tptp.pp (tptp.aa_Pro3182513528956304653t_bool (tptp.aa_a_f736957945511644770t_bool C A4) B4)))) (tptp.pp (tptp.aa_Pro8278066377857552544t_bool (tptp.produc62718094566300407t_bool C) P3)))) (forall ((P3 tptp.product_prod_int_int) (C tptp.fun_int_fun_int_bool)) (=> (forall ((A4 tptp.int) (B4 tptp.int)) (=> (= P3 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A4) B4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool C A4) B4)))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool C) P3)))) (forall ((Z tptp.bool) (C tptp.fun_a_3884643061924904137t_bool) (A tptp.a) (B tptp.produc6653097349344004940it_nat)) (=> (tptp.pp (tptp.member_bool Z (tptp.aa_Pro6887805503827732461t_bool (tptp.aa_a_f5185329350192636226t_bool C A) B))) (tptp.pp (tptp.member_bool Z (tptp.produc1590295041617796567t_bool C (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat A) B)))))) (forall ((Z tptp.nat) (C tptp.fun_a_8173838432492502368et_nat) (A tptp.a) (B tptp.produc6653097349344004940it_nat)) (let ((_let_1 (tptp.member_nat Z))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_Pro6139939891222248720et_nat (tptp.aa_a_f7156848735415605777et_nat C A) B))) (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.produc7315013382793309350et_nat C (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat A) B))))))) (forall ((Z tptp.int) (C tptp.fun_a_3360290013704583612et_int) (A tptp.a) (B tptp.produc6653097349344004940it_nat)) (let ((_let_1 (tptp.member_int Z))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.aa_Pro1962088871713052012et_int (tptp.aa_a_f4666765590483879021et_int C A) B))) (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.produc3137162363284112642et_int C (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat A) B))))))) (forall ((Z tptp.set_nat) (C tptp.fun_a_5925824989894720534et_nat) (A tptp.a) (B tptp.produc6653097349344004940it_nat)) (let ((_let_1 (tptp.member_set_nat Z))) (=> (tptp.pp (tptp.aa_set_set_nat_bool _let_1 (tptp.aa_Pro4298387719113726406et_nat (tptp.aa_a_f1497801039697847239et_nat C A) B))) (tptp.pp (tptp.aa_set_set_nat_bool _let_1 (tptp.produc8632796428668088668et_nat C (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat A) B))))))) (forall ((Z tptp.product_prod_nat_nat) (C tptp.fun_a_8304141829328133171at_nat) (A tptp.a) (B tptp.produc6653097349344004940it_nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat Z))) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.aa_Pro5139103691568615511at_nat (tptp.aa_a_f1049478142650162092at_nat C A) B))) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 (tptp.produc8253449849199807809at_nat C (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat A) B))))))) (forall ((Z tptp.bool) (C tptp.fun_fu7778341886357639804t_bool) (A tptp.fun_in6429348457993719614e_term) (B tptp.product_prod_int_int)) (=> (tptp.pp (tptp.member_bool Z (tptp.aa_Pro2764908413162897850t_bool (tptp.aa_fun2453671976794265661t_bool C A) B))) (tptp.pp (tptp.member_bool Z (tptp.produc97340315608317800t_bool C (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int A) B)))))) (forall ((Z tptp.nat) (C tptp.fun_fu4770337263308229357et_nat) (A tptp.fun_in6429348457993719614e_term) (B tptp.product_prod_int_int)) (let ((_let_1 (tptp.member_nat Z))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_Pro3599192995643711491et_nat (tptp.aa_fun1858489612225131606et_nat C A) B))) (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.produc2360586433946867413et_nat C (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int A) B))))))) (forall ((Z tptp.int) (C tptp.fun_fu9180160881375086409et_int) (A tptp.fun_in6429348457993719614e_term) (B tptp.product_prod_int_int)) (let ((_let_1 (tptp.member_int Z))) (=> (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.aa_Pro8644714012989290591et_int (tptp.aa_fun8591778504148180658et_int C A) B))) (tptp.pp (tptp.aa_set_int_bool _let_1 (tptp.produc7406107451292446513et_int C (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int A) B))))))) (forall ((Z tptp.set_nat) (C tptp.fun_fu5228850549672056227et_nat) (A tptp.fun_in6429348457993719614e_term) (B tptp.product_prod_int_int)) (let ((_let_1 (tptp.member_set_nat Z))) (=> (tptp.pp (tptp.aa_set_set_nat_bool _let_1 (tptp.aa_Pro1963545105414287545et_nat (tptp.aa_fun4553286828575894028et_nat C A) B))) (tptp.pp (tptp.aa_set_set_nat_bool _let_1 (tptp.produc7545104436737089419et_nat C (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int A) B))))))) (forall ((Z tptp.bool) (C tptp.fun_fu950101255003131299t_bool) (A tptp.fun_Pr6001797050664311790t_bool) (B tptp.produc3658429121746597890et_nat)) (=> (tptp.pp (tptp.member_bool Z (tptp.aa_Pro4218693128239598775t_bool (tptp.aa_fun3103803308129048348t_bool C A) B))) (tptp.pp (tptp.member_bool Z (tptp.produc6307439976824317361t_bool C (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat A) B)))))) (forall ((P3 tptp.produc3260487557148687353it_nat) (Z tptp.bool) (C tptp.fun_a_3884643061924904137t_bool)) (=> (forall ((A4 tptp.a) (B4 tptp.produc6653097349344004940it_nat)) (=> (= P3 (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat A4) B4)) (tptp.pp (tptp.member_bool Z (tptp.aa_Pro6887805503827732461t_bool (tptp.aa_a_f5185329350192636226t_bool C A4) B4))))) (tptp.pp (tptp.member_bool Z (tptp.produc1590295041617796567t_bool C P3))))) (forall ((P3 tptp.produc3260487557148687353it_nat) (Z tptp.nat) (C tptp.fun_a_8173838432492502368et_nat)) (=> (forall ((A4 tptp.a) (B4 tptp.produc6653097349344004940it_nat)) (=> (= P3 (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat A4) B4)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Z) (tptp.aa_Pro6139939891222248720et_nat (tptp.aa_a_f7156848735415605777et_nat C A4) B4))))) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Z) (tptp.produc7315013382793309350et_nat C P3))))) (forall ((P3 tptp.produc3260487557148687353it_nat) (Z tptp.int) (C tptp.fun_a_3360290013704583612et_int)) (=> (forall ((A4 tptp.a) (B4 tptp.produc6653097349344004940it_nat)) (=> (= P3 (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat A4) B4)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Z) (tptp.aa_Pro1962088871713052012et_int (tptp.aa_a_f4666765590483879021et_int C A4) B4))))) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Z) (tptp.produc3137162363284112642et_int C P3))))) (forall ((P3 tptp.produc3260487557148687353it_nat) (Z tptp.set_nat) (C tptp.fun_a_5925824989894720534et_nat)) (=> (forall ((A4 tptp.a) (B4 tptp.produc6653097349344004940it_nat)) (=> (= P3 (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat A4) B4)) (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat Z) (tptp.aa_Pro4298387719113726406et_nat (tptp.aa_a_f1497801039697847239et_nat C A4) B4))))) (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat Z) (tptp.produc8632796428668088668et_nat C P3))))) (forall ((P3 tptp.produc3260487557148687353it_nat) (Z tptp.product_prod_nat_nat) (C tptp.fun_a_8304141829328133171at_nat)) (=> (forall ((A4 tptp.a) (B4 tptp.produc6653097349344004940it_nat)) (=> (= P3 (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat A4) B4)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat Z) (tptp.aa_Pro5139103691568615511at_nat (tptp.aa_a_f1049478142650162092at_nat C A4) B4))))) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat Z) (tptp.produc8253449849199807809at_nat C P3))))) (forall ((P3 tptp.produc6768802789813714928nt_int) (Z tptp.bool) (C tptp.fun_fu7778341886357639804t_bool)) (=> (forall ((A4 tptp.fun_in6429348457993719614e_term) (B4 tptp.product_prod_int_int)) (=> (= P3 (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int A4) B4)) (tptp.pp (tptp.member_bool Z (tptp.aa_Pro2764908413162897850t_bool (tptp.aa_fun2453671976794265661t_bool C A4) B4))))) (tptp.pp (tptp.member_bool Z (tptp.produc97340315608317800t_bool C P3))))) (forall ((P3 tptp.produc6768802789813714928nt_int) (Z tptp.nat) (C tptp.fun_fu4770337263308229357et_nat)) (=> (forall ((A4 tptp.fun_in6429348457993719614e_term) (B4 tptp.product_prod_int_int)) (=> (= P3 (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int A4) B4)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Z) (tptp.aa_Pro3599192995643711491et_nat (tptp.aa_fun1858489612225131606et_nat C A4) B4))))) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Z) (tptp.produc2360586433946867413et_nat C P3))))) (forall ((P3 tptp.produc6768802789813714928nt_int) (Z tptp.int) (C tptp.fun_fu9180160881375086409et_int)) (=> (forall ((A4 tptp.fun_in6429348457993719614e_term) (B4 tptp.product_prod_int_int)) (=> (= P3 (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int A4) B4)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Z) (tptp.aa_Pro8644714012989290591et_int (tptp.aa_fun8591778504148180658et_int C A4) B4))))) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Z) (tptp.produc7406107451292446513et_int C P3))))) (forall ((P3 tptp.produc6768802789813714928nt_int) (Z tptp.set_nat) (C tptp.fun_fu5228850549672056227et_nat)) (=> (forall ((A4 tptp.fun_in6429348457993719614e_term) (B4 tptp.product_prod_int_int)) (=> (= P3 (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int A4) B4)) (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat Z) (tptp.aa_Pro1963545105414287545et_nat (tptp.aa_fun4553286828575894028et_nat C A4) B4))))) (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat Z) (tptp.produc7545104436737089419et_nat C P3))))) (forall ((P3 tptp.produc6108883039684432031et_nat) (Z tptp.bool) (C tptp.fun_fu950101255003131299t_bool)) (=> (forall ((A4 tptp.fun_Pr6001797050664311790t_bool) (B4 tptp.produc3658429121746597890et_nat)) (=> (= P3 (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat A4) B4)) (tptp.pp (tptp.member_bool Z (tptp.aa_Pro4218693128239598775t_bool (tptp.aa_fun3103803308129048348t_bool C A4) B4))))) (tptp.pp (tptp.member_bool Z (tptp.produc6307439976824317361t_bool C P3))))) (forall ((P3 tptp.product_prod_nat_nat) (C tptp.fun_na4786964484885125043t_bool) (X tptp.product_prod_nat_nat)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (= (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat A4) B4) P3) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool C A4) B4) X)))) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool (tptp.aa_fun174371099813217148t_bool tptp.produc5023667602222594023t_bool C) P3) X)))) (forall ((N2 tptp.nat)) (= (tptp.aa_num_option_num (tptp.bit_take_bit_num (tptp.aa_nat_nat tptp.suc N2)) tptp.one) (tptp.aa_num_option_num tptp.some_num tptp.one))) (forall ((R3 tptp.num)) (= (tptp.aa_num_option_num (tptp.bit_take_bit_num (tptp.aa_num_nat tptp.numeral_numeral_nat R3)) tptp.one) (tptp.aa_num_option_num tptp.some_num tptp.one))) (forall ((N2 tptp.nat) (M tptp.num)) (= (tptp.aa_num_option_num (tptp.bit_take_bit_num (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_opt5369159329878751634on_num (tptp.case_o6005452278849405969um_num tptp.none_num tptp.aTP_Lamm_agv) (tptp.aa_num_option_num (tptp.bit_take_bit_num N2) M)))) (forall ((M tptp.num)) (= (tptp.unique5052692396658037445od_int M tptp.one) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_num_int tptp.numeral_numeral_int M)) tptp.zero_zero_int))) (forall ((M tptp.num)) (= (tptp.unique5055182867167087721od_nat M tptp.one) (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat (tptp.aa_num_nat tptp.numeral_numeral_nat M)) tptp.zero_zero_nat))) (forall ((M tptp.num)) (= (tptp.unique3479559517661332726nteger M tptp.one) (tptp.produc1086072967326762835nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M) tptp.zero_z3403309356797280102nteger))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.bit_se1745604003318907178nteger _let_1) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2)) (tptp.case_o356765784539232260er_num tptp.zero_z3403309356797280102nteger tptp.numera6620942414471956472nteger (tptp.aa_num_option_num (tptp.bit_take_bit_num _let_1) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (= (tptp.bit_se569199155075624693atural _let_1 (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural N2)) (tptp.case_o5621594795226839503al_num tptp.zero_z2226904508553997617atural tptp.numera5444537566228673987atural (tptp.aa_num_option_num (tptp.bit_take_bit_num _let_1) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat N2)) (tptp.aa_option_num_nat (tptp.case_option_nat_num tptp.zero_zero_nat tptp.numeral_numeral_nat) (tptp.aa_num_option_num (tptp.bit_take_bit_num _let_1) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int _let_1) (tptp.aa_num_int tptp.numeral_numeral_int N2)) (tptp.aa_option_num_int (tptp.case_option_int_num tptp.zero_zero_int tptp.numeral_numeral_int) (tptp.aa_num_option_num (tptp.bit_take_bit_num _let_1) N2))))) (forall ((Z tptp.bool) (C tptp.fun_a_3884643061924904137t_bool) (P3 tptp.produc3260487557148687353it_nat)) (=> (tptp.pp (tptp.member_bool Z (tptp.produc1590295041617796567t_bool C P3))) (not (forall ((X3 tptp.a) (Y3 tptp.produc6653097349344004940it_nat)) (=> (= P3 (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat X3) Y3)) (not (tptp.pp (tptp.member_bool Z (tptp.aa_Pro6887805503827732461t_bool (tptp.aa_a_f5185329350192636226t_bool C X3) Y3))))))))) (forall ((Z tptp.nat) (C tptp.fun_a_8173838432492502368et_nat) (P3 tptp.produc3260487557148687353it_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Z) (tptp.produc7315013382793309350et_nat C P3))) (not (forall ((X3 tptp.a) (Y3 tptp.produc6653097349344004940it_nat)) (=> (= P3 (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat X3) Y3)) (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Z) (tptp.aa_Pro6139939891222248720et_nat (tptp.aa_a_f7156848735415605777et_nat C X3) Y3))))))))) (forall ((Z tptp.int) (C tptp.fun_a_3360290013704583612et_int) (P3 tptp.produc3260487557148687353it_nat)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Z) (tptp.produc3137162363284112642et_int C P3))) (not (forall ((X3 tptp.a) (Y3 tptp.produc6653097349344004940it_nat)) (=> (= P3 (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat X3) Y3)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Z) (tptp.aa_Pro1962088871713052012et_int (tptp.aa_a_f4666765590483879021et_int C X3) Y3))))))))) (forall ((Z tptp.set_nat) (C tptp.fun_a_5925824989894720534et_nat) (P3 tptp.produc3260487557148687353it_nat)) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat Z) (tptp.produc8632796428668088668et_nat C P3))) (not (forall ((X3 tptp.a) (Y3 tptp.produc6653097349344004940it_nat)) (=> (= P3 (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat X3) Y3)) (not (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat Z) (tptp.aa_Pro4298387719113726406et_nat (tptp.aa_a_f1497801039697847239et_nat C X3) Y3))))))))) (forall ((Z tptp.product_prod_nat_nat) (C tptp.fun_a_8304141829328133171at_nat) (P3 tptp.produc3260487557148687353it_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat Z) (tptp.produc8253449849199807809at_nat C P3))) (not (forall ((X3 tptp.a) (Y3 tptp.produc6653097349344004940it_nat)) (=> (= P3 (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat X3) Y3)) (not (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat Z) (tptp.aa_Pro5139103691568615511at_nat (tptp.aa_a_f1049478142650162092at_nat C X3) Y3))))))))) (forall ((Z tptp.bool) (C tptp.fun_fu7778341886357639804t_bool) (P3 tptp.produc6768802789813714928nt_int)) (=> (tptp.pp (tptp.member_bool Z (tptp.produc97340315608317800t_bool C P3))) (not (forall ((X3 tptp.fun_in6429348457993719614e_term) (Y3 tptp.product_prod_int_int)) (=> (= P3 (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int X3) Y3)) (not (tptp.pp (tptp.member_bool Z (tptp.aa_Pro2764908413162897850t_bool (tptp.aa_fun2453671976794265661t_bool C X3) Y3))))))))) (forall ((Z tptp.nat) (C tptp.fun_fu4770337263308229357et_nat) (P3 tptp.produc6768802789813714928nt_int)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Z) (tptp.produc2360586433946867413et_nat C P3))) (not (forall ((X3 tptp.fun_in6429348457993719614e_term) (Y3 tptp.product_prod_int_int)) (=> (= P3 (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int X3) Y3)) (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Z) (tptp.aa_Pro3599192995643711491et_nat (tptp.aa_fun1858489612225131606et_nat C X3) Y3))))))))) (forall ((Z tptp.int) (C tptp.fun_fu9180160881375086409et_int) (P3 tptp.produc6768802789813714928nt_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Z) (tptp.produc7406107451292446513et_int C P3))) (not (forall ((X3 tptp.fun_in6429348457993719614e_term) (Y3 tptp.product_prod_int_int)) (=> (= P3 (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int X3) Y3)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Z) (tptp.aa_Pro8644714012989290591et_int (tptp.aa_fun8591778504148180658et_int C X3) Y3))))))))) (forall ((Z tptp.set_nat) (C tptp.fun_fu5228850549672056227et_nat) (P3 tptp.produc6768802789813714928nt_int)) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat Z) (tptp.produc7545104436737089419et_nat C P3))) (not (forall ((X3 tptp.fun_in6429348457993719614e_term) (Y3 tptp.product_prod_int_int)) (=> (= P3 (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int X3) Y3)) (not (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat Z) (tptp.aa_Pro1963545105414287545et_nat (tptp.aa_fun4553286828575894028et_nat C X3) Y3))))))))) (forall ((Z tptp.bool) (C tptp.fun_fu950101255003131299t_bool) (P3 tptp.produc6108883039684432031et_nat)) (=> (tptp.pp (tptp.member_bool Z (tptp.produc6307439976824317361t_bool C P3))) (not (forall ((X3 tptp.fun_Pr6001797050664311790t_bool) (Y3 tptp.produc3658429121746597890et_nat)) (=> (= P3 (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat X3) Y3)) (not (tptp.pp (tptp.member_bool Z (tptp.aa_Pro4218693128239598775t_bool (tptp.aa_fun3103803308129048348t_bool C X3) Y3))))))))) (forall ((F tptp.fun_fu7398481913972163267t_bool) (A tptp.fun_Pr6001797050664311790t_bool) (B tptp.produc3658429121746597890et_nat)) (=> (tptp.pp (tptp.aa_Pro7454463142485379962t_bool (tptp.produc1182838020028369617t_bool F) (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat A) B))) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.aa_fun6808777976510360636t_bool F A) B)))) (forall ((F tptp.fun_fu5758690788630904038t_bool) (A tptp.fun_Pr6001797050664311790t_bool) (B tptp.produc6108883039684432031et_nat)) (=> (tptp.pp (tptp.aa_Pro6092667153363046813t_bool (tptp.produc4112941013039140468t_bool F) (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat A) B))) (tptp.pp (tptp.aa_Pro7454463142485379962t_bool (tptp.aa_fun1003322038264691679t_bool F A) B)))) (forall ((F tptp.fun_fu4196931294019812808t_bool) (A tptp.fun_Pr9164807099015279978e_term) (B tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro5031108791230793749t_bool (tptp.produc625993674133193396t_bool F) (tptp.aa_Pro3513184699142849729nt_int (tptp.aa_fun1388719692539776744nt_int tptp.produc1560874099174258678nt_int A) B))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun5300525129335604105t_bool F A) B)))) (forall ((F tptp.fun_fu5117548769634986908t_bool) (A tptp.fun_in6429348457993719614e_term) (B tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro7591400126937138665t_bool (tptp.produc6627716702706253960t_bool F) (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int A) B))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun4446166836006121821t_bool F A) B)))) (forall ((F tptp.fun_a_4602865052023851497t_bool) (A tptp.a) (B tptp.produc6653097349344004940it_nat)) (=> (tptp.pp (tptp.aa_Pro8278066377857552544t_bool (tptp.produc62718094566300407t_bool F) (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat A) B))) (tptp.pp (tptp.aa_Pro3182513528956304653t_bool (tptp.aa_a_f736957945511644770t_bool F A) B)))) (forall ((F tptp.fun_int_fun_int_bool) (A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool F) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool F A) B)))) (forall ((C tptp.fun_fu7398481913972163267t_bool) (P3 tptp.produc6108883039684432031et_nat)) (=> (tptp.pp (tptp.aa_Pro7454463142485379962t_bool (tptp.produc1182838020028369617t_bool C) P3)) (not (forall ((X3 tptp.fun_Pr6001797050664311790t_bool) (Y3 tptp.produc3658429121746597890et_nat)) (=> (= P3 (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat X3) Y3)) (not (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.aa_fun6808777976510360636t_bool C X3) Y3)))))))) (forall ((C tptp.fun_fu5758690788630904038t_bool) (P3 tptp.produc1542783094787327164et_nat)) (=> (tptp.pp (tptp.aa_Pro6092667153363046813t_bool (tptp.produc4112941013039140468t_bool C) P3)) (not (forall ((X3 tptp.fun_Pr6001797050664311790t_bool) (Y3 tptp.produc6108883039684432031et_nat)) (=> (= P3 (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat X3) Y3)) (not (tptp.pp (tptp.aa_Pro7454463142485379962t_bool (tptp.aa_fun1003322038264691679t_bool C X3) Y3)))))))) (forall ((C tptp.fun_fu4196931294019812808t_bool) (P3 tptp.produc4441460161354545860nt_int)) (=> (tptp.pp (tptp.aa_Pro5031108791230793749t_bool (tptp.produc625993674133193396t_bool C) P3)) (not (forall ((X3 tptp.fun_Pr9164807099015279978e_term) (Y3 tptp.product_prod_int_int)) (=> (= P3 (tptp.aa_Pro3513184699142849729nt_int (tptp.aa_fun1388719692539776744nt_int tptp.produc1560874099174258678nt_int X3) Y3)) (not (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun5300525129335604105t_bool C X3) Y3)))))))) (forall ((C tptp.fun_fu5117548769634986908t_bool) (P3 tptp.produc6768802789813714928nt_int)) (=> (tptp.pp (tptp.aa_Pro7591400126937138665t_bool (tptp.produc6627716702706253960t_bool C) P3)) (not (forall ((X3 tptp.fun_in6429348457993719614e_term) (Y3 tptp.product_prod_int_int)) (=> (= P3 (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int X3) Y3)) (not (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun4446166836006121821t_bool C X3) Y3)))))))) (forall ((C tptp.fun_a_4602865052023851497t_bool) (P3 tptp.produc3260487557148687353it_nat)) (=> (tptp.pp (tptp.aa_Pro8278066377857552544t_bool (tptp.produc62718094566300407t_bool C) P3)) (not (forall ((X3 tptp.a) (Y3 tptp.produc6653097349344004940it_nat)) (=> (= P3 (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat X3) Y3)) (not (tptp.pp (tptp.aa_Pro3182513528956304653t_bool (tptp.aa_a_f736957945511644770t_bool C X3) Y3)))))))) (forall ((C tptp.fun_int_fun_int_bool) (P3 tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool C) P3)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= P3 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X3) Y3)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool C X3) Y3)))))))) (forall ((R tptp.fun_na4786964484885125043t_bool) (A tptp.nat) (B tptp.nat) (C tptp.product_prod_nat_nat)) (=> (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool (tptp.aa_fun174371099813217148t_bool tptp.produc5023667602222594023t_bool R) (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat A) B)) C)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool R A) B) C)))) (forall ((C tptp.fun_na4786964484885125043t_bool) (P3 tptp.product_prod_nat_nat) (Z tptp.product_prod_nat_nat)) (=> (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool (tptp.aa_fun174371099813217148t_bool tptp.produc5023667602222594023t_bool C) P3) Z)) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= P3 (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat X3) Y3)) (not (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool C X3) Y3) Z)))))))) (forall ((Qr tptp.product_prod_int_int)) (= (tptp.aa_Pro6799258434465214121nt_int tptp.adjust_div Qr) (tptp.aa_Pro6799258434465214121nt_int (tptp.aa_fun914008879417524284nt_int tptp.produc8211389475949308722nt_int tptp.aTP_Lamm_agw) Qr))) (forall ((A3 tptp.fun_int_fun_int_bool) (B3 tptp.fun_int_fun_int_bool)) (=> (tptp.ord_le4546832483993983377t_bool A3 B3) (tptp.ord_le2843351958646193337nt_int (tptp.collec213857154873943460nt_int (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool A3)) (tptp.collec213857154873943460nt_int (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool B3))))) (forall ((G tptp.fun_nat_fun_nat_nat) (N2 tptp.nat)) (= (tptp.groups977919841031483927at_nat (tptp.produc6842872674320459806at_nat G) (tptp.collec3392354462482085612at_nat (tptp.produc8955392012077580105t_bool (tptp.aTP_Lamm_agx N2)))) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_agz G)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((G tptp.fun_nat_fun_nat_nat) (N2 tptp.nat)) (= (tptp.groups4077766827762148844at_nat (tptp.produc6842872674320459806at_nat G) (tptp.collec3392354462482085612at_nat (tptp.produc8955392012077580105t_bool (tptp.aTP_Lamm_agx N2)))) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aTP_Lamm_aha G)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((G tptp.fun_nat_fun_nat_int) (N2 tptp.nat)) (= (tptp.groups4075276357253098568at_int (tptp.produc6840382203811409530at_int G) (tptp.collec3392354462482085612at_nat (tptp.produc8955392012077580105t_bool (tptp.aTP_Lamm_agx N2)))) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aTP_Lamm_ahc G)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((F tptp.heap_Time_Heap_a) (G tptp.fun_a_6093291656547882009Heap_a) (H tptp.heap_e7401611519738050253t_unit)) (= (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a (tptp.heap_Time_bind_a_a F G)) H) (tptp.case_o6061097939050036047it_nat tptp.none_P2651198173097904984it_nat (tptp.produc7850007024774191849it_nat (tptp.aTP_Lamm_ahe G)) (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a F) H)))) (forall ((M tptp.fun_int_option_int)) (= (tptp.map_to_set_int_int M) (tptp.collec213857154873943460nt_int (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool (tptp.aTP_Lamm_ahf M))))) (forall ((M tptp.nat) (N2 tptp.num) (Q5 tptp.num)) (=> (= (tptp.aa_num_option_num (tptp.bit_take_bit_num M) N2) (tptp.aa_num_option_num tptp.some_num Q5)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.bit_se1745604003318907178nteger M) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger Q5)))) (forall ((M tptp.nat) (N2 tptp.num) (Q5 tptp.num)) (=> (= (tptp.aa_num_option_num (tptp.bit_take_bit_num M) N2) (tptp.aa_num_option_num tptp.some_num Q5)) (= (tptp.bit_se569199155075624693atural M (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural N2)) (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural Q5)))) (forall ((M tptp.nat) (N2 tptp.num) (Q5 tptp.num)) (=> (= (tptp.aa_num_option_num (tptp.bit_take_bit_num M) N2) (tptp.aa_num_option_num tptp.some_num Q5)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat M) (tptp.aa_num_nat tptp.numeral_numeral_nat N2)) (tptp.aa_num_nat tptp.numeral_numeral_nat Q5)))) (forall ((M tptp.nat) (N2 tptp.num) (Q5 tptp.num)) (=> (= (tptp.aa_num_option_num (tptp.bit_take_bit_num M) N2) (tptp.aa_num_option_num tptp.some_num Q5)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int M) (tptp.aa_num_int tptp.numeral_numeral_int N2)) (tptp.aa_num_int tptp.numeral_numeral_int Q5)))) (forall ((F tptp.heap_Time_Heap_a) (G tptp.fun_a_6093291656547882009Heap_a)) (= (tptp.heap_Time_bind_a_a F G) (tptp.heap_Time_Heap_a2 (tptp.aa_fun6119220767042692876it_nat (tptp.aTP_Lamm_ahg F) G)))) (forall ((F tptp.heap_Time_Heap_a) (G tptp.fun_a_2990225006182978344t_unit)) (= (tptp.heap_T8685611227969916822t_unit F G) (tptp.heap_T6183433275982383450t_unit (tptp.aa_fun372765568861188684it_nat (tptp.aTP_Lamm_ahj F) G)))) (= tptp.finite_psubset_nat (tptp.collec6662362479098859352et_nat (tptp.produc6837115875915843293t_bool tptp.aTP_Lamm_ahk))) (= tptp.finite_psubset_int (tptp.collec957716948307931664et_int (tptp.produc6614410065919771685t_bool tptp.aTP_Lamm_ahl))) (= tptp.finite2416775604798480986nteger (tptp.collec2770208431294612722nteger (tptp.produc7993569030129736003r_bool tptp.aTP_Lamm_ahm))) (= tptp.finite469560695537375940at_nat (tptp.collec6321179662152712658at_nat (tptp.produc4641332057840980011t_bool tptp.aTP_Lamm_ahn))) (forall ((M tptp.fun_fu6675107418524772179et_nat) (P tptp.fun_Pr3073222722562426257t_bool)) (= (tptp.rel_of5209130651707563896et_nat M P) (tptp.collec6596103000283128692et_nat (tptp.produc1182838020028369617t_bool (tptp.aa_fun8271251865843499800t_bool (tptp.aTP_Lamm_aho M) P))))) (forall ((M tptp.fun_fu1965482174671583728et_nat) (P tptp.fun_Pr229822445725053876t_bool)) (= (tptp.rel_of4733102656347104789et_nat M P) (tptp.collec8162438751352893585et_nat (tptp.produc4112941013039140468t_bool (tptp.aa_fun6031285004062638814t_bool (tptp.aTP_Lamm_ahp M) P))))) (forall ((M tptp.fun_fu4756305112005770350nt_int) (P tptp.fun_Pr6019674992625747500t_bool)) (= (tptp.rel_of8820965294950487125nt_int M P) (tptp.collec3203402231325458457nt_int (tptp.produc625993674133193396t_bool (tptp.aa_fun414483183390545080t_bool (tptp.aTP_Lamm_ahq M) P))))) (forall ((M tptp.fun_fu3249470265263746970nt_int) (P tptp.fun_Pr5504123824928244736t_bool)) (= (tptp.rel_of910228786792388993nt_int M P) (tptp.collec8164060689515068741nt_int (tptp.produc6627716702706253960t_bool (tptp.aa_fun8816120322678784096t_bool (tptp.aTP_Lamm_ahr M) P))))) (forall ((M tptp.fun_a_1313742400928293293it_nat) (P tptp.fun_Pr2906233850362575543t_bool)) (= (tptp.rel_of2761222537318653906it_nat M P) (tptp.collec4148678073425210574it_nat (tptp.produc62718094566300407t_bool (tptp.aa_fun302308005641782372t_bool (tptp.aTP_Lamm_ahs M) P))))) (forall ((M tptp.fun_int_option_int) (P tptp.fun_Pr803113274115125473t_bool)) (= (tptp.rel_of_int_int M P) (tptp.collec213857154873943460nt_int (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool (tptp.aa_fun7489457930223801746t_bool (tptp.aTP_Lamm_aht M) P))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N2))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int M))) (= (tptp.unique5052692396658037445od_int M N2) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int _let_2) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int _let_2) _let_1)))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N2))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int M))) (= (tptp.unique5052692396658037445od_int M N2) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int _let_2) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int _let_2) _let_1)))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N2))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (= (tptp.unique5055182867167087721od_nat M N2) (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_2) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat _let_2) _let_1)))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2))) (let ((_let_2 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) (= (tptp.unique3479559517661332726nteger M N2) (tptp.produc1086072967326762835nteger (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger _let_2) _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger _let_2) _let_1)))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N2))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (= (tptp.unique5055182867167087721od_nat M N2) (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_2) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat _let_2) _let_1)))))) (forall ((F tptp.fun_nat_nat) (R tptp.set_Pr1261947904930325089at_nat)) (= (tptp.mlex_prod_nat F R) (tptp.collec3392354462482085612at_nat (tptp.produc8955392012077580105t_bool (tptp.aa_set1256819327649670340t_bool (tptp.aTP_Lamm_ahu F) R))))) (forall ((F tptp.fun_int_nat) (R tptp.set_Pr958786334691620121nt_int)) (= (tptp.mlex_prod_int F R) (tptp.collec213857154873943460nt_int (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool (tptp.aa_set8965632145344517972t_bool (tptp.aTP_Lamm_ahv F) R))))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.unique5052692396658037445od_int (tptp.aa_num_num tptp.bit1 M) (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_Pro6970504127699319548nt_int (tptp.aa_fun8026974734089330650nt_int tptp.produc4245557441103728435nt_int tptp.aTP_Lamm_ahw) (tptp.unique5052692396658037445od_int M N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.unique5055182867167087721od_nat (tptp.aa_num_num tptp.bit1 M) (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_Pro262675715343573244at_nat (tptp.produc2626176000494625587at_nat tptp.aTP_Lamm_ahx) (tptp.unique5055182867167087721od_nat M N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.unique3479559517661332726nteger (tptp.aa_num_num tptp.bit1 M) (tptp.aa_num_num tptp.bit0 N2)) (tptp.produc6916734918728496179nteger tptp.aTP_Lamm_ahy (tptp.unique3479559517661332726nteger M N2)))) (forall ((D2 tptp.int)) (= (tptp.int_ge_less_than2 D2) (tptp.collec213857154873943460nt_int (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool (tptp.aTP_Lamm_ahz D2))))) (forall ((D2 tptp.int)) (= (tptp.int_ge_less_than D2) (tptp.collec213857154873943460nt_int (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool (tptp.aTP_Lamm_aia D2))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (let ((_let_2 (tptp.aa_num_num tptp.bit1 M))) (let ((_let_3 (tptp.unique5055182867167087721od_nat _let_2 _let_1))) (let ((_let_4 (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N2)))) (and (=> _let_4 (= _let_3 (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat tptp.zero_zero_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_2)))) (=> (not _let_4) (= _let_3 (tptp.aa_Pro262675715343573244at_nat (tptp.unique5026877609467782581ep_nat _let_1) (tptp.unique5055182867167087721od_nat _let_2 (tptp.aa_num_num tptp.bit0 _let_1))))))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (let ((_let_2 (tptp.aa_num_num tptp.bit1 M))) (let ((_let_3 (tptp.unique5052692396658037445od_int _let_2 _let_1))) (let ((_let_4 (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N2)))) (and (=> _let_4 (= _let_3 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) (tptp.aa_num_int tptp.numeral_numeral_int _let_2)))) (=> (not _let_4) (= _let_3 (tptp.aa_Pro6970504127699319548nt_int (tptp.unique5024387138958732305ep_int _let_1) (tptp.unique5052692396658037445od_int _let_2 (tptp.aa_num_num tptp.bit0 _let_1))))))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (let ((_let_2 (tptp.aa_num_num tptp.bit1 M))) (let ((_let_3 (tptp.unique3479559517661332726nteger _let_2 _let_1))) (let ((_let_4 (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N2)))) (and (=> _let_4 (= _let_3 (tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger _let_2)))) (=> (not _let_4) (= _let_3 (tptp.unique4921790084139445826nteger _let_1 (tptp.unique3479559517661332726nteger _let_2 (tptp.aa_num_num tptp.bit0 _let_1))))))))))) (forall ((P tptp.bool) (Q tptp.fun_int_fun_int_bool) (X5 tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool (tptp.aa_fun8168818243683596540t_bool (tptp.aTP_Lamm_aib P) Q)) X5)) (and (tptp.pp P) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool Q) X5))))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_num tptp.bit1 N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_num tptp.bit1 N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_num_num tptp.bit1 N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_num tptp.bit0 N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N2)))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num tptp.bit1 M)) tptp.one)))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num tptp.one) (tptp.aa_num_num tptp.bit1 N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_num tptp.bit0 N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_num_num tptp.bit1 N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) N2)))) (forall ((N2 tptp.nat) (M tptp.num)) (= (tptp.aa_num_option_num (tptp.bit_take_bit_num (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_option_num tptp.some_num (tptp.aa_option_num_num (tptp.case_option_num_num tptp.one tptp.bit1) (tptp.aa_num_option_num (tptp.bit_take_bit_num N2) M))))) (forall ((N2 tptp.num)) (= (tptp.unique5052692396658037445od_int tptp.one (tptp.aa_num_num tptp.bit1 N2)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) (tptp.aa_num_int tptp.numeral_numeral_int tptp.one)))) (forall ((N2 tptp.num)) (= (tptp.unique5055182867167087721od_nat tptp.one (tptp.aa_num_num tptp.bit1 N2)) (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat tptp.zero_zero_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one)))) (forall ((N2 tptp.num)) (= (tptp.unique3479559517661332726nteger tptp.one (tptp.aa_num_num tptp.bit1 N2)) (tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger tptp.one)))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (let ((_let_2 (tptp.aa_num_num tptp.bit0 M))) (let ((_let_3 (tptp.unique5055182867167087721od_nat _let_2 _let_1))) (let ((_let_4 (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) N2)))) (and (=> _let_4 (= _let_3 (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat tptp.zero_zero_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_2)))) (=> (not _let_4) (= _let_3 (tptp.aa_Pro262675715343573244at_nat (tptp.unique5026877609467782581ep_nat _let_1) (tptp.unique5055182867167087721od_nat _let_2 (tptp.aa_num_num tptp.bit0 _let_1))))))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (let ((_let_2 (tptp.aa_num_num tptp.bit0 M))) (let ((_let_3 (tptp.unique5052692396658037445od_int _let_2 _let_1))) (let ((_let_4 (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) N2)))) (and (=> _let_4 (= _let_3 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) (tptp.aa_num_int tptp.numeral_numeral_int _let_2)))) (=> (not _let_4) (= _let_3 (tptp.aa_Pro6970504127699319548nt_int (tptp.unique5024387138958732305ep_int _let_1) (tptp.unique5052692396658037445od_int _let_2 (tptp.aa_num_num tptp.bit0 _let_1))))))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (let ((_let_2 (tptp.aa_num_num tptp.bit0 M))) (let ((_let_3 (tptp.unique3479559517661332726nteger _let_2 _let_1))) (let ((_let_4 (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) N2)))) (and (=> _let_4 (= _let_3 (tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger _let_2)))) (=> (not _let_4) (= _let_3 (tptp.unique4921790084139445826nteger _let_1 (tptp.unique3479559517661332726nteger _let_2 (tptp.aa_num_num tptp.bit0 _let_1))))))))))) (forall ((Prod tptp.product_prod_int_int)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool tptp.aTP_Lamm_nc) Prod))) (forall ((X tptp.product_prod_num_num)) (=> (not (= X (tptp.product_Pair_num_num tptp.one tptp.one))) (=> (forall ((N5 tptp.num)) (not (= X (tptp.product_Pair_num_num tptp.one (tptp.aa_num_num tptp.bit0 N5))))) (=> (forall ((N5 tptp.num)) (not (= X (tptp.product_Pair_num_num tptp.one (tptp.aa_num_num tptp.bit1 N5))))) (=> (forall ((M5 tptp.num)) (not (= X (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M5) tptp.one)))) (=> (forall ((M5 tptp.num) (N5 tptp.num)) (not (= X (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M5) (tptp.aa_num_num tptp.bit0 N5))))) (=> (forall ((M5 tptp.num) (N5 tptp.num)) (not (= X (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M5) (tptp.aa_num_num tptp.bit1 N5))))) (=> (forall ((M5 tptp.num)) (not (= X (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M5) tptp.one)))) (=> (forall ((M5 tptp.num) (N5 tptp.num)) (not (= X (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M5) (tptp.aa_num_num tptp.bit0 N5))))) (not (forall ((M5 tptp.num) (N5 tptp.num)) (not (= X (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M5) (tptp.aa_num_num tptp.bit1 N5))))))))))))))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N2))) (= (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N2))) (= (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2))) (= (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit1 N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger _let_1) _let_1)) tptp.one_one_Code_integer)))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat N2))) (= (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit1 N2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat _let_1) _let_1)) tptp.one_one_rat)))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural N2))) (= (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit1 N2)) (tptp.plus_p4538020629002901425atural (tptp.plus_p4538020629002901425atural _let_1 _let_1) tptp.one_one_Code_natural)))) (forall ((Z tptp.code_integer) (W2 tptp.num)) (let ((_let_1 (tptp.power_8256067586552552935nteger Z))) (let ((_let_2 (tptp.aa_nat_Code_integer _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W2)))) (= (tptp.aa_nat_Code_integer _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 W2))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger Z) _let_2)) _let_2))))) (forall ((Z tptp.assn) (W2 tptp.num)) (let ((_let_1 (tptp.power_power_assn Z))) (let ((_let_2 (tptp.aa_nat_assn _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W2)))) (= (tptp.aa_nat_assn _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 W2))) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn Z) _let_2)) _let_2))))) (forall ((Z tptp.rat) (W2 tptp.num)) (let ((_let_1 (tptp.power_power_rat Z))) (let ((_let_2 (tptp.aa_nat_rat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W2)))) (= (tptp.aa_nat_rat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 W2))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Z) _let_2)) _let_2))))) (forall ((Z tptp.nat) (W2 tptp.num)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Z))) (let ((_let_2 (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W2)))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 W2))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Z) _let_2)) _let_2))))) (forall ((Z tptp.int) (W2 tptp.num)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int Z))) (let ((_let_2 (tptp.aa_nat_int _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W2)))) (= (tptp.aa_nat_int _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 W2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Z) _let_2)) _let_2))))) (forall ((A tptp.code_integer)) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) A)) A))) (forall ((A tptp.assn)) (= (tptp.aa_nat_assn (tptp.power_power_assn A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn A) A)) A))) (forall ((A tptp.rat)) (= (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat A) A)) A))) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) A)) A))) (forall ((A tptp.int)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) A)) A))) (forall ((N2 tptp.nat) (K tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.bit_se1745604003318907178nteger (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit1 K))) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.bit_se1745604003318907178nteger N2) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger K))) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_Code_integer))) (forall ((N2 tptp.nat) (K tptp.num)) (= (tptp.bit_se569199155075624693atural (tptp.aa_nat_nat tptp.suc N2) (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit1 K))) (tptp.plus_p4538020629002901425atural (tptp.times_2397367101498566445atural (tptp.bit_se569199155075624693atural N2 (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural K)) (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.one_one_Code_natural))) (forall ((N2 tptp.nat) (K tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 K))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N2) (tptp.aa_num_nat tptp.numeral_numeral_nat K))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_nat))) (forall ((N2 tptp.nat) (K tptp.num)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 K))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) (tptp.aa_num_int tptp.numeral_numeral_int K))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_int))) (forall ((M tptp.num)) (= (tptp.unique5052692396658037445od_int (tptp.aa_num_num tptp.bitM M) (tptp.aa_num_num tptp.bit0 tptp.one)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_num_int tptp.numeral_numeral_int M)) tptp.one_one_int)) tptp.one_one_int))) (forall ((R3 tptp.num) (M tptp.num)) (= (tptp.aa_num_option_num (tptp.bit_take_bit_num (tptp.aa_num_nat tptp.numeral_numeral_nat R3)) (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_opt5369159329878751634on_num (tptp.case_o6005452278849405969um_num tptp.none_num tptp.aTP_Lamm_agv) (tptp.aa_num_option_num (tptp.bit_take_bit_num (tptp.aa_num_nat tptp.pred_numeral R3)) M)))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.bit_se1745604003318907178nteger (tptp.aa_num_nat tptp.numeral_numeral_nat L)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit1 K))) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.bit_se1745604003318907178nteger (tptp.aa_num_nat tptp.pred_numeral L)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger K))) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_Code_integer))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.bit_se569199155075624693atural (tptp.aa_num_nat tptp.numeral_numeral_nat L) (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit1 K))) (tptp.plus_p4538020629002901425atural (tptp.times_2397367101498566445atural (tptp.bit_se569199155075624693atural (tptp.aa_num_nat tptp.pred_numeral L) (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural K)) (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.one_one_Code_natural))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat (tptp.aa_num_nat tptp.numeral_numeral_nat L)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 K))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat (tptp.aa_num_nat tptp.pred_numeral L)) (tptp.aa_num_nat tptp.numeral_numeral_nat K))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_nat))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int (tptp.aa_num_nat tptp.numeral_numeral_nat L)) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 K))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int (tptp.aa_num_nat tptp.pred_numeral L)) (tptp.aa_num_int tptp.numeral_numeral_int K))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_int))) (forall ((G tptp.fun_nat_fun_nat_nat) (N2 tptp.nat)) (= (tptp.groups4077766827762148844at_nat (tptp.produc6842872674320459806at_nat G) (tptp.collec3392354462482085612at_nat (tptp.produc8955392012077580105t_bool (tptp.aTP_Lamm_aic N2)))) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aTP_Lamm_aha G)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))) (forall ((G tptp.fun_nat_fun_nat_int) (N2 tptp.nat)) (= (tptp.groups4075276357253098568at_int (tptp.produc6840382203811409530at_int G) (tptp.collec3392354462482085612at_nat (tptp.produc8955392012077580105t_bool (tptp.aTP_Lamm_aic N2)))) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aTP_Lamm_ahc G)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))) (forall ((N2 tptp.nat) (M tptp.num)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N2) (tptp.aa_num_nat tptp.numeral_numeral_nat M)))) (let ((_let_2 (tptp.aa_num_option_num (tptp.bit_take_bit_num N2) M))) (let ((_let_3 (= _let_1 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.none_num)) (=> (not _let_3) (= _let_2 (tptp.aa_num_option_num tptp.some_num (tptp.aa_nat_num tptp.num_of_nat _let_1))))))))) (forall ((I2 tptp.bool) (K tptp.bool)) (= (tptp.pp (tptp.member_bool I2 (tptp.set_or4454636193642143162n_bool K))) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.ord_less_bool I2) K)))) (forall ((I2 tptp.set_nat) (K tptp.set_nat)) (= (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat I2) (tptp.set_or890127255671739683et_nat K))) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat I2) K)))) (forall ((I2 tptp.assn) (K tptp.assn)) (= (tptp.member_assn I2 (tptp.set_or7637083652282234053n_assn K)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn I2) K)))) (forall ((I2 tptp.rat) (K tptp.rat)) (= (tptp.member_rat I2 (tptp.set_ord_lessThan_rat K)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat I2) K)))) (forall ((I2 tptp.num) (K tptp.num)) (= (tptp.member_num I2 (tptp.set_ord_lessThan_num K)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num I2) K)))) (forall ((I2 tptp.nat) (K tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I2) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat K))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) K)))) (forall ((I2 tptp.int) (K tptp.int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I2) (tptp.set_ord_lessThan_int K))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int I2) K)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.ord_less_eq_set_rat (tptp.set_ord_lessThan_rat X) (tptp.set_ord_lessThan_rat Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.ord_less_eq_set_num (tptp.set_ord_lessThan_num X) (tptp.set_ord_lessThan_num Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat X)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.set_ord_lessThan_int X)) (tptp.set_ord_lessThan_int Y))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)))) (= (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat) (forall ((N2 tptp.nat) (K tptp.num)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_num_nat tptp.numeral_numeral_nat K))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_num_nat tptp.pred_numeral K))))) (forall ((K tptp.num) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (tptp.aa_nat_nat tptp.suc N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_num_nat tptp.pred_numeral K)) N2)))) (forall ((G tptp.fun_nat_Code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.groups3455450783089532116nteger G))) (= (tptp.aa_set871585252387937313nteger _let_1 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_set871585252387937313nteger _let_1 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (tptp.aa_nat_Code_integer G N2))))) (forall ((G tptp.fun_nat_assn) (N2 tptp.nat)) (= (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (tptp.aa_nat_assn G N2)))) (forall ((G tptp.fun_nat_rat) (N2 tptp.nat)) (let ((_let_1 (tptp.groups73079841787564623at_rat G))) (= (tptp.aa_set_nat_rat _let_1 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_set_nat_rat _let_1 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (tptp.aa_nat_rat G N2))))) (forall ((G tptp.fun_nat_nat) (N2 tptp.nat)) (let ((_let_1 (tptp.groups708209901874060359at_nat G))) (= (tptp.aa_set_nat_nat _let_1 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_set_nat_nat _let_1 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (tptp.aa_nat_nat G N2))))) (forall ((G tptp.fun_nat_int) (N2 tptp.nat)) (let ((_let_1 (tptp.groups705719431365010083at_int G))) (= (tptp.aa_set_nat_int _let_1 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_set_nat_int _let_1 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (tptp.aa_nat_int G N2))))) (forall ((N2 tptp.nat) (K tptp.num)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_num_nat tptp.numeral_numeral_nat K))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) (tptp.aa_num_nat tptp.pred_numeral K))))) (forall ((K tptp.num) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (tptp.aa_nat_nat tptp.suc N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.pred_numeral K)) N2)))) (forall ((R3 tptp.num) (M tptp.num)) (= (tptp.aa_num_option_num (tptp.bit_take_bit_num (tptp.aa_num_nat tptp.numeral_numeral_nat R3)) (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_option_num tptp.some_num (tptp.aa_option_num_num (tptp.case_option_num_num tptp.one tptp.bit1) (tptp.aa_num_option_num (tptp.bit_take_bit_num (tptp.aa_num_nat tptp.pred_numeral R3)) M))))) (forall ((X tptp.int)) (not (= (tptp.set_ord_lessThan_int X) tptp.bot_bot_set_int))) (forall ((U tptp.set_nat)) (= (tptp.set_or890127255671739683et_nat U) (tptp.collect_set_nat (tptp.aa_set5116768664143533222t_bool tptp.aTP_Lamm_da U)))) (forall ((U tptp.assn)) (= (tptp.set_or7637083652282234053n_assn U) (tptp.collect_assn (tptp.aa_ass5323576183532441186n_bool tptp.aTP_Lamm_dc U)))) (forall ((U tptp.rat)) (= (tptp.set_ord_lessThan_rat U) (tptp.collect_rat (tptp.aa_rat_fun_rat_bool tptp.aTP_Lamm_di U)))) (forall ((U tptp.num)) (= (tptp.set_ord_lessThan_num U) (tptp.collect_num (tptp.aa_num_fun_num_bool tptp.aTP_Lamm_fb U)))) (forall ((U tptp.nat)) (= (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat U) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_dg U)))) (forall ((U tptp.int)) (= (tptp.set_ord_lessThan_int U) (tptp.collect_int (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_dk U)))) (forall ((N2 tptp.nat)) (= (= (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2) tptp.bot_bot_set_nat) (= N2 tptp.zero_zero_nat))) (forall ((N2 tptp.bool)) (= (= (tptp.set_or4454636193642143162n_bool N2) tptp.bot_bot_set_bool) (= (tptp.pp N2) tptp.bot_bot_bool))) (forall ((N2 tptp.nat)) (= (= (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2) tptp.bot_bot_set_nat) (= N2 tptp.bot_bot_nat))) (forall ((S tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (exists ((K3 tptp.nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat S) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat K3)))))) (forall ((S tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (exists ((K2 tptp.nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat S) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat K2)))))) (forall ((M tptp.rat) (N2 tptp.rat)) (= (tptp.ord_less_set_rat (tptp.set_ord_lessThan_rat M) (tptp.set_ord_lessThan_rat N2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.ord_less_set_num (tptp.set_ord_lessThan_num M) (tptp.set_ord_lessThan_num N2)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat M)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (forall ((M tptp.int) (N2 tptp.int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int (tptp.set_ord_lessThan_int M)) (tptp.set_ord_lessThan_int N2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int M) N2)))) (forall ((G tptp.fun_nat_nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_aid G) N2)) _let_1) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) _let_1)))) (forall ((G tptp.fun_nat_nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_aid G) N2)) _let_1) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat G) _let_1)))) (forall ((G tptp.fun_nat_int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (= (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_aie G) N2)) _let_1) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int G) _let_1)))) (forall ((L tptp.rat) (U tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat L) U)) (= (tptp.sup_sup_set_rat (tptp.set_ord_lessThan_rat L) (tptp.set_or4029947393144176647an_rat L U)) (tptp.set_ord_lessThan_rat U)))) (forall ((L tptp.num) (U tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num L) U)) (= (tptp.sup_sup_set_num (tptp.set_ord_lessThan_num L) (tptp.set_or1222409239386451017an_num L U)) (tptp.set_ord_lessThan_num U)))) (forall ((L tptp.nat) (U tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat L) U)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat L)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat L) U)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat U)))) (forall ((L tptp.int) (U tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int L) U)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int (tptp.set_ord_lessThan_int L)) (tptp.set_or4662586982721622107an_int L U)) (tptp.set_ord_lessThan_int U)))) (forall ((L tptp.code_integer) (U tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger L) U)) (= (tptp.sup_su848401254843788991nteger (tptp.set_or5754767410780653050nteger L) (tptp.set_or8404916559141939852nteger L U)) (tptp.set_or5754767410780653050nteger U)))) (forall ((L tptp.bool) (U tptp.bool)) (= (tptp.inf_inf_set_bool (tptp.set_or4454636193642143162n_bool L) (tptp.set_or1454250544011482060t_bool L U)) tptp.bot_bot_set_bool)) (forall ((L tptp.int) (U tptp.int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int (tptp.set_ord_lessThan_int L)) (tptp.set_or1266510415728281911st_int L U)) tptp.bot_bot_set_int)) (forall ((L tptp.nat) (U tptp.nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat L)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat L) U)) tptp.bot_bot_set_nat)) (forall ((L tptp.code_integer) (U tptp.code_integer)) (= (tptp.inf_in1364745209274528805nteger (tptp.set_or5754767410780653050nteger L) (tptp.set_or189985376899183464nteger L U)) tptp.bot_bo3990330152332043303nteger)) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.ord_less_eq_set_rat (tptp.set_ord_atMost_rat A) (tptp.set_ord_lessThan_rat B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)))) (forall ((A tptp.num) (B tptp.num)) (= (tptp.ord_less_eq_set_num (tptp.set_ord_atMost_num A) (tptp.set_ord_lessThan_num B)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B)))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat A)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat B))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.set_ord_atMost_int A)) (tptp.set_ord_lessThan_int B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)))) (forall ((L tptp.bool) (U tptp.bool)) (= (tptp.inf_inf_set_bool (tptp.set_or4454636193642143162n_bool L) (tptp.set_or8576162586734908840n_bool L U)) tptp.bot_bot_set_bool)) (forall ((L tptp.nat) (U tptp.nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat L)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat L) U)) tptp.bot_bot_set_nat)) (forall ((L tptp.int) (U tptp.int)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int (tptp.set_ord_lessThan_int L)) (tptp.set_or4662586982721622107an_int L U)) tptp.bot_bot_set_int)) (forall ((L tptp.code_integer) (U tptp.code_integer)) (= (tptp.inf_in1364745209274528805nteger (tptp.set_or5754767410780653050nteger L) (tptp.set_or8404916559141939852nteger L U)) tptp.bot_bo3990330152332043303nteger)) (forall ((Q tptp.fun_int_nat) (P tptp.fun_int_nat) (N2 tptp.int)) (let ((_let_1 (tptp.set_ord_lessThan_int N2))) (=> (forall ((X3 tptp.int)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat Q X3)) (tptp.aa_int_nat P X3)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.groups4541462559716669496nt_nat P _let_1)) (tptp.groups4541462559716669496nt_nat Q _let_1)) (tptp.groups4541462559716669496nt_nat (tptp.aa_fun6506752150744536624nt_nat (tptp.aTP_Lamm_lh Q) P) _let_1))))) (forall ((Q tptp.fun_nat_nat) (P tptp.fun_nat_nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (=> (forall ((X3 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat Q X3)) (tptp.aa_nat_nat P X3)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat P) _let_1)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat Q) _let_1)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_li Q) P)) _let_1))))) (forall ((G tptp.fun_na2338080690716861136at_nat) (N2 tptp.nat)) (= (tptp.groups6857163185585827899at_nat G (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat (tptp.aa_nat2240542744625857721at_nat G tptp.zero_zero_nat)) (tptp.groups6857163185585827899at_nat (tptp.aTP_Lamm_ka G) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (forall ((G tptp.fun_nat_rat) (N2 tptp.nat)) (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat G) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat G tptp.zero_zero_nat)) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_kb G)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (forall ((G tptp.fun_nat_int) (N2 tptp.nat)) (= (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int G) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int G tptp.zero_zero_nat)) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_kc G)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (forall ((G tptp.fun_nat_nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat G tptp.zero_zero_nat)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_jx G)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (forall ((F tptp.fun_nat_rat) (M tptp.nat)) (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_oc F)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat M)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_nat_rat F tptp.zero_zero_nat)) (tptp.aa_nat_rat F M)))) (forall ((F tptp.fun_nat_int) (M tptp.nat)) (= (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_od F)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat M)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int F tptp.zero_zero_nat)) (tptp.aa_nat_int F M)))) (forall ((F tptp.fun_nat_rat) (M tptp.nat)) (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_kd F)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat M)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_nat_rat F M)) (tptp.aa_nat_rat F tptp.zero_zero_nat)))) (forall ((F tptp.fun_nat_int) (M tptp.nat)) (= (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_ke F)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat M)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int F M)) (tptp.aa_nat_int F tptp.zero_zero_nat)))) (forall ((G tptp.fun_nat_Code_integer) (N2 tptp.nat)) (= (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger G) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer G tptp.zero_zero_nat)) (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger (tptp.aTP_Lamm_nk G)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (forall ((G tptp.fun_nat_assn) (N2 tptp.nat)) (= (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.aa_nat_assn G tptp.zero_zero_nat)) (tptp.groups6906906614972039071t_assn (tptp.aTP_Lamm_nl G) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (forall ((G tptp.fun_nat_rat) (N2 tptp.nat)) (= (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat G) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat G tptp.zero_zero_nat)) (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat (tptp.aTP_Lamm_kb G)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (forall ((G tptp.fun_nat_nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat G) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat G tptp.zero_zero_nat)) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aTP_Lamm_jx G)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (forall ((G tptp.fun_nat_int) (N2 tptp.nat)) (= (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int G) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int G tptp.zero_zero_nat)) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aTP_Lamm_kc G)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_nat_num tptp.num_of_nat N2)) N2))) (forall ((G tptp.fun_nat_nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N2)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_jx G)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) tptp.one_one_nat)) (= (tptp.aa_nat_num tptp.num_of_nat N2) tptp.one))) (forall ((G tptp.fun_nat_nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat G) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N2)) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aTP_Lamm_jx G)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))) (forall ((G tptp.fun_nat_int) (N2 tptp.nat)) (= (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int G) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N2)) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aTP_Lamm_kc G)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))) (forall ((F tptp.fun_nat_nat) (Mm tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_jx F)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat Mm)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat tptp.one_one_nat) Mm)))) (forall ((G tptp.fun_nat_nat) (K tptp.nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_aif G) K)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) K))))) (forall ((G tptp.fun_nat_nat) (K tptp.nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_aig G) K)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat G) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) K))))) (forall ((G tptp.fun_nat_int) (K tptp.nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_aih G) K)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int G) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) K))))) (forall ((A tptp.fun_nat_fun_nat_nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_aii A)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_abq A) N2)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))) (forall ((A tptp.fun_nat_fun_nat_nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aTP_Lamm_aij A)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_abt A) N2)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))) (forall ((A tptp.fun_nat_fun_nat_int) (N2 tptp.nat)) (= (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aTP_Lamm_aik A)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_abv A) N2)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))) (forall ((K tptp.num)) (= (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int K)) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int (tptp.aa_num_nat tptp.pred_numeral K))))) (forall ((K tptp.num)) (= (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger K)) (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger (tptp.aa_num_nat tptp.pred_numeral K))))) (forall ((K tptp.num)) (= (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat K)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat (tptp.aa_num_nat tptp.pred_numeral K))))) (forall ((K tptp.num)) (= (tptp.aa_nat_Code_natural tptp.semiri2447717529341329178atural (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (tptp.times_2397367101498566445atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural K) (tptp.aa_nat_Code_natural tptp.semiri2447717529341329178atural (tptp.aa_num_nat tptp.pred_numeral K))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat K))) (= (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat (tptp.aa_num_nat tptp.pred_numeral K)))))) (forall ((L tptp.rat) (U tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat L) U)) (= (tptp.sup_sup_set_rat (tptp.set_ord_lessThan_rat L) (tptp.set_or633870826150836451st_rat L U)) (tptp.set_ord_atMost_rat U)))) (forall ((L tptp.num) (U tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num L) U)) (= (tptp.sup_sup_set_num (tptp.set_ord_lessThan_num L) (tptp.set_or7049704709247886629st_num L U)) (tptp.set_ord_atMost_num U)))) (forall ((L tptp.int) (U tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int L) U)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.sup_sup_set_int (tptp.set_ord_lessThan_int L)) (tptp.set_or1266510415728281911st_int L U)) (tptp.set_ord_atMost_int U)))) (forall ((L tptp.nat) (U tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat L) U)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat L)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat L) U)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat U)))) (forall ((L tptp.code_integer) (U tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger L) U)) (= (tptp.sup_su848401254843788991nteger (tptp.set_or5754767410780653050nteger L) (tptp.set_or189985376899183464nteger L U)) (tptp.set_or9101266186257409494nteger U)))) (forall ((X tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger X))) (let ((_let_2 (tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer))) (= (tptp.aa_Cod1783974652533396728nteger _let_2 (tptp.aa_nat_Code_integer _let_1 N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger _let_2 X)) (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger _let_1) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))))) (forall ((X tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_power_rat X))) (let ((_let_2 (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat tptp.one_one_rat))) (= (tptp.aa_rat_rat _let_2 (tptp.aa_nat_rat _let_1 N2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat _let_2 X)) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat _let_1) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))))) (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int X))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.minus_minus_int tptp.one_one_int))) (= (tptp.aa_int_int _let_2 (tptp.aa_nat_int _let_1 N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int _let_2 X)) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int _let_1) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))))) (forall ((X tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger X))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_nat_Code_integer _let_1 N2)) tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger X) tptp.one_one_Code_integer)) (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger _let_1) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))))) (forall ((X tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_power_rat X))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_nat_rat _let_1 N2)) tptp.one_one_rat) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat X) tptp.one_one_rat)) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat _let_1) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))))) (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int X))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int _let_1 N2)) tptp.one_one_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) tptp.one_one_int)) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int _let_1) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))))) (forall ((X tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_power_rat X))) (=> (not (= X tptp.one_one_rat)) (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat _let_1) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_nat_rat _let_1 N2)) tptp.one_one_rat)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat X) tptp.one_one_rat)))))) (forall ((U tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) U)) (= (tptp.set_or4662586982721622107an_int tptp.zero_zero_int U) (tptp.image_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_int_nat tptp.nat2 U)))))) (forall ((G tptp.fun_na2338080690716861136at_nat) (N2 tptp.nat)) (= (tptp.groups6857163185585827899at_nat G (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat (tptp.aa_nat2240542744625857721at_nat G tptp.zero_zero_nat)) (tptp.groups6857163185585827899at_nat (tptp.aTP_Lamm_ka G) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (forall ((G tptp.fun_nat_rat) (N2 tptp.nat)) (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat G tptp.zero_zero_nat)) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_kb G)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (forall ((G tptp.fun_nat_int) (N2 tptp.nat)) (= (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int G tptp.zero_zero_nat)) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_kc G)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (forall ((G tptp.fun_nat_nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat G tptp.zero_zero_nat)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_jx G)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (forall ((G tptp.fun_nat_Code_integer) (N2 tptp.nat)) (= (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer G tptp.zero_zero_nat)) (tptp.aa_set871585252387937313nteger (tptp.groups3455450783089532116nteger (tptp.aTP_Lamm_nk G)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (forall ((G tptp.fun_nat_assn) (N2 tptp.nat)) (= (tptp.groups6906906614972039071t_assn G (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.aa_nat_assn G tptp.zero_zero_nat)) (tptp.groups6906906614972039071t_assn (tptp.aTP_Lamm_nl G) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (forall ((G tptp.fun_nat_rat) (N2 tptp.nat)) (= (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat G tptp.zero_zero_nat)) (tptp.aa_set_nat_rat (tptp.groups73079841787564623at_rat (tptp.aTP_Lamm_kb G)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (forall ((G tptp.fun_nat_nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat G tptp.zero_zero_nat)) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aTP_Lamm_jx G)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (forall ((G tptp.fun_nat_int) (N2 tptp.nat)) (= (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int G tptp.zero_zero_nat)) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aTP_Lamm_kc G)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_nat_num tptp.num_of_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) N2)) (tptp.aa_num_num tptp.bit0 (tptp.aa_nat_num tptp.num_of_nat N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 M)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 N2)) (= (tptp.aa_nat_num tptp.num_of_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2)) (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num (tptp.aa_nat_num tptp.num_of_nat M)) (tptp.aa_nat_num tptp.num_of_nat N2))))))) (forall ((X tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (tptp.power_power_rat X))) (let ((_let_3 (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat _let_2) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))) (let ((_let_4 (= X tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))) (=> (not _let_4) (= _let_3 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat _let_1 (tptp.aa_nat_rat _let_2 N2))) (tptp.aa_rat_rat _let_1 X)))))))))) (forall ((X tptp.code_integer) (N2 tptp.nat) (Y tptp.code_integer)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) _let_1)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Y) _let_1)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger X) Y)) (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger (tptp.aa_Cod1578151519121547077nteger (tptp.aa_nat2351529209232473362nteger (tptp.aTP_Lamm_ail X) N2) Y)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat _let_1)))))) (forall ((X tptp.rat) (N2 tptp.nat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat X) Y)) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_nat298952458717073160at_rat (tptp.aTP_Lamm_aim X) N2) Y)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat _let_1)))))) (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Y) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) Y)) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aa_nat6704147566042551216at_int (tptp.aTP_Lamm_ain X) N2) Y)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat _let_1)))))) (forall ((X tptp.code_integer) (N2 tptp.nat) (Y tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) N2)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Y) N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger X) Y)) (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger (tptp.aa_Cod1578151519121547077nteger (tptp.aa_nat2351529209232473362nteger (tptp.aTP_Lamm_aio X) N2) Y)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (forall ((X tptp.rat) (N2 tptp.nat) (Y tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_nat_rat (tptp.power_power_rat X) N2)) (tptp.aa_nat_rat (tptp.power_power_rat Y) N2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat X) Y)) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_nat298952458717073160at_rat (tptp.aTP_Lamm_aip X) N2) Y)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int X) N2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Y) N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) Y)) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aa_nat6704147566042551216at_int (tptp.aTP_Lamm_aiq X) N2) Y)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.bit_se1745604003318907178nteger (tptp.aa_num_nat tptp.numeral_numeral_nat L)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 K))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.bit_se1745604003318907178nteger (tptp.aa_num_nat tptp.pred_numeral L)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger K))) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.bit_se569199155075624693atural (tptp.aa_num_nat tptp.numeral_numeral_nat L) (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 K))) (tptp.times_2397367101498566445atural (tptp.bit_se569199155075624693atural (tptp.aa_num_nat tptp.pred_numeral L) (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural K)) (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat (tptp.aa_num_nat tptp.numeral_numeral_nat L)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 K))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat (tptp.aa_num_nat tptp.pred_numeral L)) (tptp.aa_num_nat tptp.numeral_numeral_nat K))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int (tptp.aa_num_nat tptp.numeral_numeral_nat L)) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 K))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int (tptp.aa_num_nat tptp.pred_numeral L)) (tptp.aa_num_int tptp.numeral_numeral_int K))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((X tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer))) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger _let_1 X)) (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger (tptp.aa_nat2010205248571845816nteger (tptp.aTP_Lamm_air X) N2)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))))) (forall ((X tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat tptp.one_one_rat))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_nat_rat (tptp.power_power_rat X) N2)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat _let_1 X)) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aa_nat_fun_nat_rat (tptp.aTP_Lamm_ais X) N2)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))))) (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.minus_minus_int tptp.one_one_int))) (= (tptp.aa_int_int _let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int X) N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int _let_1 X)) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_ait X) N2)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))))) (forall ((G tptp.fun_nat_fun_nat_nat) (N2 tptp.nat)) (= (tptp.groups977919841031483927at_nat (tptp.produc6842872674320459806at_nat G) (tptp.collec3392354462482085612at_nat (tptp.produc8955392012077580105t_bool (tptp.aTP_Lamm_aic N2)))) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_agz G)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))) (forall ((N2 tptp.num)) (= (tptp.aa_nat_Code_integer tptp.bit_se2119862282449309892nteger (tptp.aa_num_nat tptp.numeral_numeral_nat N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_Code_integer tptp.bit_se2119862282449309892nteger (tptp.aa_num_nat tptp.pred_numeral N2)))))) (forall ((N2 tptp.num)) (= (tptp.aa_nat_Code_natural tptp.bit_se943457434206027407atural (tptp.aa_num_nat tptp.numeral_numeral_nat N2)) (tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural (tptp.times_2397367101498566445atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)) (tptp.aa_nat_Code_natural tptp.bit_se943457434206027407atural (tptp.aa_num_nat tptp.pred_numeral N2)))))) (forall ((N2 tptp.num)) (= (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat (tptp.aa_num_nat tptp.numeral_numeral_nat N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat (tptp.aa_num_nat tptp.pred_numeral N2)))))) (forall ((N2 tptp.num)) (= (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int (tptp.aa_num_nat tptp.numeral_numeral_nat N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int (tptp.aa_num_nat tptp.pred_numeral N2)))))) (forall ((Bs tptp.list_bool)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.groups4048646594741130792ol_int tptp.zero_n2684676970156552555ol_int _let_1 Bs)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int _let_1) (tptp.size_size_list_bool Bs)))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 X))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) (tptp.aa_num_nat tptp.numeral_numeral_nat Y)))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.bit_se3222712562003087583nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 X))) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit1 Y))) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_Cod1783974652533396728nteger (tptp.bit_se3222712562003087583nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger X)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger Y)))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.bit_se2046307713759805098atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 X)) (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit1 Y))) (tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural (tptp.times_2397367101498566445atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)) (tptp.bit_se2046307713759805098atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural X) (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural Y)))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 X))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 Y))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int (tptp.aa_num_int tptp.numeral_numeral_int X)) (tptp.aa_num_int tptp.numeral_numeral_int Y)))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 X))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Y))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) (tptp.aa_num_nat tptp.numeral_numeral_nat Y)))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.bit_se3222712562003087583nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit1 X))) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 Y))) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_Cod1783974652533396728nteger (tptp.bit_se3222712562003087583nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger X)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger Y)))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.bit_se2046307713759805098atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit1 X)) (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 Y))) (tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural (tptp.times_2397367101498566445atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)) (tptp.bit_se2046307713759805098atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural X) (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural Y)))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 X))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Y))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int (tptp.aa_num_int tptp.numeral_numeral_int X)) (tptp.aa_num_int tptp.numeral_numeral_int Y)))))) (forall ((L tptp.num) (Qr tptp.produc8923325533196201883nteger)) (= (tptp.unique4921790084139445826nteger L Qr) (tptp.produc6916734918728496179nteger (tptp.aTP_Lamm_afe L) Qr))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat N2))) (tptp.pp (tptp.aa_nat_bool _let_1 N2))))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int K) L))) (= (tptp.pp (tptp.aa_int_bool _let_1 K)) (tptp.pp (tptp.aa_int_bool _let_1 L)))))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int K) L)) tptp.zero_zero_int)) (not (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int L) tptp.zero_zero_int)))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 X))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Y))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) (tptp.aa_num_nat tptp.numeral_numeral_nat Y))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.bit_se3222712562003087583nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 X))) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 Y))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_Cod1783974652533396728nteger (tptp.bit_se3222712562003087583nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger X)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger Y))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.bit_se2046307713759805098atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 X)) (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 Y))) (tptp.times_2397367101498566445atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)) (tptp.bit_se2046307713759805098atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural X) (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural Y))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 X))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Y))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int (tptp.aa_num_int tptp.numeral_numeral_int X)) (tptp.aa_num_int tptp.numeral_numeral_int Y))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 X))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 Y))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) (tptp.aa_num_nat tptp.numeral_numeral_nat Y))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.bit_se3222712562003087583nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit1 X))) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit1 Y))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_Cod1783974652533396728nteger (tptp.bit_se3222712562003087583nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger X)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger Y))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.bit_se2046307713759805098atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit1 X)) (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit1 Y))) (tptp.times_2397367101498566445atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 tptp.one)) (tptp.bit_se2046307713759805098atural (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural X) (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural Y))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 X))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 Y))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int (tptp.aa_num_int tptp.numeral_numeral_int X)) (tptp.aa_num_int tptp.numeral_numeral_int Y))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2))) (let ((_let_2 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) (= (tptp.unique3479559517661332726nteger M N2) (tptp.produc1086072967326762835nteger (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger _let_2) _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger _let_2) _let_1)))))) (forall ((X tptp.produc5207004643709237345nteger)) (not (forall ((F2 tptp.fun_Co6545587727236015215e_term) (D tptp.code_integer) (I3 tptp.code_integer)) (not (= X (tptp.produc4282985567423050387nteger F2 (tptp.produc1086072967326762835nteger D I3))))))) (forall ((X tptp.produc1616345218596728535nteger)) (not (forall ((F2 tptp.fun_Pr272337284026993017e_term) (D tptp.code_integer) (I3 tptp.code_integer)) (not (= X (tptp.produc7384524951051686153nteger F2 (tptp.produc1086072967326762835nteger D I3))))))) (forall ((L tptp.code_integer) (U tptp.code_integer)) (= (tptp.image_4470545334726330049nteger (tptp.aTP_Lamm_hv L) (tptp.set_or8404916559141939852nteger tptp.zero_z3403309356797280102nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger U) L))) (tptp.set_or8404916559141939852nteger L U))) _let_40 (forall ((K tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer K))) (let ((_let_2 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger K) tptp.zero_z3403309356797280102nteger)))) (let ((_let_3 (= K tptp.zero_z3403309356797280102nteger))) (and (=> _let_3 (= _let_1 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (and (=> _let_2 (= _let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (=> (not _let_2) (= _let_1 tptp.one_one_Code_integer))))))))) (forall ((L tptp.code_integer) (U tptp.code_integer)) (= (tptp.set_or8404916559141939852nteger L (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger U) tptp.one_one_Code_integer)) (tptp.set_or189985376899183464nteger L U))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat N2)))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int X) Y))))))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int N2)))) (forall ((N2 tptp.nat)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int N2)) tptp.zero_zero_int)))) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat N2))))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (forall ((S tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (exists ((K3 tptp.int)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int (tptp.image_int_int tptp.abs_abs_int S)) (tptp.set_ord_lessThan_int K3)))))) (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) X)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) _let_1)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int X) Y)) _let_1))))))) (forall ((F tptp.fun_int_Code_integer) (A tptp.code_integer) (Xs tptp.list_int)) (= (tptp.groups8594936613892548326nteger F A Xs) (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger (tptp.aa_lis2169558292809893284nteger (tptp.aa_Cod4217156690935544446nteger (tptp.aTP_Lamm_aiu F) A) Xs)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (tptp.size_size_list_int Xs))))) (forall ((F tptp.fun_nat_Code_integer) (A tptp.code_integer) (Xs tptp.list_nat)) (= (tptp.groups8223283053655703690nteger F A Xs) (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger (tptp.aa_lis7000467330633774408nteger (tptp.aa_Cod9048065728759425570nteger (tptp.aTP_Lamm_aiv F) A) Xs)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (tptp.aa_list_nat_nat tptp.size_size_list_nat Xs))))) (forall ((F tptp.fun_bo7282069421189217543nteger) (A tptp.code_integer) (Xs tptp.list_bool)) (= (tptp.groups7755797274146815065nteger F A Xs) (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger (tptp.aa_lis7128949495651308427nteger (tptp.aa_Cod4918889179898416383nteger (tptp.aTP_Lamm_aiw F) A) Xs)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (tptp.size_size_list_bool Xs))))) (forall ((F tptp.fun_int_rat) (A tptp.rat) (Xs tptp.list_int)) (= (tptp.groups7852591826665563233nt_rat F A Xs) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aa_lis1742918661435654559at_rat (tptp.aa_rat8348276666120063220at_rat (tptp.aTP_Lamm_aix F) A) Xs)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (tptp.size_size_list_int Xs))))) (forall ((F tptp.fun_nat_rat) (A tptp.rat) (Xs tptp.list_nat)) (= (tptp.aa_list_nat_rat (tptp.groups6853238114764508677at_rat F A) Xs) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aa_lis7014846069874721091at_rat (tptp.aa_rat4396832037704353944at_rat (tptp.aTP_Lamm_aiy F) A) Xs)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (tptp.aa_list_nat_nat tptp.size_size_list_nat Xs))))) (forall ((F tptp.fun_bool_rat) (A tptp.rat) (Xs tptp.list_bool)) (= (tptp.groups3416007005163685332ol_rat F A Xs) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aa_lis1392928297027365766at_rat (tptp.aa_rat954805563275384383at_rat (tptp.aTP_Lamm_aiz F) A) Xs)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (tptp.size_size_list_bool Xs))))) (forall ((F tptp.fun_int_int) (A tptp.int) (Xs tptp.list_int)) (= (tptp.groups8485231416243008693nt_int F A Xs) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aa_lis1073296200319854579at_int (tptp.aa_int2572695527019912092at_int (tptp.aTP_Lamm_aja F) A) Xs)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (tptp.size_size_list_int Xs))))) (forall ((F tptp.fun_nat_int) (A tptp.int) (Xs tptp.list_nat)) (= (tptp.groups7485877704341954137at_int F A Xs) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aa_lis6345223608758921111at_int (tptp.aa_int7844622935458978624at_int (tptp.aTP_Lamm_ajb F) A) Xs)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (tptp.aa_list_nat_nat tptp.size_size_list_nat Xs))))) (forall ((F tptp.fun_int_nat) (A tptp.nat) (Xs tptp.list_int)) (= (tptp.groups8487721886752058969nt_nat F A Xs) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_lis5251147219829051287at_nat (tptp.aa_nat3853594844976941284at_nat (tptp.aTP_Lamm_ajc F) A) Xs)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (tptp.size_size_list_int Xs))))) (forall ((F tptp.fun_nat_nat) (A tptp.nat) (Xs tptp.list_nat)) (= (tptp.aa_list_nat_nat (tptp.groups7488368174851004413at_nat F A) Xs) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_lis1299702591413342011at_nat (tptp.aa_nat9125522253416007816at_nat (tptp.aTP_Lamm_ajd F) A) Xs)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (tptp.aa_list_nat_nat tptp.size_size_list_nat Xs))))) (forall ((K tptp.int)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int _let_1))) (let ((_let_3 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger _let_1)) (tptp.aa_int_Code_integer tptp.code_integer_of_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int K) _let_2))))) (let ((_let_4 (tptp.aa_int_Code_integer tptp.code_integer_of_int K))) (let ((_let_5 (= K tptp.zero_zero_int))) (let ((_let_6 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)))) (and (=> _let_6 (= _let_4 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_int_Code_integer tptp.code_integer_of_int (tptp.aa_int_int tptp.uminus_uminus_int K))))) (=> (not _let_6) (and (=> _let_5 (= _let_4 tptp.zero_z3403309356797280102nteger)) (=> (not _let_5) (= _let_4 (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int K) _let_2)) tptp.zero_zero_int) _let_3) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger _let_3) tptp.one_one_Code_integer)))))))))))))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.code_integer_of_num N2))) (= (tptp.code_integer_of_num (tptp.aa_num_num tptp.bit1 N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger _let_1) _let_1)) tptp.one_one_Code_integer)))) (forall ((N2 tptp.nat) (M tptp.num)) (= (tptp.aa_num_option_num (tptp.bit_take_bit_num N2) M) (tptp.produc478579273971653890on_num tptp.aTP_Lamm_ajh (tptp.product_Pair_nat_num N2 M)))) (forall ((A3 tptp.set_bool) (F tptp.fun_bool_nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.finite_finite_bool A3) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.groups5768501273728744877ol_nat F A3))) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.finite_card_bool (tptp.collect_bool (tptp.aa_fun7969004623323359937l_bool (tptp.aTP_Lamm_aji A3) F))))))))) (forall ((A3 tptp.set_int) (F tptp.fun_int_nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.groups4541462559716669496nt_nat F A3))) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.finite_card_int (tptp.collect_int (tptp.aa_fun5627573752281863885t_bool (tptp.aTP_Lamm_ajj A3) F))))))))) (forall ((A3 tptp.set_Code_integer) (F tptp.fun_Code_integer_nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.groups7237345082560585321er_nat F A3))) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.finite4902975817058060853nteger (tptp.collect_Code_integer (tptp.aa_fun3540204951715082475r_bool (tptp.aTP_Lamm_ajk A3) F))))))))) (forall ((A3 tptp.set_bool) (F tptp.fun_bool_int)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (=> (tptp.finite_finite_bool A3) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int _let_1)) (tptp.groups5766010803219694601ol_int F A3))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) (tptp.finite_card_bool (tptp.collect_bool (tptp.aa_fun1758939502137048349l_bool (tptp.aTP_Lamm_ajl A3) F))))))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_int)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int _let_1)) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int F) A3))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.collect_nat (tptp.aa_fun8175233552433550377t_bool (tptp.aTP_Lamm_ajm A3) F))))))))) (forall ((A3 tptp.set_Code_integer) (F tptp.fun_Code_integer_int)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int _let_1)) (tptp.groups7234854612051535045er_int F A3))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) (tptp.finite4902975817058060853nteger (tptp.collect_Code_integer (tptp.aa_fun6578047036179216271r_bool (tptp.aTP_Lamm_ajn A3) F))))))))) (forall ((A3 tptp.set_bool) (F tptp.fun_bo7282069421189217543nteger)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (=> (tptp.finite_finite_bool A3) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger _let_1)) (tptp.groups1682264926906508858nteger F A3))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) (tptp.finite_card_bool (tptp.collect_bool (tptp.aa_fun7063430368917475406l_bool (tptp.aTP_Lamm_ajo A3) F))))))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_Code_integer)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger _let_1)) (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger F) A3))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.collect_nat (tptp.aa_fun1752071697927428280t_bool (tptp.aTP_Lamm_ajp A3) F))))))))) (forall ((A3 tptp.set_int) (F tptp.fun_int_Code_integer)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger _let_1)) (tptp.groups7873554091576472773nteger F A3))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) (tptp.finite_card_int (tptp.collect_int (tptp.aa_fun3610984093196804608t_bool (tptp.aTP_Lamm_ajq A3) F))))))))) (forall ((A3 tptp.set_Code_integer) (F tptp.fun_Co8499238673658658103nteger)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger _let_1)) (tptp.groups879477027807139574nteger F A3))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) (tptp.finite4902975817058060853nteger (tptp.collect_Code_integer (tptp.aa_fun6999757421500609566r_bool (tptp.aTP_Lamm_ajr A3) F))))))))) (forall ((N2 tptp.nat)) (= (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_dg N2))) N2)) (forall ((L tptp.code_integer) (U tptp.code_integer)) (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.set_or8404916559141939852nteger L U)))) (forall ((L tptp.code_integer) (U tptp.code_integer)) (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.set_or189985376899183464nteger L U)))) (forall ((N2 tptp.nat)) (= (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_df N2))) (tptp.aa_nat_nat tptp.suc N2))) (= (tptp.finite_card_set_nat tptp.bot_bot_set_set_nat) tptp.zero_zero_nat) (= (tptp.finite_card_list_nat tptp.bot_bot_set_list_nat) tptp.zero_zero_nat) (= (tptp.finite711546835091564841at_nat tptp.bot_bo2099793752762293965at_nat) tptp.zero_zero_nat) (= (tptp.finite_card_bool tptp.bot_bot_set_bool) tptp.zero_zero_nat) (= (tptp.aa_set_nat_nat tptp.finite_card_nat tptp.bot_bot_set_nat) tptp.zero_zero_nat) (= (tptp.finite_card_int tptp.bot_bot_set_int) tptp.zero_zero_nat) (forall ((Y tptp.nat) (A3 tptp.set_set_nat)) (= (tptp.groups4248547760180025341at_nat (tptp.aTP_Lamm_ajs Y) A3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Y) (tptp.finite_card_set_nat A3)))) (forall ((Y tptp.nat) (A3 tptp.set_list_nat)) (= (tptp.groups2907647131375434839at_nat (tptp.aTP_Lamm_ajt Y) A3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Y) (tptp.finite_card_list_nat A3)))) (forall ((Y tptp.int) (A3 tptp.set_set_nat)) (= (tptp.groups4246057289670975065at_int (tptp.aTP_Lamm_aju Y) A3) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Y) (tptp.finite_card_set_nat A3)))) (forall ((Y tptp.int) (A3 tptp.set_list_nat)) (= (tptp.groups2905156660866384563at_int (tptp.aTP_Lamm_ajv Y) A3) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Y) (tptp.finite_card_list_nat A3)))) (forall ((Y tptp.nat) (A3 tptp.set_nat)) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_ajw Y)) A3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Y) (tptp.aa_set_nat_nat tptp.finite_card_nat A3)))) (forall ((Y tptp.int) (A3 tptp.set_nat)) (= (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_int_fun_nat_int tptp.aTP_Lamm_ajx Y)) A3) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Y) (tptp.aa_set_nat_nat tptp.finite_card_nat A3)))) (forall ((Y tptp.int) (A3 tptp.set_int)) (= (tptp.groups1705073143266064639nt_int (tptp.aa_int_fun_int_int tptp.aTP_Lamm_ajy Y) A3) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Y) (tptp.finite_card_int A3)))) (forall ((A tptp.option_num) (F tptp.fun_nat_option_num) (V tptp.num)) (= (tptp.aa_nat_option_num (tptp.case_nat_option_num A F) (tptp.aa_num_nat tptp.numeral_numeral_nat V)) (tptp.aa_nat_option_num F (tptp.aa_num_nat tptp.pred_numeral V)))) (forall ((A tptp.bool) (F tptp.fun_nat_bool) (V tptp.num)) (= (tptp.pp (tptp.aa_nat_bool (tptp.case_nat_bool A F) (tptp.aa_num_nat tptp.numeral_numeral_nat V))) (tptp.pp (tptp.aa_nat_bool F (tptp.aa_num_nat tptp.pred_numeral V))))) (forall ((A tptp.nat) (F tptp.fun_nat_nat) (V tptp.num)) (= (tptp.aa_nat_nat (tptp.case_nat_nat A F) (tptp.aa_num_nat tptp.numeral_numeral_nat V)) (tptp.aa_nat_nat F (tptp.aa_num_nat tptp.pred_numeral V)))) (forall ((A3 tptp.set_set_nat)) (=> (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat A3)) (= (= (tptp.finite_card_set_nat A3) tptp.zero_zero_nat) (= A3 tptp.bot_bot_set_set_nat)))) (forall ((A3 tptp.set_list_nat)) (=> (tptp.finite8100373058378681591st_nat A3) (= (= (tptp.finite_card_list_nat A3) tptp.zero_zero_nat) (= A3 tptp.bot_bot_set_list_nat)))) (forall ((A3 tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (= (tptp.finite4902975817058060853nteger A3) tptp.zero_zero_nat) (= A3 tptp.bot_bo3990330152332043303nteger)))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat A3)) (= (= (tptp.finite711546835091564841at_nat A3) tptp.zero_zero_nat) (= A3 tptp.bot_bo2099793752762293965at_nat)))) (forall ((A3 tptp.set_bool)) (=> (tptp.finite_finite_bool A3) (= (= (tptp.finite_card_bool A3) tptp.zero_zero_nat) (= A3 tptp.bot_bot_set_bool)))) (forall ((A3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (= (tptp.aa_set_nat_nat tptp.finite_card_nat A3) tptp.zero_zero_nat) (= A3 tptp.bot_bot_set_nat)))) (forall ((A3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (= (tptp.finite_card_int A3) tptp.zero_zero_nat) (= A3 tptp.bot_bot_set_int)))) (forall ((Y tptp.rat) (A3 tptp.set_nat)) (= (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_ajz Y)) A3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_set_nat_nat tptp.finite_card_nat A3))) Y))) (forall ((Y tptp.int) (A3 tptp.set_nat)) (= (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int tptp.aTP_Lamm_ajx Y)) A3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_set_nat_nat tptp.finite_card_nat A3))) Y))) (forall ((Y tptp.code_integer) (A3 tptp.set_nat)) (= (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger (tptp.aTP_Lamm_aka Y)) A3) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_set_nat_nat tptp.finite_card_nat A3))) Y))) (forall ((Y tptp.nat) (A3 tptp.set_nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_ajw Y)) A3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_set_nat_nat tptp.finite_card_nat A3))) Y))) (forall ((Y tptp.int) (A3 tptp.set_int)) (= (tptp.groups4538972089207619220nt_int (tptp.aa_int_fun_int_int tptp.aTP_Lamm_ajy Y) A3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.finite_card_int A3))) Y))) (forall ((Y tptp.rat) (A3 tptp.set_set_nat)) (= (tptp.groups7659867448343625626at_rat (tptp.aTP_Lamm_akb Y) A3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.finite_card_set_nat A3))) Y))) (forall ((Y tptp.rat) (A3 tptp.set_list_nat)) (= (tptp.groups3760926236672600436at_rat (tptp.aTP_Lamm_akc Y) A3) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.finite_card_list_nat A3))) Y))) (forall ((Y tptp.int) (A3 tptp.set_set_nat)) (= (tptp.groups8292507037921071086at_int (tptp.aTP_Lamm_aju Y) A3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.finite_card_set_nat A3))) Y))) (forall ((Y tptp.int) (A3 tptp.set_list_nat)) (= (tptp.groups4393565826250045896at_int (tptp.aTP_Lamm_ajv Y) A3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.finite_card_list_nat A3))) Y))) (forall ((Y tptp.nat) (A3 tptp.set_set_nat)) (= (tptp.groups8294997508430121362at_nat (tptp.aTP_Lamm_ajs Y) A3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.finite_card_set_nat A3))) Y))) (forall ((A tptp.option_num) (F tptp.fun_nat_option_num) (V tptp.num) (N2 tptp.nat)) (= (tptp.aa_nat_option_num (tptp.case_nat_option_num A F) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat V)) N2)) (tptp.aa_nat_option_num F (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.pred_numeral V)) N2)))) (forall ((A tptp.bool) (F tptp.fun_nat_bool) (V tptp.num) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.case_nat_bool A F) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat V)) N2))) (tptp.pp (tptp.aa_nat_bool F (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.pred_numeral V)) N2))))) (forall ((A tptp.nat) (F tptp.fun_nat_nat) (V tptp.num) (N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.case_nat_nat A F) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat V)) N2)) (tptp.aa_nat_nat F (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.pred_numeral V)) N2)))) (forall ((A3 tptp.set_int) (P tptp.fun_int_bool)) (let ((_let_1 (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)))) (=> _let_1 (=> _let_1 (= (tptp.groups7873554091576472773nteger (tptp.aTP_Lamm_akd P) A3) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.finite_card_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) (tptp.collect_int P))))))))) (forall ((A3 tptp.set_Code_integer) (P tptp.fun_Co8822979462182099027r_bool)) (let ((_let_1 (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)))) (=> _let_1 (=> _let_1 (= (tptp.groups879477027807139574nteger (tptp.aTP_Lamm_ake P) A3) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.finite4902975817058060853nteger (tptp.inf_in1364745209274528805nteger A3 (tptp.collect_Code_integer P))))))))) (forall ((A3 tptp.set_nat) (P tptp.fun_nat_bool)) (let ((_let_1 (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)))) (=> _let_1 (=> _let_1 (= (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger (tptp.aTP_Lamm_akf P)) A3) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) (tptp.collect_nat P))))))))) (forall ((A3 tptp.set_int) (P tptp.fun_int_bool)) (let ((_let_1 (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)))) (=> _let_1 (=> _let_1 (= (tptp.groups4541462559716669496nt_nat (tptp.aTP_Lamm_akg P) A3) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.finite_card_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) (tptp.collect_int P))))))))) (forall ((A3 tptp.set_Code_integer) (P tptp.fun_Co8822979462182099027r_bool)) (let ((_let_1 (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)))) (=> _let_1 (=> _let_1 (= (tptp.groups7237345082560585321er_nat (tptp.aTP_Lamm_akh P) A3) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.finite4902975817058060853nteger (tptp.inf_in1364745209274528805nteger A3 (tptp.collect_Code_integer P))))))))) (forall ((A3 tptp.set_Code_integer) (P tptp.fun_Co8822979462182099027r_bool)) (let ((_let_1 (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)))) (=> _let_1 (=> _let_1 (= (tptp.groups7234854612051535045er_int (tptp.aTP_Lamm_aki P) A3) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.finite4902975817058060853nteger (tptp.inf_in1364745209274528805nteger A3 (tptp.collect_Code_integer P))))))))) (forall ((A3 tptp.set_nat) (P tptp.fun_nat_bool)) (let ((_let_1 (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)))) (=> _let_1 (=> _let_1 (= (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_akj P)) A3) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) (tptp.collect_nat P))))))))) (forall ((A3 tptp.set_nat) (P tptp.fun_nat_bool)) (let ((_let_1 (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)))) (=> _let_1 (=> _let_1 (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_akk P)) A3) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat A3) (tptp.collect_nat P))))))))) (forall ((A3 tptp.set_int) (P tptp.fun_int_bool)) (let ((_let_1 (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)))) (=> _let_1 (=> _let_1 (= (tptp.groups4538972089207619220nt_int (tptp.aTP_Lamm_akl P) A3) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.finite_card_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.inf_inf_set_int A3) (tptp.collect_int P))))))))) (forall ((A3 tptp.set_set_nat) (P tptp.fun_set_nat_bool)) (let ((_let_1 (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat A3)))) (=> _let_1 (=> _let_1 (= (tptp.groups9190459664516455967nteger (tptp.aTP_Lamm_akm P) A3) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.finite_card_set_nat (tptp.inf_inf_set_set_nat A3 (tptp.collect_set_nat P))))))))) (forall ((K tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer K))) (let ((_let_2 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger K) tptp.zero_z3403309356797280102nteger)))) (and (=> _let_2 (= _let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger K))) (=> (not _let_2) (= _let_1 K)))))) _let_38 (forall ((Xa2 tptp.int) (X tptp.int)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_int_Code_integer tptp.code_integer_of_int Xa2)) (tptp.aa_int_Code_integer tptp.code_integer_of_int X))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Xa2) X)))) (forall ((U tptp.code_integer)) (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.set_or8404916559141939852nteger tptp.zero_z3403309356797280102nteger U)))) (forall ((H tptp.fun_op8989173174992673105on_num) (F1 tptp.option_num) (F22 tptp.fun_nat_option_num) (Nat tptp.nat)) (= (tptp.aa_opt5369159329878751634on_num H (tptp.aa_nat_option_num (tptp.case_nat_option_num F1 F22) Nat)) (tptp.aa_nat_option_num (tptp.case_nat_option_num (tptp.aa_opt5369159329878751634on_num H F1) (tptp.aa_fun7716400287237121964on_num (tptp.aTP_Lamm_akn H) F22)) Nat))) (forall ((H tptp.fun_option_num_bool) (F1 tptp.option_num) (F22 tptp.fun_nat_option_num) (Nat tptp.nat)) (= (tptp.pp (tptp.aa_option_num_bool H (tptp.aa_nat_option_num (tptp.case_nat_option_num F1 F22) Nat))) (tptp.pp (tptp.aa_nat_bool (tptp.case_nat_bool (tptp.aa_option_num_bool H F1) (tptp.aa_fun5457149469851336939t_bool (tptp.aTP_Lamm_ako H) F22)) Nat)))) (forall ((H tptp.fun_option_num_nat) (F1 tptp.option_num) (F22 tptp.fun_nat_option_num) (Nat tptp.nat)) (= (tptp.aa_option_num_nat H (tptp.aa_nat_option_num (tptp.case_nat_option_num F1 F22) Nat)) (tptp.aa_nat_nat (tptp.case_nat_nat (tptp.aa_option_num_nat H F1) (tptp.aa_fun7387201323300553874at_nat (tptp.aTP_Lamm_akp H) F22)) Nat))) (forall ((H tptp.fun_bool_option_num) (F1 tptp.bool) (F22 tptp.fun_nat_bool) (Nat tptp.nat)) (= (tptp.aa_bool_option_num H (tptp.aa_nat_bool (tptp.case_nat_bool F1 F22) Nat)) (tptp.aa_nat_option_num (tptp.case_nat_option_num (tptp.aa_bool_option_num H F1) (tptp.aa_fun4234090970126001947on_num (tptp.aTP_Lamm_akq H) F22)) Nat))) (forall ((H tptp.fun_bool_bool) (F1 tptp.bool) (F22 tptp.fun_nat_bool) (Nat tptp.nat)) (= (tptp.pp (tptp.aa_bool_bool H (tptp.aa_nat_bool (tptp.case_nat_bool F1 F22) Nat))) (tptp.pp (tptp.aa_nat_bool (tptp.case_nat_bool (tptp.aa_bool_bool H F1) (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_akr H) F22)) Nat)))) (forall ((H tptp.fun_bool_nat) (F1 tptp.bool) (F22 tptp.fun_nat_bool) (Nat tptp.nat)) (= (tptp.aa_bool_nat H (tptp.aa_nat_bool (tptp.case_nat_bool F1 F22) Nat)) (tptp.aa_nat_nat (tptp.case_nat_nat (tptp.aa_bool_nat H F1) (tptp.aa_fun9164390667347105409at_nat (tptp.aTP_Lamm_aks H) F22)) Nat))) (forall ((H tptp.fun_nat_option_num) (F1 tptp.nat) (F22 tptp.fun_nat_nat) (Nat tptp.nat)) (= (tptp.aa_nat_option_num H (tptp.aa_nat_nat (tptp.case_nat_nat F1 F22) Nat)) (tptp.aa_nat_option_num (tptp.case_nat_option_num (tptp.aa_nat_option_num H F1) (tptp.aa_fun6517009837249254290on_num (tptp.aTP_Lamm_akt H) F22)) Nat))) (forall ((H tptp.fun_nat_bool) (F1 tptp.nat) (F22 tptp.fun_nat_nat) (Nat tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool H (tptp.aa_nat_nat (tptp.case_nat_nat F1 F22) Nat))) (tptp.pp (tptp.aa_nat_bool (tptp.case_nat_bool (tptp.aa_nat_bool H F1) (tptp.aa_fun1783405840085286277t_bool (tptp.aTP_Lamm_aku H) F22)) Nat)))) (forall ((H tptp.fun_nat_nat) (F1 tptp.nat) (F22 tptp.fun_nat_nat) (Nat tptp.nat)) (= (tptp.aa_nat_nat H (tptp.aa_nat_nat (tptp.case_nat_nat F1 F22) Nat)) (tptp.aa_nat_nat (tptp.case_nat_nat (tptp.aa_nat_nat H F1) (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_il H) F22)) Nat))) (forall ((H tptp.fun_op8989173174992673105on_num) (F1 tptp.option_num) (F22 tptp.fun_num_option_num) (F32 tptp.fun_num_option_num) (Num tptp.num)) (let ((_let_1 (tptp.aTP_Lamm_dz H))) (= (tptp.aa_opt5369159329878751634on_num H (tptp.aa_num_option_num (tptp.case_num_option_num F1 F22 F32) Num)) (tptp.aa_num_option_num (tptp.case_num_option_num (tptp.aa_opt5369159329878751634on_num H F1) (tptp.aa_fun3636977833914307392on_num _let_1 F22) (tptp.aa_fun3636977833914307392on_num _let_1 F32)) Num)))) (forall ((A3 tptp.set_set_nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat A3)) (= (tptp.finite1149291290879098388et_nat (tptp.collect_set_set_nat (tptp.aa_nat7515184090834925478t_bool (tptp.aTP_Lamm_akv A3) K))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.finite_card_set_nat A3)) K)))) (forall ((A3 tptp.set_list_nat) (K tptp.nat)) (=> (tptp.finite8100373058378681591st_nat A3) (= (tptp.finite2364142230527598318st_nat (tptp.collect_set_list_nat (tptp.aa_nat87836351786748620t_bool (tptp.aTP_Lamm_akw A3) K))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.finite_card_list_nat A3)) K)))) (forall ((A3 tptp.set_nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (= (tptp.finite_card_set_nat (tptp.collect_set_nat (tptp.aa_nat8857836526276733660t_bool (tptp.aTP_Lamm_akx A3) K))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_set_nat_nat tptp.finite_card_nat A3)) K)))) (forall ((A3 tptp.set_Code_integer) (K tptp.nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (= (tptp.finite1340570857867686763nteger (tptp.collec574505750873337192nteger (tptp.aa_nat1024103762897335311r_bool (tptp.aTP_Lamm_aky A3) K))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.finite4902975817058060853nteger A3)) K)))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat A3)) (= (tptp.finite4356350796350151305at_nat (tptp.collec5514110066124741708at_nat (tptp.aa_nat1303072629729950279t_bool (tptp.aTP_Lamm_akz A3) K))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.finite711546835091564841at_nat A3)) K)))) (forall ((A3 tptp.set_int) (K tptp.nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (= (tptp.finite_card_set_int (tptp.collect_set_int (tptp.aa_nat8397553574630087040t_bool (tptp.aTP_Lamm_ala A3) K))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.finite_card_int A3)) K)))) (forall ((F1 tptp.option_num) (F22 tptp.fun_nat_option_num)) (= (tptp.aa_nat_option_num (tptp.case_nat_option_num F1 F22) tptp.zero_zero_nat) F1)) (forall ((F1 tptp.bool) (F22 tptp.fun_nat_bool)) (= (tptp.pp (tptp.aa_nat_bool (tptp.case_nat_bool F1 F22) tptp.zero_zero_nat)) (tptp.pp F1))) (forall ((F1 tptp.nat) (F22 tptp.fun_nat_nat)) (= (tptp.aa_nat_nat (tptp.case_nat_nat F1 F22) tptp.zero_zero_nat) F1)) (forall ((F1 tptp.option_num) (F22 tptp.fun_nat_option_num) (X2 tptp.nat)) (= (tptp.aa_nat_option_num (tptp.case_nat_option_num F1 F22) (tptp.aa_nat_nat tptp.suc X2)) (tptp.aa_nat_option_num F22 X2))) (forall ((F1 tptp.bool) (F22 tptp.fun_nat_bool) (X2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.case_nat_bool F1 F22) (tptp.aa_nat_nat tptp.suc X2))) (tptp.pp (tptp.aa_nat_bool F22 X2)))) (forall ((F1 tptp.nat) (F22 tptp.fun_nat_nat) (X2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.case_nat_nat F1 F22) (tptp.aa_nat_nat tptp.suc X2)) (tptp.aa_nat_nat F22 X2))) (forall ((A3 tptp.set_set_nat) (N2 tptp.nat)) (=> (not (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat A3))) (exists ((B9 tptp.set_set_nat)) (and (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat B9)) (= (tptp.finite_card_set_nat B9) N2) (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat B9) A3)))))) (forall ((A3 tptp.set_list_nat) (N2 tptp.nat)) (=> (not (tptp.finite8100373058378681591st_nat A3)) (exists ((B9 tptp.set_list_nat)) (and (tptp.finite8100373058378681591st_nat B9) (= (tptp.finite_card_list_nat B9) N2) (tptp.ord_le6045566169113846134st_nat B9 A3))))) (forall ((A3 tptp.set_nat) (N2 tptp.nat)) (=> (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3))) (exists ((B9 tptp.set_nat)) (and (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B9)) (= (tptp.aa_set_nat_nat tptp.finite_card_nat B9) N2) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat B9) A3)))))) (forall ((A3 tptp.set_Code_integer) (N2 tptp.nat)) (=> (not (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3))) (exists ((B9 tptp.set_Code_integer)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B9)) (= (tptp.finite4902975817058060853nteger B9) N2) (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger B9) A3)))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (N2 tptp.nat)) (=> (not (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat A3))) (exists ((B9 tptp.set_Pr1261947904930325089at_nat)) (and (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat B9)) (= (tptp.finite711546835091564841at_nat B9) N2) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat B9) A3)))))) (forall ((A3 tptp.set_int) (N2 tptp.nat)) (=> (not (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3))) (exists ((B9 tptp.set_int)) (and (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B9)) (= (tptp.finite_card_int B9) N2) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int B9) A3)))))) (forall ((B3 tptp.set_set_nat) (A3 tptp.set_set_nat)) (=> (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat B3)) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat A3) B3)) (=> (= (tptp.finite_card_set_nat A3) (tptp.finite_card_set_nat B3)) (= A3 B3))))) (forall ((B3 tptp.set_list_nat) (A3 tptp.set_list_nat)) (=> (tptp.finite8100373058378681591st_nat B3) (=> (tptp.ord_le6045566169113846134st_nat A3 B3) (=> (= (tptp.finite_card_list_nat A3) (tptp.finite_card_list_nat B3)) (= A3 B3))))) (forall ((B3 tptp.set_nat) (A3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) B3)) (=> (= (tptp.aa_set_nat_nat tptp.finite_card_nat A3) (tptp.aa_set_nat_nat tptp.finite_card_nat B3)) (= A3 B3))))) (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) B3)) (=> (= (tptp.finite4902975817058060853nteger A3) (tptp.finite4902975817058060853nteger B3)) (= A3 B3))))) (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat B3)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A3) B3)) (=> (= (tptp.finite711546835091564841at_nat A3) (tptp.finite711546835091564841at_nat B3)) (= A3 B3))))) (forall ((B3 tptp.set_int) (A3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (=> (= (tptp.finite_card_int A3) (tptp.finite_card_int B3)) (= A3 B3))))) (forall ((B3 tptp.set_bool) (A3 tptp.set_bool) (R3 tptp.fun_bo1841576699660343469l_bool)) (=> (tptp.finite_finite_bool B3) (=> (forall ((A4 tptp.bool)) (=> (tptp.pp (tptp.member_bool A4 A3)) (exists ((B10 tptp.bool)) (and (tptp.pp (tptp.member_bool B10 B3)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool R3 A4) B10)))))) (=> (forall ((A12 tptp.bool) (A23 tptp.bool) (B4 tptp.bool)) (=> (tptp.pp (tptp.member_bool A12 A3)) (=> (tptp.pp (tptp.member_bool A23 A3)) (=> (tptp.pp (tptp.member_bool B4 B3)) (=> (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool R3 A12) B4)) (=> (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool R3 A23) B4)) (= (tptp.pp A12) (tptp.pp A23)))))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_bool A3)) (tptp.finite_card_bool B3))))))) (forall ((B3 tptp.set_bool) (A3 tptp.set_int) (R3 tptp.fun_in3865155034416861484l_bool)) (=> (tptp.finite_finite_bool B3) (=> (forall ((A4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A4) A3)) (exists ((B10 tptp.bool)) (and (tptp.pp (tptp.member_bool B10 B3)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_int_fun_bool_bool R3 A4) B10)))))) (=> (forall ((A12 tptp.int) (A23 tptp.int) (B4 tptp.bool)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A12) A3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A23) A3)) (=> (tptp.pp (tptp.member_bool B4 B3)) (=> (tptp.pp (tptp.aa_bool_bool (tptp.aa_int_fun_bool_bool R3 A12) B4)) (=> (tptp.pp (tptp.aa_bool_bool (tptp.aa_int_fun_bool_bool R3 A23) B4)) (= A12 A23))))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_int A3)) (tptp.finite_card_bool B3))))))) (forall ((B3 tptp.set_bool) (A3 tptp.set_nat) (R3 tptp.fun_na9137082442855928016l_bool)) (=> (tptp.finite_finite_bool B3) (=> (forall ((A4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A4) A3)) (exists ((B10 tptp.bool)) (and (tptp.pp (tptp.member_bool B10 B3)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_nat_fun_bool_bool R3 A4) B10)))))) (=> (forall ((A12 tptp.nat) (A23 tptp.nat) (B4 tptp.bool)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A12) A3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A23) A3)) (=> (tptp.pp (tptp.member_bool B4 B3)) (=> (tptp.pp (tptp.aa_bool_bool (tptp.aa_nat_fun_bool_bool R3 A12) B4)) (=> (tptp.pp (tptp.aa_bool_bool (tptp.aa_nat_fun_bool_bool R3 A23) B4)) (= A12 A23))))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat tptp.finite_card_nat A3)) (tptp.finite_card_bool B3))))))) (forall ((B3 tptp.set_nat) (A3 tptp.set_bool) (R3 tptp.fun_bo3288154511880838028t_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (forall ((A4 tptp.bool)) (=> (tptp.pp (tptp.member_bool A4 A3)) (exists ((B10 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B10) B3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_bool_fun_nat_bool R3 A4) B10)))))) (=> (forall ((A12 tptp.bool) (A23 tptp.bool) (B4 tptp.nat)) (=> (tptp.pp (tptp.member_bool A12 A3)) (=> (tptp.pp (tptp.member_bool A23 A3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B4) B3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_bool_fun_nat_bool R3 A12) B4)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_bool_fun_nat_bool R3 A23) B4)) (= (tptp.pp A12) (tptp.pp A23)))))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_bool A3)) (tptp.aa_set_nat_nat tptp.finite_card_nat B3))))))) (forall ((B3 tptp.set_nat) (A3 tptp.set_int) (R3 tptp.fun_int_fun_nat_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (forall ((A4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A4) A3)) (exists ((B10 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B10) B3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool R3 A4) B10)))))) (=> (forall ((A12 tptp.int) (A23 tptp.int) (B4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A12) A3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A23) A3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B4) B3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool R3 A12) B4)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool R3 A23) B4)) (= A12 A23))))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_int A3)) (tptp.aa_set_nat_nat tptp.finite_card_nat B3))))))) (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (R3 tptp.fun_nat_fun_nat_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (forall ((A4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A4) A3)) (exists ((B10 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B10) B3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R3 A4) B10)))))) (=> (forall ((A12 tptp.nat) (A23 tptp.nat) (B4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A12) A3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A23) A3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B4) B3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R3 A12) B4)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R3 A23) B4)) (= A12 A23))))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat tptp.finite_card_nat A3)) (tptp.aa_set_nat_nat tptp.finite_card_nat B3))))))) (forall ((B3 tptp.set_int) (A3 tptp.set_bool) (R3 tptp.fun_bo2827871560234191408t_bool)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (forall ((A4 tptp.bool)) (=> (tptp.pp (tptp.member_bool A4 A3)) (exists ((B10 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int B10) B3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_bool_fun_int_bool R3 A4) B10)))))) (=> (forall ((A12 tptp.bool) (A23 tptp.bool) (B4 tptp.int)) (=> (tptp.pp (tptp.member_bool A12 A3)) (=> (tptp.pp (tptp.member_bool A23 A3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int B4) B3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_bool_fun_int_bool R3 A12) B4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_bool_fun_int_bool R3 A23) B4)) (= (tptp.pp A12) (tptp.pp A23)))))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_bool A3)) (tptp.finite_card_int B3))))))) (forall ((B3 tptp.set_int) (A3 tptp.set_int) (R3 tptp.fun_int_fun_int_bool)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (forall ((A4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A4) A3)) (exists ((B10 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int B10) B3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool R3 A4) B10)))))) (=> (forall ((A12 tptp.int) (A23 tptp.int) (B4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A12) A3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int A23) A3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int B4) B3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool R3 A12) B4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool R3 A23) B4)) (= A12 A23))))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_int A3)) (tptp.finite_card_int B3))))))) (forall ((B3 tptp.set_int) (A3 tptp.set_nat) (R3 tptp.fun_nat_fun_int_bool)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (forall ((A4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A4) A3)) (exists ((B10 tptp.int)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int B10) B3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_nat_fun_int_bool R3 A4) B10)))))) (=> (forall ((A12 tptp.nat) (A23 tptp.nat) (B4 tptp.int)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A12) A3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A23) A3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int B4) B3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_nat_fun_int_bool R3 A12) B4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_nat_fun_int_bool R3 A23) B4)) (= A12 A23))))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat tptp.finite_card_nat A3)) (tptp.finite_card_int B3))))))) (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_bool) (R3 tptp.fun_bo284609390884453567r_bool)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (forall ((A4 tptp.bool)) (=> (tptp.pp (tptp.member_bool A4 A3)) (exists ((B10 tptp.code_integer)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer B10) B3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_boo5858427943822696632r_bool R3 A4) B10)))))) (=> (forall ((A12 tptp.bool) (A23 tptp.bool) (B4 tptp.code_integer)) (=> (tptp.pp (tptp.member_bool A12 A3)) (=> (tptp.pp (tptp.member_bool A23 A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer B4) B3)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_boo5858427943822696632r_bool R3 A12) B4)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_boo5858427943822696632r_bool R3 A23) B4)) (= (tptp.pp A12) (tptp.pp A23)))))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_bool A3)) (tptp.finite4902975817058060853nteger B3))))))) (forall ((Xa2 tptp.int) (X tptp.int)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_int_Code_integer tptp.code_integer_of_int Xa2)) (tptp.aa_int_Code_integer tptp.code_integer_of_int X))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Xa2) X)))) (forall ((S2 tptp.set_bool) (T5 tptp.set_bool) (R tptp.fun_bo1841576699660343469l_bool) (K tptp.fun_bool_nat)) (=> (tptp.finite_finite_bool S2) (=> (tptp.finite_finite_bool T5) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 T5)) (= (tptp.finite_card_bool (tptp.collect_bool (tptp.aa_boo8970175072276269406l_bool (tptp.aa_fun1447330757145981436l_bool (tptp.aTP_Lamm_alb S2) R) X3))) (tptp.aa_bool_nat K X3)))) (= (tptp.groups5768501273728744877ol_nat (tptp.aa_fun3941158123937086921ol_nat (tptp.aTP_Lamm_ald T5) R) S2) (tptp.groups5768501273728744877ol_nat K T5)))))) (forall ((S2 tptp.set_bool) (T5 tptp.set_int) (R tptp.fun_bo2827871560234191408t_bool) (K tptp.fun_int_nat)) (=> (tptp.finite_finite_bool S2) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T5)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) T5)) (= (tptp.finite_card_bool (tptp.collect_bool (tptp.aa_int_fun_bool_bool (tptp.aa_fun6035399485891414554l_bool (tptp.aTP_Lamm_rv S2) R) X3))) (tptp.aa_int_nat K X3)))) (= (tptp.groups5768501273728744877ol_nat (tptp.aa_fun7155190969624455820ol_nat (tptp.aTP_Lamm_ale T5) R) S2) (tptp.groups4541462559716669496nt_nat K T5)))))) (forall ((S2 tptp.set_bool) (T5 tptp.set_Code_integer) (R tptp.fun_bo284609390884453567r_bool) (K tptp.fun_Code_integer_nat)) (=> (tptp.finite_finite_bool S2) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T5)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) T5)) (= (tptp.finite_card_bool (tptp.collect_bool (tptp.aa_Cod8494480694608518558l_bool (tptp.aa_fun9176172261886745818l_bool (tptp.aTP_Lamm_ada S2) R) X3))) (tptp.aa_Code_integer_nat K X3)))) (= (tptp.groups5768501273728744877ol_nat (tptp.aa_fun4256929549349463485ol_nat (tptp.aTP_Lamm_alg T5) R) S2) (tptp.groups7237345082560585321er_nat K T5)))))) (forall ((S2 tptp.set_int) (T5 tptp.set_bool) (R tptp.fun_in3865155034416861484l_bool) (K tptp.fun_bool_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S2)) (=> (tptp.finite_finite_bool T5) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 T5)) (= (tptp.finite_card_int (tptp.collect_int (tptp.aa_bool_fun_int_bool (tptp.aa_fun2580392495071267866t_bool (tptp.aTP_Lamm_alh S2) R) X3))) (tptp.aa_bool_nat K X3)))) (= (tptp.groups4541462559716669496nt_nat (tptp.aa_fun6244226199881115619nt_nat (tptp.aTP_Lamm_alj T5) R) S2) (tptp.groups5768501273728744877ol_nat K T5)))))) (forall ((S2 tptp.set_int) (T5 tptp.set_int) (R tptp.fun_int_fun_int_bool) (K tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S2)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T5)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) T5)) (= (tptp.finite_card_int (tptp.collect_int (tptp.aa_int_fun_int_bool (tptp.aa_fun8168818243683596540t_bool (tptp.aTP_Lamm_adb S2) R) X3))) (tptp.aa_int_nat K X3)))) (= (tptp.groups4541462559716669496nt_nat (tptp.aa_fun8170219554457397550nt_nat (tptp.aTP_Lamm_all T5) R) S2) (tptp.groups4541462559716669496nt_nat K T5)))))) (forall ((S2 tptp.set_int) (T5 tptp.set_Code_integer) (R tptp.fun_in5519481650651148416r_bool) (K tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S2)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T5)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) T5)) (= (tptp.finite_card_int (tptp.collect_int (tptp.aa_Cod8597349444926882409t_bool (tptp.aa_fun2469241947764354620t_bool (tptp.aTP_Lamm_adc S2) R) X3))) (tptp.aa_Code_integer_nat K X3)))) (= (tptp.groups4541462559716669496nt_nat (tptp.aa_fun6776377250481993149nt_nat (tptp.aTP_Lamm_aln T5) R) S2) (tptp.groups7237345082560585321er_nat K T5)))))) (forall ((S2 tptp.set_Code_integer) (T5 tptp.set_bool) (R tptp.fun_Co3748208068438171869l_bool) (K tptp.fun_bool_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S2)) (=> (tptp.finite_finite_bool T5) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 T5)) (= (tptp.finite4902975817058060853nteger (tptp.collect_Code_integer (tptp.aa_boo5858427943822696632r_bool (tptp.aa_fun6233448402170926554r_bool (tptp.aTP_Lamm_alo S2) R) X3))) (tptp.aa_bool_nat K X3)))) (= (tptp.groups7237345082560585321er_nat (tptp.aa_fun4083829879951944645er_nat (tptp.aTP_Lamm_alq T5) R) S2) (tptp.groups5768501273728744877ol_nat K T5)))))) (forall ((S2 tptp.set_Code_integer) (T5 tptp.set_int) (R tptp.fun_Co8197081679332685312t_bool) (K tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S2)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T5)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) T5)) (= (tptp.finite4902975817058060853nteger (tptp.collect_Code_integer (tptp.aa_int3865899974016033897r_bool (tptp.aa_fun4269100936724824892r_bool (tptp.aTP_Lamm_se S2) R) X3))) (tptp.aa_int_nat K X3)))) (= (tptp.groups7237345082560585321er_nat (tptp.aa_fun4709405206220679534er_nat (tptp.aTP_Lamm_alr T5) R) S2) (tptp.groups4541462559716669496nt_nat K T5)))))) (forall ((S2 tptp.set_Code_integer) (T5 tptp.set_Code_integer) (R tptp.fun_Co8310303586393106575r_bool) (K tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S2)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T5)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) T5)) (= (tptp.finite4902975817058060853nteger (tptp.collect_Code_integer (tptp.aa_Cod7250484176784686200r_bool (tptp.aa_fun2374795795022016636r_bool (tptp.aTP_Lamm_als S2) R) X3))) (tptp.aa_Code_integer_nat K X3)))) (= (tptp.groups7237345082560585321er_nat (tptp.aa_fun4547260061994548733er_nat (tptp.aTP_Lamm_alu T5) R) S2) (tptp.groups7237345082560585321er_nat K T5)))))) (forall ((S2 tptp.set_bool) (T5 tptp.set_nat) (R tptp.fun_bo3288154511880838028t_bool) (K tptp.fun_nat_nat)) (=> (tptp.finite_finite_bool S2) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T5)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) T5)) (= (tptp.finite_card_bool (tptp.collect_bool (tptp.aa_nat_fun_bool_bool (tptp.aa_fun4163026448321506586l_bool (tptp.aTP_Lamm_rg S2) R) X3))) (tptp.aa_nat_nat K X3)))) (= (tptp.groups5768501273728744877ol_nat (tptp.aa_fun7928520491197679664ol_nat (tptp.aTP_Lamm_alv T5) R) S2) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat K) T5)))))) (forall ((A3 tptp.set_set_nat)) (= (tptp.finite_card_set_nat A3) (tptp.groups8294997508430121362at_nat tptp.aTP_Lamm_alw A3))) (forall ((A3 tptp.set_list_nat)) (= (tptp.finite_card_list_nat A3) (tptp.groups4396056296759096172at_nat tptp.aTP_Lamm_alx A3))) (forall ((A3 tptp.set_nat)) (= (tptp.aa_set_nat_nat tptp.finite_card_nat A3) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat tptp.aTP_Lamm_mj) A3))) (forall ((A3 tptp.set_set_nat)) (= (= (tptp.finite_card_set_nat A3) tptp.zero_zero_nat) (or (= A3 tptp.bot_bot_set_set_nat) (not (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat A3)))))) (forall ((A3 tptp.set_list_nat)) (= (= (tptp.finite_card_list_nat A3) tptp.zero_zero_nat) (or (= A3 tptp.bot_bot_set_list_nat) (not (tptp.finite8100373058378681591st_nat A3))))) (forall ((A3 tptp.set_Code_integer)) (= (= (tptp.finite4902975817058060853nteger A3) tptp.zero_zero_nat) (or (= A3 tptp.bot_bo3990330152332043303nteger) (not (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (= (tptp.finite711546835091564841at_nat A3) tptp.zero_zero_nat) (or (= A3 tptp.bot_bo2099793752762293965at_nat) (not (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat A3)))))) (forall ((A3 tptp.set_bool)) (= (= (tptp.finite_card_bool A3) tptp.zero_zero_nat) (or (= A3 tptp.bot_bot_set_bool) (not (tptp.finite_finite_bool A3))))) (forall ((A3 tptp.set_nat)) (= (= (tptp.aa_set_nat_nat tptp.finite_card_nat A3) tptp.zero_zero_nat) (or (= A3 tptp.bot_bot_set_nat) (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)))))) (forall ((A3 tptp.set_int)) (= (= (tptp.finite_card_int A3) tptp.zero_zero_nat) (or (= A3 tptp.bot_bot_set_int) (not (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)))))) (forall ((A3 tptp.set_set_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.finite_card_set_nat A3))) (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat A3)))) (forall ((A3 tptp.set_list_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.finite_card_list_nat A3))) (tptp.finite8100373058378681591st_nat A3))) (forall ((A3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_set_nat_nat tptp.finite_card_nat A3))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)))) (forall ((A3 tptp.set_int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.finite_card_int A3))) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)))) (forall ((A3 tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.finite4902975817058060853nteger A3))) (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.finite711546835091564841at_nat A3))) (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat A3)))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_int (tptp.image_nat_int F A3))) (tptp.aa_set_nat_nat tptp.finite_card_nat A3))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.image_nat_nat F A3))) (tptp.aa_set_nat_nat tptp.finite_card_nat A3))))) (forall ((A3 tptp.set_int) (F tptp.fun_int_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_int (tptp.image_int_int F A3))) (tptp.finite_card_int A3))))) (forall ((A3 tptp.set_int) (F tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.image_int_nat F A3))) (tptp.finite_card_int A3))))) (forall ((A3 tptp.set_Code_integer) (F tptp.fun_Code_integer_nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.image_951025933927791156er_nat F A3))) (tptp.finite4902975817058060853nteger A3))))) (forall ((A3 tptp.set_set_nat) (F tptp.fun_set_nat_nat)) (=> (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.image_set_nat_nat F A3))) (tptp.finite_card_set_nat A3))))) (forall ((A3 tptp.set_list_nat) (F tptp.fun_list_nat_nat)) (=> (tptp.finite8100373058378681591st_nat A3) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.image_list_nat_nat F A3))) (tptp.finite_card_list_nat A3))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_set_nat (tptp.image_nat_set_nat F A3))) (tptp.aa_set_nat_nat tptp.finite_card_nat A3))))) (forall ((A3 tptp.set_nat) (F tptp.fun_nat_list_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_list_nat (tptp.image_nat_list_nat F A3))) (tptp.aa_set_nat_nat tptp.finite_card_nat A3))))) (forall ((A3 tptp.set_int) (F tptp.fun_int_set_nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_set_nat (tptp.image_int_set_nat F A3))) (tptp.finite_card_int A3))))) (forall ((F3 tptp.set_set_nat) (C3 tptp.nat)) (=> (forall ((G3 tptp.set_set_nat)) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat G3) F3)) (=> (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat G3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_set_nat G3)) C3))))) (and (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat F3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_set_nat F3)) C3))))) (forall ((F3 tptp.set_list_nat) (C3 tptp.nat)) (=> (forall ((G3 tptp.set_list_nat)) (=> (tptp.ord_le6045566169113846134st_nat G3 F3) (=> (tptp.finite8100373058378681591st_nat G3) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_list_nat G3)) C3))))) (and (tptp.finite8100373058378681591st_nat F3) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_list_nat F3)) C3))))) (forall ((F3 tptp.set_nat) (C3 tptp.nat)) (=> (forall ((G3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat G3) F3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat G3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat tptp.finite_card_nat G3)) C3))))) (and (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat F3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat tptp.finite_card_nat F3)) C3))))) (forall ((F3 tptp.set_Code_integer) (C3 tptp.nat)) (=> (forall ((G3 tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger G3) F3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger G3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite4902975817058060853nteger G3)) C3))))) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger F3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite4902975817058060853nteger F3)) C3))))) (forall ((F3 tptp.set_Pr1261947904930325089at_nat) (C3 tptp.nat)) (=> (forall ((G3 tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat G3) F3)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat G3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite711546835091564841at_nat G3)) C3))))) (and (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat F3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite711546835091564841at_nat F3)) C3))))) (forall ((F3 tptp.set_int) (C3 tptp.nat)) (=> (forall ((G3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int G3) F3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int G3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_int G3)) C3))))) (and (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int F3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_int F3)) C3))))) (forall ((B3 tptp.set_set_nat) (A3 tptp.set_set_nat)) (=> (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat B3)) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat A3) B3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_set_nat B3)) (tptp.finite_card_set_nat A3))) (= A3 B3))))) (forall ((B3 tptp.set_list_nat) (A3 tptp.set_list_nat)) (=> (tptp.finite8100373058378681591st_nat B3) (=> (tptp.ord_le6045566169113846134st_nat A3 B3) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_list_nat B3)) (tptp.finite_card_list_nat A3))) (= A3 B3))))) (forall ((B3 tptp.set_nat) (A3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) B3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat tptp.finite_card_nat B3)) (tptp.aa_set_nat_nat tptp.finite_card_nat A3))) (= A3 B3))))) (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) B3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite4902975817058060853nteger B3)) (tptp.finite4902975817058060853nteger A3))) (= A3 B3))))) (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat B3)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A3) B3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite711546835091564841at_nat B3)) (tptp.finite711546835091564841at_nat A3))) (= A3 B3))))) (forall ((B3 tptp.set_int) (A3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_int B3)) (tptp.finite_card_int A3))) (= A3 B3))))) (forall ((B3 tptp.set_set_nat) (A3 tptp.set_set_nat)) (=> (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat B3)) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat A3) B3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_set_nat A3)) (tptp.finite_card_set_nat B3)))))) (forall ((B3 tptp.set_list_nat) (A3 tptp.set_list_nat)) (=> (tptp.finite8100373058378681591st_nat B3) (=> (tptp.ord_le6045566169113846134st_nat A3 B3) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_list_nat A3)) (tptp.finite_card_list_nat B3)))))) (forall ((B3 tptp.set_nat) (A3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) B3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat tptp.finite_card_nat A3)) (tptp.aa_set_nat_nat tptp.finite_card_nat B3)))))) (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger A3) B3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite4902975817058060853nteger A3)) (tptp.finite4902975817058060853nteger B3)))))) (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat B3)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat A3) B3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite711546835091564841at_nat A3)) (tptp.finite711546835091564841at_nat B3)))))) (forall ((B3 tptp.set_int) (A3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int A3) B3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_int A3)) (tptp.finite_card_int B3)))))) (forall ((N2 tptp.nat) (S tptp.set_set_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) (tptp.finite_card_set_nat S))) (not (forall ((T6 tptp.set_set_nat)) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat T6) S)) (=> (= (tptp.finite_card_set_nat T6) N2) (not (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat T6))))))))) (forall ((N2 tptp.nat) (S tptp.set_list_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) (tptp.finite_card_list_nat S))) (not (forall ((T6 tptp.set_list_nat)) (=> (tptp.ord_le6045566169113846134st_nat T6 S) (=> (= (tptp.finite_card_list_nat T6) N2) (not (tptp.finite8100373058378681591st_nat T6)))))))) (forall ((N2 tptp.nat) (S tptp.set_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) (tptp.aa_set_nat_nat tptp.finite_card_nat S))) (not (forall ((T6 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat T6) S)) (=> (= (tptp.aa_set_nat_nat tptp.finite_card_nat T6) N2) (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T6))))))))) (forall ((N2 tptp.nat) (S tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) (tptp.finite4902975817058060853nteger S))) (not (forall ((T6 tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger T6) S)) (=> (= (tptp.finite4902975817058060853nteger T6) N2) (not (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T6))))))))) (forall ((N2 tptp.nat) (S tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) (tptp.finite711546835091564841at_nat S))) (not (forall ((T6 tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat T6) S)) (=> (= (tptp.finite711546835091564841at_nat T6) N2) (not (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat T6))))))))) (forall ((N2 tptp.nat) (S tptp.set_int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) (tptp.finite_card_int S))) (not (forall ((T6 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int T6) S)) (=> (= (tptp.finite_card_int T6) N2) (not (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T6))))))))) (forall ((A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (=> (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat A3)) (=> (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat B3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.finite_card_set_nat A3)) (tptp.finite_card_set_nat B3))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.finite_card_set_nat (tptp.minus_2163939370556025621et_nat A3 B3))) (tptp.finite_card_set_nat (tptp.minus_2163939370556025621et_nat B3 A3)))))))) (forall ((A3 tptp.set_list_nat) (B3 tptp.set_list_nat)) (=> (tptp.finite8100373058378681591st_nat A3) (=> (tptp.finite8100373058378681591st_nat B3) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.finite_card_list_nat A3)) (tptp.finite_card_list_nat B3))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.finite_card_list_nat (tptp.minus_7954133019191499631st_nat A3 B3))) (tptp.finite_card_list_nat (tptp.minus_7954133019191499631st_nat B3 A3)))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.finite_card_int A3)) (tptp.finite_card_int B3))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.finite_card_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3))) (tptp.finite_card_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int B3) A3)))))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.finite4902975817058060853nteger A3)) (tptp.finite4902975817058060853nteger B3))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.finite4902975817058060853nteger (tptp.minus_2355218937544613996nteger A3 B3))) (tptp.finite4902975817058060853nteger (tptp.minus_2355218937544613996nteger B3 A3)))))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat A3)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat B3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.finite711546835091564841at_nat A3)) (tptp.finite711546835091564841at_nat B3))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.finite711546835091564841at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat A3) B3))) (tptp.finite711546835091564841at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat B3) A3)))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_set_nat_nat tptp.finite_card_nat A3)) (tptp.aa_set_nat_nat tptp.finite_card_nat B3))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3))) (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat B3) A3)))))))) (forall ((A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (=> (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat A3)) (=> (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat B3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_set_nat A3)) (tptp.finite_card_set_nat B3))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_set_nat (tptp.minus_2163939370556025621et_nat A3 B3))) (tptp.finite_card_set_nat (tptp.minus_2163939370556025621et_nat B3 A3)))))))) (forall ((A3 tptp.set_list_nat) (B3 tptp.set_list_nat)) (=> (tptp.finite8100373058378681591st_nat A3) (=> (tptp.finite8100373058378681591st_nat B3) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_list_nat A3)) (tptp.finite_card_list_nat B3))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_list_nat (tptp.minus_7954133019191499631st_nat A3 B3))) (tptp.finite_card_list_nat (tptp.minus_7954133019191499631st_nat B3 A3)))))))) (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_int A3)) (tptp.finite_card_int B3))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int A3) B3))) (tptp.finite_card_int (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int B3) A3)))))))) (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite4902975817058060853nteger A3)) (tptp.finite4902975817058060853nteger B3))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite4902975817058060853nteger (tptp.minus_2355218937544613996nteger A3 B3))) (tptp.finite4902975817058060853nteger (tptp.minus_2355218937544613996nteger B3 A3)))))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat A3)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat B3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite711546835091564841at_nat A3)) (tptp.finite711546835091564841at_nat B3))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite711546835091564841at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat A3) B3))) (tptp.finite711546835091564841at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat B3) A3)))))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat tptp.finite_card_nat A3)) (tptp.aa_set_nat_nat tptp.finite_card_nat B3))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat A3) B3))) (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat B3) A3)))))))) (forall ((B3 tptp.set_set_nat) (A3 tptp.set_set_nat)) (=> (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat B3)) (=> (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_less_set_set_nat A3) B3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.finite_card_set_nat A3)) (tptp.finite_card_set_nat B3)))))) (forall ((B3 tptp.set_list_nat) (A3 tptp.set_list_nat)) (=> (tptp.finite8100373058378681591st_nat B3) (=> (tptp.ord_le1190675801316882794st_nat A3 B3) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.finite_card_list_nat A3)) (tptp.finite_card_list_nat B3)))))) (forall ((B3 tptp.set_nat) (A3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat A3) B3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_set_nat_nat tptp.finite_card_nat A3)) (tptp.aa_set_nat_nat tptp.finite_card_nat B3)))))) (forall ((B3 tptp.set_int) (A3 tptp.set_int)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int B3)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int A3) B3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.finite_card_int A3)) (tptp.finite_card_int B3)))))) (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger B3)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le1307284697595431911nteger A3) B3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.finite4902975817058060853nteger A3)) (tptp.finite4902975817058060853nteger B3)))))) (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat B3)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le7866589430770878221at_nat A3) B3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.finite711546835091564841at_nat A3)) (tptp.finite711546835091564841at_nat B3)))))) (forall ((A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_set_nat (tptp.sup_sup_set_set_nat A3 B3))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.finite_card_set_nat A3)) (tptp.finite_card_set_nat B3))))) (forall ((A3 tptp.set_list_nat) (B3 tptp.set_list_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite_card_list_nat (tptp.sup_sup_set_list_nat A3 B3))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.finite_card_list_nat A3)) (tptp.finite_card_list_nat B3))))) (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite1207074278014112911at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat A3) B3))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.finite1207074278014112911at_nat A3)) (tptp.finite1207074278014112911at_nat B3))))) (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite7007076676225009423at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat A3) B3))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.finite7007076676225009423at_nat A3)) (tptp.finite7007076676225009423at_nat B3))))) (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.finite3771342082235030671at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat A3) B3))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.finite3771342082235030671at_nat A3)) (tptp.finite3771342082235030671at_nat B3))))) (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat A3) B3))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_set_nat_nat tptp.finite_card_nat A3)) (tptp.aa_set_nat_nat tptp.finite_card_nat B3))))) (forall ((M6 tptp.set_nat) (I2 tptp.nat)) (=> (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) M6))) (= (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_aly M6) I2))) (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_alz M6) I2)))))) (forall ((M6 tptp.set_nat) (I2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) M6)) (= (tptp.aa_nat_nat tptp.suc (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_aly M6) I2)))) (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_alz M6) I2)))))) (forall ((M6 tptp.set_nat) (I2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) M6)) (not (= (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_alz M6) I2))) tptp.zero_zero_nat)))) (forall ((A3 tptp.set_nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) (tptp.aa_set_nat_nat tptp.finite_card_nat A3))))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat A3) _let_1)) (= A3 _let_1)))) (forall ((F tptp.fun_set_nat_nat) (A3 tptp.set_set_nat)) (= (tptp.groups8294997508430121362at_nat (tptp.aTP_Lamm_ama F) A3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.groups8294997508430121362at_nat F A3)) (tptp.finite_card_set_nat A3)))) (forall ((F tptp.fun_list_nat_nat) (A3 tptp.set_list_nat)) (= (tptp.groups4396056296759096172at_nat (tptp.aTP_Lamm_amb F) A3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.groups4396056296759096172at_nat F A3)) (tptp.finite_card_list_nat A3)))) (forall ((F tptp.fun_nat_nat) (A3 tptp.set_nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_amc F)) A3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A3)) (tptp.aa_set_nat_nat tptp.finite_card_nat A3)))) (forall ((S tptp.set_bool) (T tptp.set_bool) (R tptp.fun_bo1841576699660343469l_bool) (K tptp.nat)) (=> (tptp.finite_finite_bool S) (=> (tptp.finite_finite_bool T) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 T)) (= (tptp.finite_card_bool (tptp.collect_bool (tptp.aa_boo8970175072276269406l_bool (tptp.aa_fun1447330757145981436l_bool (tptp.aTP_Lamm_alb S) R) X3))) K))) (= (tptp.groups5768501273728744877ol_nat (tptp.aa_fun3941158123937086921ol_nat (tptp.aTP_Lamm_ald T) R) S) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K) (tptp.finite_card_bool T))))))) (forall ((S tptp.set_bool) (T tptp.set_nat) (R tptp.fun_bo3288154511880838028t_bool) (K tptp.nat)) (=> (tptp.finite_finite_bool S) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) T)) (= (tptp.finite_card_bool (tptp.collect_bool (tptp.aa_nat_fun_bool_bool (tptp.aa_fun4163026448321506586l_bool (tptp.aTP_Lamm_rg S) R) X3))) K))) (= (tptp.groups5768501273728744877ol_nat (tptp.aa_fun7928520491197679664ol_nat (tptp.aTP_Lamm_alv T) R) S) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K) (tptp.aa_set_nat_nat tptp.finite_card_nat T))))))) (forall ((S tptp.set_bool) (T tptp.set_int) (R tptp.fun_bo2827871560234191408t_bool) (K tptp.nat)) (=> (tptp.finite_finite_bool S) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) T)) (= (tptp.finite_card_bool (tptp.collect_bool (tptp.aa_int_fun_bool_bool (tptp.aa_fun6035399485891414554l_bool (tptp.aTP_Lamm_rv S) R) X3))) K))) (= (tptp.groups5768501273728744877ol_nat (tptp.aa_fun7155190969624455820ol_nat (tptp.aTP_Lamm_ale T) R) S) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K) (tptp.finite_card_int T))))))) (forall ((S tptp.set_bool) (T tptp.set_Code_integer) (R tptp.fun_bo284609390884453567r_bool) (K tptp.nat)) (=> (tptp.finite_finite_bool S) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) T)) (= (tptp.finite_card_bool (tptp.collect_bool (tptp.aa_Cod8494480694608518558l_bool (tptp.aa_fun9176172261886745818l_bool (tptp.aTP_Lamm_ada S) R) X3))) K))) (= (tptp.groups5768501273728744877ol_nat (tptp.aa_fun4256929549349463485ol_nat (tptp.aTP_Lamm_alg T) R) S) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K) (tptp.finite4902975817058060853nteger T))))))) (forall ((S tptp.set_int) (T tptp.set_bool) (R tptp.fun_in3865155034416861484l_bool) (K tptp.nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (=> (tptp.finite_finite_bool T) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 T)) (= (tptp.finite_card_int (tptp.collect_int (tptp.aa_bool_fun_int_bool (tptp.aa_fun2580392495071267866t_bool (tptp.aTP_Lamm_alh S) R) X3))) K))) (= (tptp.groups4541462559716669496nt_nat (tptp.aa_fun6244226199881115619nt_nat (tptp.aTP_Lamm_alj T) R) S) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K) (tptp.finite_card_bool T))))))) (forall ((S tptp.set_int) (T tptp.set_nat) (R tptp.fun_int_fun_nat_bool) (K tptp.nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) T)) (= (tptp.finite_card_int (tptp.collect_int (tptp.aa_nat_fun_int_bool (tptp.aa_fun3035398748895483388t_bool (tptp.aTP_Lamm_rl S) R) X3))) K))) (= (tptp.groups4541462559716669496nt_nat (tptp.aa_fun5132377469993263754nt_nat (tptp.aTP_Lamm_amd T) R) S) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K) (tptp.aa_set_nat_nat tptp.finite_card_nat T))))))) (forall ((S tptp.set_int) (T tptp.set_int) (R tptp.fun_int_fun_int_bool) (K tptp.nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int T)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X3) T)) (= (tptp.finite_card_int (tptp.collect_int (tptp.aa_int_fun_int_bool (tptp.aa_fun8168818243683596540t_bool (tptp.aTP_Lamm_adb S) R) X3))) K))) (= (tptp.groups4541462559716669496nt_nat (tptp.aa_fun8170219554457397550nt_nat (tptp.aTP_Lamm_all T) R) S) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K) (tptp.finite_card_int T))))))) (forall ((S tptp.set_int) (T tptp.set_Code_integer) (R tptp.fun_in5519481650651148416r_bool) (K tptp.nat)) (=> (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int S)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger T)) (=> (forall ((X3 tptp.code_integer)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer X3) T)) (= (tptp.finite_card_int (tptp.collect_int (tptp.aa_Cod8597349444926882409t_bool (tptp.aa_fun2469241947764354620t_bool (tptp.aTP_Lamm_adc S) R) X3))) K))) (= (tptp.groups4541462559716669496nt_nat (tptp.aa_fun6776377250481993149nt_nat (tptp.aTP_Lamm_aln T) R) S) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K) (tptp.finite4902975817058060853nteger T))))))) (forall ((S tptp.set_Code_integer) (T tptp.set_bool) (R tptp.fun_Co3748208068438171869l_bool) (K tptp.nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S)) (=> (tptp.finite_finite_bool T) (=> (forall ((X3 tptp.bool)) (=> (tptp.pp (tptp.member_bool X3 T)) (= (tptp.finite4902975817058060853nteger (tptp.collect_Code_integer (tptp.aa_boo5858427943822696632r_bool (tptp.aa_fun6233448402170926554r_bool (tptp.aTP_Lamm_alo S) R) X3))) K))) (= (tptp.groups7237345082560585321er_nat (tptp.aa_fun4083829879951944645er_nat (tptp.aTP_Lamm_alq T) R) S) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K) (tptp.finite_card_bool T))))))) (forall ((S tptp.set_Code_integer) (T tptp.set_nat) (R tptp.fun_Co8657364630979331932t_bool) (K tptp.nat)) (=> (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger S)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) T)) (= (tptp.finite4902975817058060853nteger (tptp.collect_Code_integer (tptp.aa_nat6120813132205607877r_bool (tptp.aa_fun8839232882156773436r_bool (tptp.aTP_Lamm_rq S) R) X3))) K))) (= (tptp.groups7237345082560585321er_nat (tptp.aa_fun2949368542467568330er_nat (tptp.aTP_Lamm_ame T) R) S) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat K) (tptp.aa_set_nat_nat tptp.finite_card_nat T))))))) (forall ((A3 tptp.set_set_nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.finite_card_set_nat A3))) (and (not (= A3 tptp.bot_bot_set_set_nat)) (tptp.pp (tptp.aa_set_set_nat_bool tptp.finite1152437895449049373et_nat A3))))) (forall ((A3 tptp.set_list_nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.finite_card_list_nat A3))) (and (not (= A3 tptp.bot_bot_set_list_nat)) (tptp.finite8100373058378681591st_nat A3)))) (forall ((A3 tptp.set_Code_integer)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.finite4902975817058060853nteger A3))) (and (not (= A3 tptp.bot_bo3990330152332043303nteger)) (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger A3))))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.finite711546835091564841at_nat A3))) (and (not (= A3 tptp.bot_bo2099793752762293965at_nat)) (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat A3))))) (forall ((A3 tptp.set_bool)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.finite_card_bool A3))) (and (not (= A3 tptp.bot_bot_set_bool)) (tptp.finite_finite_bool A3)))) (forall ((A3 tptp.set_nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_set_nat_nat tptp.finite_card_nat A3))) (and (not (= A3 tptp.bot_bot_set_nat)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A3))))) (forall ((A3 tptp.set_int)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.finite_card_int A3))) (and (not (= A3 tptp.bot_bot_set_int)) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int A3))))) (forall ((A3 tptp.set_nat) (K5 tptp.code_integer) (F tptp.fun_nat_Code_integer)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) A3)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger K5) (tptp.aa_nat_Code_integer F I3))))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_set_nat_nat tptp.finite_card_nat A3))) K5)) (tptp.aa_set871585252387937313nteger (tptp.groups7501900531339628137nteger F) A3))))) (forall ((A3 tptp.set_bool) (K5 tptp.rat) (F tptp.fun_bool_rat)) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat K5) (tptp.aa_bool_rat F I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.finite_card_bool A3))) K5)) (tptp.groups5133371213642249141ol_rat F A3))))) (forall ((A3 tptp.set_int) (K5 tptp.rat) (F tptp.fun_int_rat)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat K5) (tptp.aa_int_rat F I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.finite_card_int A3))) K5)) (tptp.groups3906332499630173760nt_rat F A3))))) (forall ((A3 tptp.set_nat) (K5 tptp.rat) (F tptp.fun_nat_rat)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat K5) (tptp.aa_nat_rat F I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_set_nat_nat tptp.finite_card_nat A3))) K5)) (tptp.aa_set_nat_rat (tptp.groups2906978787729119204at_rat F) A3))))) (forall ((A3 tptp.set_bool) (K5 tptp.nat) (F tptp.fun_bool_nat)) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K5) (tptp.aa_bool_nat F I3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.finite_card_bool A3))) K5)) (tptp.groups5768501273728744877ol_nat F A3))))) (forall ((A3 tptp.set_int) (K5 tptp.nat) (F tptp.fun_int_nat)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K5) (tptp.aa_int_nat F I3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.finite_card_int A3))) K5)) (tptp.groups4541462559716669496nt_nat F A3))))) (forall ((A3 tptp.set_bool) (K5 tptp.int) (F tptp.fun_bool_int)) (=> (forall ((I3 tptp.bool)) (=> (tptp.pp (tptp.member_bool I3 A3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K5) (tptp.aa_bool_int F I3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.finite_card_bool A3))) K5)) (tptp.groups5766010803219694601ol_int F A3))))) (forall ((A3 tptp.set_nat) (K5 tptp.int) (F tptp.fun_nat_int)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) A3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K5) (tptp.aa_nat_int F I3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_set_nat_nat tptp.finite_card_nat A3))) K5)) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int F) A3))))) (forall ((A3 tptp.set_nat) (K5 tptp.nat) (F tptp.fun_nat_nat)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K5) (tptp.aa_nat_nat F I3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_set_nat_nat tptp.finite_card_nat A3))) K5)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A3))))) (forall ((A3 tptp.set_int) (K5 tptp.int) (F tptp.fun_int_int)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int I3) A3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K5) (tptp.aa_int_int F I3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.finite_card_int A3))) K5)) (tptp.groups4538972089207619220nt_int F A3))))) (forall ((N7 tptp.set_nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat N7) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat tptp.finite_card_nat N7)) N2)))) (forall ((S tptp.set_nat)) (let ((_let_1 (tptp.groups3542108847815614940at_nat tptp.aTP_Lamm_fu))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (tptp.aa_set_nat_nat tptp.finite_card_nat S)))) (tptp.aa_set_nat_nat _let_1 S))))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.code_integer_of_num N2))) (= (tptp.code_integer_of_num (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger _let_1) _let_1)))) (forall ((K tptp.code_integer)) (let ((_let_1 (tptp.code_num_of_integer K))) (let ((_let_2 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger K) tptp.one_one_Code_integer)))) (and (=> _let_2 (= _let_1 tptp.one)) (=> (not _let_2) (= _let_1 (tptp.produc7336495610019696514er_num tptp.aTP_Lamm_amf (tptp.code_divmod_integer K (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))))))))) (forall ((K tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.code_bit_cut_integer K) (tptp.produc5135875973608410785r_bool (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger K) _let_1) (tptp.aa_bool_bool tptp.fNot (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) K)))))) (forall ((K tptp.code_integer)) (let ((_let_1 (tptp.aa_Code_integer_int tptp.code_int_of_integer K))) (let ((_let_2 (= K tptp.zero_z3403309356797280102nteger))) (let ((_let_3 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger K) tptp.zero_z3403309356797280102nteger)))) (and (=> _let_3 (= _let_1 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_Code_integer_int tptp.code_int_of_integer (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger K))))) (=> (not _let_3) (and (=> _let_2 (= _let_1 tptp.zero_zero_int)) (=> (not _let_2) (= _let_1 (tptp.produc1553301316500091796er_int tptp.aTP_Lamm_amg (tptp.code_divmod_integer K (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))))))))))) (forall ((K tptp.code_integer) (L tptp.code_integer)) (= (tptp.code_divmod_integer K L) (tptp.produc1086072967326762835nteger (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger K) L) (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger K) L)))) (forall ((Nat tptp.nat)) (= (not (= Nat tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.case_nat_bool tptp.fFalse tptp.aTP_Lamm_amh) Nat)))) (forall ((Nat tptp.nat)) (= (= Nat tptp.zero_zero_nat) (tptp.pp (tptp.aa_nat_bool (tptp.case_nat_bool tptp.fTrue tptp.aTP_Lamm_bg) Nat)))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_Code_integer_int tptp.code_int_of_integer X)) (tptp.aa_Code_integer_int tptp.code_int_of_integer Y))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger X) Y)))) (forall ((K tptp.code_integer) (L tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger K) L)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_Code_integer_int tptp.code_int_of_integer K)) (tptp.aa_Code_integer_int tptp.code_int_of_integer L))))) (forall ((X tptp.code_integer) (Xa2 tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger X) Xa2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_Code_integer_int tptp.code_int_of_integer X)) (tptp.aa_Code_integer_int tptp.code_int_of_integer Xa2))))) (forall ((K tptp.code_integer) (L tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger K) L)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_Code_integer_int tptp.code_int_of_integer K)) (tptp.aa_Code_integer_int tptp.code_int_of_integer L))))) (forall ((X tptp.code_integer) (Xa2 tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger X) Xa2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_Code_integer_int tptp.code_int_of_integer X)) (tptp.aa_Code_integer_int tptp.code_int_of_integer Xa2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc M)) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.case_nat_bool tptp.fFalse (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M)) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_nat_nat (tptp.case_nat_nat tptp.zero_zero_nat tptp.aTP_Lamm_fu) (tptp.aa_nat_nat _let_1 N2))))) (forall ((K tptp.code_integer)) (let ((_let_1 (tptp.code_bit_cut_integer K))) (let ((_let_2 (= K tptp.zero_z3403309356797280102nteger))) (and (=> _let_2 (= _let_1 (tptp.produc5135875973608410785r_bool tptp.zero_z3403309356797280102nteger tptp.fFalse))) (=> (not _let_2) (= _let_1 (tptp.produc6117575242473779287r_bool (tptp.aTP_Lamm_ami K) (tptp.code_divmod_abs K (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))))))))) (forall ((K tptp.code_integer)) (let ((_let_1 (tptp.aa_Code_integer_nat tptp.code_nat_of_integer K))) (let ((_let_2 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger K) tptp.zero_z3403309356797280102nteger)))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (tptp.produc1555791787009142072er_nat tptp.aTP_Lamm_amj (tptp.code_divmod_integer K (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))))))))) (forall ((K tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger K) tptp.zero_z3403309356797280102nteger)) (= (tptp.aa_Code_integer_nat tptp.code_nat_of_integer K) tptp.zero_zero_nat))) (forall ((J tptp.code_integer)) (= (tptp.code_divmod_abs tptp.zero_z3403309356797280102nteger J) (tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger tptp.zero_z3403309356797280102nteger))) (forall ((J tptp.code_integer)) (= (tptp.code_divmod_abs J tptp.zero_z3403309356797280102nteger) (tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer J)))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 X)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 Y)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_Code_integer_nat tptp.code_nat_of_integer X)) (tptp.aa_Code_integer_nat tptp.code_nat_of_integer Y))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger X) Y))))))) (forall ((U tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) U)) (= (tptp.set_or8404916559141939852nteger tptp.zero_z3403309356797280102nteger U) (tptp.image_1215581382706833972nteger tptp.semiri4939895301339042750nteger (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_Code_integer_nat tptp.code_nat_of_integer U)))))) (forall ((K tptp.code_integer) (L tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer L))) (let ((_let_2 (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer K))) (= (tptp.code_divmod_abs K L) (tptp.produc1086072967326762835nteger (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger _let_2) _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.modulo364778990260209775nteger _let_2) _let_1)))))) (forall ((K tptp.code_integer) (L tptp.code_integer)) (let ((_let_1 (tptp.code_divmod_abs K L))) (let ((_let_2 (tptp.code_divmod_integer K L))) (let ((_let_3 (= L tptp.zero_z3403309356797280102nteger))) (let ((_let_4 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_5 (tptp.pp (tptp.aa_Code_integer_bool _let_4 L)))) (let ((_let_6 (tptp.pp (tptp.aa_Code_integer_bool _let_4 K)))) (let ((_let_7 (= K tptp.zero_z3403309356797280102nteger))) (and (=> _let_7 (= _let_2 (tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger tptp.zero_z3403309356797280102nteger))) (=> (not _let_7) (and (=> _let_5 (and (=> _let_6 (= _let_2 _let_1)) (=> (not _let_6) (= _let_2 (tptp.produc6916734918728496179nteger (tptp.aTP_Lamm_amk L) _let_1))))) (=> (not _let_5) (and (=> _let_3 (= _let_2 (tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger K))) (=> (not _let_3) (= _let_2 (tptp.aa_Pro4693618923521437820nteger (tptp.aa_fun2509385170507305080nteger tptp.produc6499014454317279255nteger tptp.uminus1351360451143612070nteger) (tptp.if_Pro6119634080678213985nteger (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger K) tptp.zero_z3403309356797280102nteger) _let_1 (tptp.produc6916734918728496179nteger (tptp.aTP_Lamm_aml L) _let_1)))))))))))))))))) (forall ((N2 tptp.nat) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2) K))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N2))))) (forall ((N2 tptp.nat) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2) K)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N2)))) (forall ((K tptp.int) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat (tptp.aa_int_nat tptp.nat2 K)) N2)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N2))))) (forall ((N2 tptp.nat) (M tptp.nat) (K tptp.int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int M) K)))))) (forall ((K tptp.int)) (not (forall ((N5 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K))) (=> (forall ((M4 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N5) M4)) (= (tptp.pp (tptp.aa_nat_bool _let_1 M4)) (tptp.pp (tptp.aa_nat_bool _let_1 N5)))))) (not (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N5)) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N5) tptp.one_one_nat))) (not (tptp.pp (tptp.aa_nat_bool _let_1 N5))))))))))) (forall ((Nat tptp.nat)) (= (tptp.aa_nat_nat tptp.pred Nat) (tptp.aa_nat_nat (tptp.case_nat_nat tptp.zero_zero_nat tptp.aTP_Lamm_fu) Nat))) (forall ((S tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (exists ((R2 tptp.fun_nat_nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.strict1292158309912662752at_nat R2) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_set_nat_nat tptp.finite_card_nat S)))) (forall ((N8 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N8) (tptp.aa_set_nat_nat tptp.finite_card_nat S))) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat (tptp.aa_nat_nat R2 N8)) S)))))))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int K) L))) (and (tptp.pp (tptp.aa_int_bool _let_1 K)) (tptp.pp (tptp.aa_int_bool _let_1 L)))))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int N2) K))) (tptp.pp (tptp.aa_int_bool _let_1 K))))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int K) L)) tptp.zero_zero_int)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int L) tptp.zero_zero_int))))) (forall ((N2 tptp.nat) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int N2) K)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int X) Y))))))) (forall ((L tptp.int) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) L)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int K) L))))) (forall ((M tptp.nat) (K tptp.int) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int M) K)) N2)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M)))))) (forall ((M tptp.nat) (Q5 tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat M) Q5)) N2)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bit_se1148574629649215175it_nat Q5) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M)))))) (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) X)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) _let_1)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int X) Y)) _let_1))))))) (= (tptp.aa_set_nat_nat tptp.complete_Sup_Sup_nat tptp.bot_bot_set_nat) tptp.zero_zero_nat) (forall ((K tptp.code_integer) (L tptp.code_integer)) (let ((_let_1 (tptp.code_divmod_abs K L))) (let ((_let_2 (tptp.code_divmod_integer K L))) (let ((_let_3 (= L tptp.zero_z3403309356797280102nteger))) (let ((_let_4 (= K tptp.zero_z3403309356797280102nteger))) (and (=> _let_4 (= _let_2 (tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger tptp.zero_z3403309356797280102nteger))) (=> (not _let_4) (and (=> _let_3 (= _let_2 (tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger K))) (=> (not _let_3) (= _let_2 (tptp.aa_Pro4693618923521437820nteger (tptp.comp_C7848664941760151970nteger (tptp.comp_f6739083541385432444nteger tptp.produc6499014454317279255nteger tptp.times_3573771949741848930nteger) tptp.sgn_sgn_Code_integer L) (tptp.if_Pro6119634080678213985nteger (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer K)) (tptp.aa_Cod1783974652533396728nteger tptp.sgn_sgn_Code_integer L)) _let_1 (tptp.produc6916734918728496179nteger (tptp.aTP_Lamm_amm L) _let_1))))))))))))) (forall ((K5 tptp.set_nat)) (=> (not (= K5 tptp.bot_bot_set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat (tptp.aa_set_nat_nat tptp.complete_Inf_Inf_nat K5)) K5)))) (= (tptp.comple7399068483239264473et_nat (tptp.image_nat_set_nat tptp.set_ord_atMost_nat tptp.top_top_set_nat)) tptp.top_top_set_nat) (= (tptp.comple7399068483239264473et_nat (tptp.image_nat_set_nat tptp.set_ord_lessThan_nat tptp.top_top_set_nat)) tptp.top_top_set_nat) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.image_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_amn N2) tptp.top_top_set_nat) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_num_option_num (tptp.bit_and_not_num (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_opt5369159329878751634on_num (tptp.case_o6005452278849405969um_num (tptp.aa_num_option_num tptp.some_num tptp.one) tptp.aTP_Lamm_amo) (tptp.aa_num_option_num (tptp.bit_and_not_num M) N2)))) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn tptp.top_top_assn) tptp.top_top_assn) tptp.top_top_assn) (not (= tptp.top_top_assn tptp.bot_bot_assn)) (not (= tptp.top_top_assn tptp.one_one_assn)) (forall ((N2 tptp.nat)) (= (tptp.compow_fun_nat_nat N2 tptp.suc) (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int K) L))) (or (tptp.pp (tptp.aa_int_bool _let_1 K)) (tptp.pp (tptp.aa_int_bool _let_1 L)))))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int K) L)) tptp.zero_zero_int)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int L) tptp.zero_zero_int))))) (forall ((H tptp.produc3658429121746597890et_nat)) (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn tptp.top_top_assn) H)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range H)))) (forall ((K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int K)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)))) (forall ((K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int K))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N2)))) (tptp.aa_option_num_int (tptp.case_option_int_num tptp.zero_zero_int tptp.numeral_numeral_int) (tptp.aa_num_option_num (tptp.bit_and_not_num M) (tptp.aa_num_num tptp.bit0 N2))))) (forall ((N2 tptp.num) (M tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N2)))) (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_option_num_int (tptp.case_option_int_num tptp.zero_zero_int tptp.numeral_numeral_int) (tptp.aa_num_option_num (tptp.bit_and_not_num M) (tptp.aa_num_num tptp.bit0 N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N2)))) (tptp.aa_option_num_int (tptp.case_option_int_num tptp.zero_zero_int tptp.numeral_numeral_int) (tptp.aa_num_option_num (tptp.bit_and_not_num M) (tptp.aa_num_num tptp.bitM N2))))) (forall ((N2 tptp.num) (M tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N2)))) (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_option_num_int (tptp.case_option_int_num tptp.zero_zero_int tptp.numeral_numeral_int) (tptp.aa_num_option_num (tptp.bit_and_not_num M) (tptp.aa_num_num tptp.bitM N2))))) (forall ((P tptp.assn)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.entails P) tptp.top_top_assn))) (forall ((M tptp.num) (N2 tptp.num) (Q5 tptp.num)) (= (= (tptp.aa_num_option_num (tptp.bit_and_not_num M) N2) (tptp.aa_num_option_num tptp.some_num Q5)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int N2))) (tptp.aa_num_int tptp.numeral_numeral_int Q5)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int M))) (tptp.aa_num_int tptp.numeral_numeral_int N2)) (tptp.aa_option_num_int (tptp.case_option_int_num tptp.zero_zero_int tptp.numeral_numeral_int) (tptp.aa_num_option_num (tptp.bit_and_not_num N2) M)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int N2))) (tptp.aa_option_num_int (tptp.case_option_int_num tptp.zero_zero_int tptp.numeral_numeral_int) (tptp.aa_num_option_num (tptp.bit_and_not_num M) N2)))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int X) Y)))))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) X)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int X) Y)) X)))) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int X) Y)) Y)))) (forall ((Y tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int Y) Ya)) Z))))) (forall ((Y tptp.int) (Z tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int X) Y)) Z))))) (forall ((P tptp.assn) (H tptp.produc3658429121746597890et_nat)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn P) H)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn P) tptp.top_top_assn)) H)))) (forall ((P tptp.assn) (H tptp.produc3658429121746597890et_nat)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn P) tptp.top_top_assn)) H)) (not (forall ((H5 tptp.produc3658429121746597890et_nat)) (not (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn P) H5))))))) (= tptp.top_top_assn (tptp.abs_assn tptp.in_range)) (forall ((L tptp.int) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int L) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int K) L)) K)))) (forall ((Y tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int Y) Ya)) Z))))) (forall ((Y tptp.int) (Z tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int X) Y)) Z))))) (forall ((H tptp.heap_e7401611519738050253t_unit)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn tptp.top_top_assn) (tptp.produc7507926704131184380et_nat H tptp.bot_bot_set_nat)))) (forall ((N2 tptp.num)) (= (tptp.aa_num_option_num (tptp.bit_and_not_num tptp.one) (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_num_option_num tptp.some_num tptp.one))) (forall ((M tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 M))) (= (tptp.aa_num_option_num (tptp.bit_and_not_num _let_1) tptp.one) (tptp.aa_num_option_num tptp.some_num _let_1)))) (forall ((M tptp.num)) (= (tptp.aa_num_option_num (tptp.bit_and_not_num (tptp.aa_num_num tptp.bit1 M)) tptp.one) (tptp.aa_num_option_num tptp.some_num (tptp.aa_num_num tptp.bit0 M)))) (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1))) (let ((_let_3 (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool _let_2 X))) (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool _let_2 Xa2)))))) (let ((_let_4 (tptp.insert_int tptp.zero_zero_int (tptp.insert_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int) tptp.bot_bot_set_int)))) (let ((_let_5 (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X) _let_4)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa2) _let_4))))) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int X) Xa2) Y) (and (=> _let_5 (= Y (tptp.aa_int_int tptp.uminus_uminus_int _let_3))) (=> (not _let_5) (= Y (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int X) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int Xa2) _let_1)))))))))))))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1))) (let ((_let_3 (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool _let_2 K))) (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool _let_2 L)))))) (let ((_let_4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int K) L))) (let ((_let_5 (tptp.insert_int tptp.zero_zero_int (tptp.insert_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int) tptp.bot_bot_set_int)))) (let ((_let_6 (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int K) _let_5)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int L) _let_5))))) (and (=> _let_6 (= _let_4 (tptp.aa_int_int tptp.uminus_uminus_int _let_3))) (=> (not _let_6) (= _let_4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int K) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int L) _let_1)))))))))))))) (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X) Xa2))))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_3 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_2))) (let ((_let_4 (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool _let_3 X))) (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool _let_3 Xa2)))))) (let ((_let_5 (tptp.insert_int tptp.zero_zero_int (tptp.insert_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int) tptp.bot_bot_set_int)))) (let ((_let_6 (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X) _let_5)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Xa2) _let_5))))) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_6 (= Y (tptp.aa_int_int tptp.uminus_uminus_int _let_4))) (=> (not _let_6) (= Y (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_4) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int X) _let_2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int Xa2) _let_2))))))) (not _let_1)))))))))))) (forall ((M tptp.int) (N2 tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) N2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int M) _let_1)) (= (tptp.set_or1266510415728281911st_int M _let_1) (tptp.insert_int _let_1 (tptp.set_or1266510415728281911st_int M N2)))))) (forall ((J tptp.int) (I2 tptp.int)) (let ((_let_1 (tptp.set_or1266510415728281911st_int I2 J))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int J) I2)))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_int)) (=> (not _let_2) (= _let_1 (tptp.insert_int I2 (tptp.set_or1266510415728281911st_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I2) tptp.one_one_int) J)))))))) (forall ((A0 tptp.int) (A1 tptp.int) (P tptp.fun_int_fun_int_bool)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A0) A1))) (=> (forall ((K2 tptp.int) (L4 tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.insert_int tptp.zero_zero_int (tptp.insert_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int) tptp.bot_bot_set_int)))) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int K2) L4))) (=> (=> (not (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int K2) _let_2)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int L4) _let_2)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int K2) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int L4) _let_1)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P K2) L4))))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A0) A1))))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1))) (let ((_let_3 (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool _let_2 K))) (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool _let_2 L)))))) (let ((_let_4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int K) L))) (let ((_let_5 (tptp.insert_int tptp.zero_zero_int (tptp.insert_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int) tptp.bot_bot_set_int)))) (let ((_let_6 (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int K) _let_5)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int L) _let_5))))) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int K) L))) (and (=> _let_6 (= _let_4 (tptp.aa_int_int tptp.uminus_uminus_int _let_3))) (=> (not _let_6) (= _let_4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int K) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int L) _let_1))))))))))))))) (forall ((M tptp.nat)) (= (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) (tptp.aa_nat_nat tptp.suc M)) (tptp.insert_nat M tptp.bot_bot_set_nat))) (= (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat tptp.zero_zero_nat) (tptp.insert_nat tptp.zero_zero_nat tptp.bot_bot_set_nat)) (= tptp.top_top_set_bool (tptp.insert_bool tptp.fFalse _let_9)) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.insert_nat M (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M)) N2)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_2)) (= (tptp.aa_nat_set_nat _let_1 _let_2) (tptp.insert_nat _let_2 (tptp.aa_nat_set_nat _let_1 N2))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat M) N2) (tptp.insert_nat M (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M)) N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (tptp.aa_nat_set_nat _let_1 (tptp.aa_nat_nat tptp.suc N2)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (and (=> _let_3 (= _let_2 (tptp.insert_nat N2 (tptp.aa_nat_set_nat _let_1 N2)))) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_nat))))))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N2) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (tptp.insert_nat tptp.zero_zero_nat tptp.bot_bot_set_nat)))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N2) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)) (tptp.insert_nat tptp.zero_zero_nat tptp.bot_bot_set_nat)))) (forall ((M tptp.nat) (K tptp.num)) (let ((_let_1 (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (tptp.aa_nat_set_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat K)))) (let ((_let_3 (tptp.aa_num_nat tptp.pred_numeral K))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_3)))) (and (=> _let_4 (= _let_2 (tptp.insert_nat _let_3 (tptp.aa_nat_set_nat _let_1 _let_3)))) (=> (not _let_4) (= _let_2 tptp.bot_bot_set_nat)))))))) (forall ((C tptp.nat) (Y tptp.nat) (X tptp.nat)) (let ((_let_1 (tptp.image_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_amp C) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat X) Y)))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C) Y)))) (and (=> _let_3 (= _let_1 (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat X) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Y) C)))) (=> (not _let_3) (and (=> _let_2 (= _let_1 (tptp.insert_nat tptp.zero_zero_nat tptp.bot_bot_set_nat))) (=> (not _let_2) (= _let_1 tptp.bot_bot_set_nat))))))))) (forall ((X tptp.num) (Xa2 tptp.num) (Y tptp.option_num)) (let ((_let_1 (not (= Y tptp.none_num)))) (let ((_let_2 (= X tptp.one))) (=> (= (tptp.aa_num_option_num (tptp.bit_and_not_num X) Xa2) Y) (=> (=> _let_2 (=> (= Xa2 tptp.one) _let_1)) (=> (=> _let_2 (=> (exists ((N5 tptp.num)) (= Xa2 (tptp.aa_num_num tptp.bit0 N5))) (not (= Y (tptp.aa_num_option_num tptp.some_num tptp.one))))) (=> (=> _let_2 (=> (exists ((N5 tptp.num)) (= Xa2 (tptp.aa_num_num tptp.bit1 N5))) _let_1)) (=> (forall ((M5 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 M5))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (not (= Y (tptp.aa_num_option_num tptp.some_num _let_1))))))) (=> (forall ((M5 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M5)) (forall ((N5 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit0 N5)) (not (= Y (tptp.aa_opt5369159329878751634on_num (tptp.map_option_num_num tptp.bit0) (tptp.aa_num_option_num (tptp.bit_and_not_num M5) N5)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M5)) (forall ((N5 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit1 N5)) (not (= Y (tptp.aa_opt5369159329878751634on_num (tptp.map_option_num_num tptp.bit0) (tptp.aa_num_option_num (tptp.bit_and_not_num M5) N5)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M5)) (=> (= Xa2 tptp.one) (not (= Y (tptp.aa_num_option_num tptp.some_num (tptp.aa_num_num tptp.bit0 M5))))))) (=> (forall ((M5 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M5)) (forall ((N5 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit0 N5)) (not (= Y (tptp.aa_opt5369159329878751634on_num (tptp.case_o6005452278849405969um_num (tptp.aa_num_option_num tptp.some_num tptp.one) tptp.aTP_Lamm_amo) (tptp.aa_num_option_num (tptp.bit_and_not_num M5) N5)))))))) (not (forall ((M5 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M5)) (forall ((N5 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit1 N5)) (not (= Y (tptp.aa_opt5369159329878751634on_num (tptp.map_option_num_num tptp.bit0) (tptp.aa_num_option_num (tptp.bit_and_not_num M5) N5))))))))))))))))))))) (forall ((X tptp.num) (Xa2 tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X tptp.one))) (let ((_let_2 (tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel))) (=> (= (tptp.aa_num_option_num (tptp.bit_and_not_num X) Xa2) Y) (=> (tptp.pp (tptp.aa_Pro762926636801165566m_bool _let_2 (tptp.product_Pair_num_num X Xa2))) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y tptp.none_num) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool _let_2 (tptp.product_Pair_num_num tptp.one tptp.one))))))) (=> (=> _let_1 (forall ((N5 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 N5))) (=> (= Xa2 _let_1) (=> (= Y (tptp.aa_num_option_num tptp.some_num tptp.one)) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (tptp.product_Pair_num_num tptp.one _let_1))))))))) (=> (=> _let_1 (forall ((N5 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N5))) (=> (= Xa2 _let_1) (=> (= Y tptp.none_num) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (tptp.product_Pair_num_num tptp.one _let_1))))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 M5))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y (tptp.aa_num_option_num tptp.some_num _let_1)) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (tptp.product_Pair_num_num _let_1 tptp.one))))))))) (=> (forall ((M5 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M5)) (forall ((N5 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 N5))) (=> (= Xa2 _let_1) (=> (= Y (tptp.aa_opt5369159329878751634on_num (tptp.map_option_num_num tptp.bit0) (tptp.aa_num_option_num (tptp.bit_and_not_num M5) N5))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M5) _let_1)))))))))) (=> (forall ((M5 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M5)) (forall ((N5 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N5))) (=> (= Xa2 _let_1) (=> (= Y (tptp.aa_opt5369159329878751634on_num (tptp.map_option_num_num tptp.bit0) (tptp.aa_num_option_num (tptp.bit_and_not_num M5) N5))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M5) _let_1)))))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 M5))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y (tptp.aa_num_option_num tptp.some_num (tptp.aa_num_num tptp.bit0 M5))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (tptp.product_Pair_num_num _let_1 tptp.one))))))))) (=> (forall ((M5 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M5)) (forall ((N5 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 N5))) (=> (= Xa2 _let_1) (=> (= Y (tptp.aa_opt5369159329878751634on_num (tptp.case_o6005452278849405969um_num (tptp.aa_num_option_num tptp.some_num tptp.one) tptp.aTP_Lamm_amo) (tptp.aa_num_option_num (tptp.bit_and_not_num M5) N5))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M5) _let_1)))))))))) (not (forall ((M5 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M5)) (forall ((N5 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N5))) (=> (= Xa2 _let_1) (=> (= Y (tptp.aa_opt5369159329878751634on_num (tptp.map_option_num_num tptp.bit0) (tptp.aa_num_option_num (tptp.bit_and_not_num M5) N5))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M5) _let_1)))))))))))))))))))))))) (forall ((X tptp.num) (Xa2 tptp.num) (Y tptp.option_num)) (let ((_let_1 (not (= Y (tptp.aa_num_option_num tptp.some_num tptp.one))))) (let ((_let_2 (= Xa2 tptp.one))) (let ((_let_3 (=> _let_2 _let_1))) (let ((_let_4 (not (= Y tptp.none_num)))) (let ((_let_5 (= X tptp.one))) (=> (= (tptp.aa_num_option_num (tptp.bit_un7362597486090784418nd_num X) Xa2) Y) (=> (=> _let_5 _let_3) (=> (=> _let_5 (=> (exists ((N5 tptp.num)) (= Xa2 (tptp.aa_num_num tptp.bit0 N5))) _let_4)) (=> (=> _let_5 (=> (exists ((N5 tptp.num)) (= Xa2 (tptp.aa_num_num tptp.bit1 N5))) _let_1)) (=> (=> (exists ((M5 tptp.num)) (= X (tptp.aa_num_num tptp.bit0 M5))) (=> _let_2 _let_4)) (=> (forall ((M5 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M5)) (forall ((N5 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit0 N5)) (not (= Y (tptp.aa_opt5369159329878751634on_num (tptp.map_option_num_num tptp.bit0) (tptp.aa_num_option_num (tptp.bit_un7362597486090784418nd_num M5) N5)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M5)) (forall ((N5 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit1 N5)) (not (= Y (tptp.aa_opt5369159329878751634on_num (tptp.map_option_num_num tptp.bit0) (tptp.aa_num_option_num (tptp.bit_un7362597486090784418nd_num M5) N5)))))))) (=> (=> (exists ((M5 tptp.num)) (= X (tptp.aa_num_num tptp.bit1 M5))) _let_3) (=> (forall ((M5 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M5)) (forall ((N5 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit0 N5)) (not (= Y (tptp.aa_opt5369159329878751634on_num (tptp.map_option_num_num tptp.bit0) (tptp.aa_num_option_num (tptp.bit_un7362597486090784418nd_num M5) N5)))))))) (not (forall ((M5 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M5)) (forall ((N5 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit1 N5)) (not (= Y (tptp.aa_opt5369159329878751634on_num (tptp.case_o6005452278849405969um_num (tptp.aa_num_option_num tptp.some_num tptp.one) tptp.aTP_Lamm_amo) (tptp.aa_num_option_num (tptp.bit_un7362597486090784418nd_num M5) N5)))))))))))))))))))))))) (forall ((X tptp.num) (Xa2 tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X tptp.one))) (=> (= (tptp.aa_num_option_num (tptp.bit_un2480387367778600638or_num X) Xa2) Y) (=> (=> _let_1 (=> (= Xa2 tptp.one) (not (= Y tptp.none_num)))) (=> (=> _let_1 (forall ((N5 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit0 N5)) (not (= Y (tptp.aa_num_option_num tptp.some_num (tptp.aa_num_num tptp.bit1 N5))))))) (=> (=> _let_1 (forall ((N5 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit1 N5)) (not (= Y (tptp.aa_num_option_num tptp.some_num (tptp.aa_num_num tptp.bit0 N5))))))) (=> (forall ((M5 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M5)) (=> (= Xa2 tptp.one) (not (= Y (tptp.aa_num_option_num tptp.some_num (tptp.aa_num_num tptp.bit1 M5))))))) (=> (forall ((M5 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M5)) (forall ((N5 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit0 N5)) (not (= Y (tptp.aa_opt5369159329878751634on_num (tptp.map_option_num_num tptp.bit0) (tptp.aa_num_option_num (tptp.bit_un2480387367778600638or_num M5) N5)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M5)) (forall ((N5 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit1 N5)) (not (= Y (tptp.aa_num_option_num tptp.some_num (tptp.aa_option_num_num (tptp.case_option_num_num tptp.one tptp.bit1) (tptp.aa_num_option_num (tptp.bit_un2480387367778600638or_num M5) N5))))))))) (=> (forall ((M5 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M5)) (=> (= Xa2 tptp.one) (not (= Y (tptp.aa_num_option_num tptp.some_num (tptp.aa_num_num tptp.bit0 M5))))))) (=> (forall ((M5 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M5)) (forall ((N5 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit0 N5)) (not (= Y (tptp.aa_num_option_num tptp.some_num (tptp.aa_option_num_num (tptp.case_option_num_num tptp.one tptp.bit1) (tptp.aa_num_option_num (tptp.bit_un2480387367778600638or_num M5) N5))))))))) (not (forall ((M5 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M5)) (forall ((N5 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit1 N5)) (not (= Y (tptp.aa_opt5369159329878751634on_num (tptp.map_option_num_num tptp.bit0) (tptp.aa_num_option_num (tptp.bit_un2480387367778600638or_num M5) N5)))))))))))))))))))) (= (tptp.aa_num_option_num (tptp.bit_un7362597486090784418nd_num tptp.one) tptp.one) (tptp.aa_num_option_num tptp.some_num tptp.one)) (forall ((N2 tptp.num)) (= (tptp.aa_num_option_num (tptp.bit_un7362597486090784418nd_num tptp.one) (tptp.aa_num_num tptp.bit1 N2)) (tptp.aa_num_option_num tptp.some_num tptp.one))) (forall ((M tptp.num)) (= (tptp.aa_num_option_num (tptp.bit_un7362597486090784418nd_num (tptp.aa_num_num tptp.bit1 M)) tptp.one) (tptp.aa_num_option_num tptp.some_num tptp.one))) (forall ((N2 tptp.num)) (= (tptp.aa_num_option_num (tptp.bit_un2480387367778600638or_num tptp.one) (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_num_option_num tptp.some_num (tptp.aa_num_num tptp.bit1 N2)))) (forall ((N2 tptp.num)) (= (tptp.aa_num_option_num (tptp.bit_un2480387367778600638or_num tptp.one) (tptp.aa_num_num tptp.bit1 N2)) (tptp.aa_num_option_num tptp.some_num (tptp.aa_num_num tptp.bit0 N2)))) (forall ((M tptp.num)) (= (tptp.aa_num_option_num (tptp.bit_un2480387367778600638or_num (tptp.aa_num_num tptp.bit0 M)) tptp.one) (tptp.aa_num_option_num tptp.some_num (tptp.aa_num_num tptp.bit1 M)))) (forall ((M tptp.num)) (= (tptp.aa_num_option_num (tptp.bit_un2480387367778600638or_num (tptp.aa_num_num tptp.bit1 M)) tptp.one) (tptp.aa_num_option_num tptp.some_num (tptp.aa_num_num tptp.bit0 M)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_num_option_num (tptp.bit_un7362597486090784418nd_num (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_num tptp.bit1 N2)) (tptp.aa_opt5369159329878751634on_num (tptp.case_o6005452278849405969um_num (tptp.aa_num_option_num tptp.some_num tptp.one) tptp.aTP_Lamm_amo) (tptp.aa_num_option_num (tptp.bit_un7362597486090784418nd_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_num_option_num (tptp.bit_un2480387367778600638or_num (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_num_num tptp.bit1 N2)) (tptp.aa_num_option_num tptp.some_num (tptp.aa_option_num_num (tptp.case_option_num_num tptp.one tptp.bit1) (tptp.aa_num_option_num (tptp.bit_un2480387367778600638or_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_num_option_num (tptp.bit_un2480387367778600638or_num (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_num_option_num tptp.some_num (tptp.aa_option_num_num (tptp.case_option_num_num tptp.one tptp.bit1) (tptp.aa_num_option_num (tptp.bit_un2480387367778600638or_num M) N2))))) (forall ((X tptp.num) (Xa2 tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X tptp.one))) (let ((_let_2 (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel))) (=> (= (tptp.aa_num_option_num (tptp.bit_un7362597486090784418nd_num X) Xa2) Y) (=> (tptp.pp (tptp.aa_Pro762926636801165566m_bool _let_2 (tptp.product_Pair_num_num X Xa2))) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y (tptp.aa_num_option_num tptp.some_num tptp.one)) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool _let_2 (tptp.product_Pair_num_num tptp.one tptp.one))))))) (=> (=> _let_1 (forall ((N5 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 N5))) (=> (= Xa2 _let_1) (=> (= Y tptp.none_num) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (tptp.product_Pair_num_num tptp.one _let_1))))))))) (=> (=> _let_1 (forall ((N5 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N5))) (=> (= Xa2 _let_1) (=> (= Y (tptp.aa_num_option_num tptp.some_num tptp.one)) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (tptp.product_Pair_num_num tptp.one _let_1))))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 M5))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y tptp.none_num) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (tptp.product_Pair_num_num _let_1 tptp.one))))))))) (=> (forall ((M5 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M5)) (forall ((N5 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 N5))) (=> (= Xa2 _let_1) (=> (= Y (tptp.aa_opt5369159329878751634on_num (tptp.map_option_num_num tptp.bit0) (tptp.aa_num_option_num (tptp.bit_un7362597486090784418nd_num M5) N5))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M5) _let_1)))))))))) (=> (forall ((M5 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M5)) (forall ((N5 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N5))) (=> (= Xa2 _let_1) (=> (= Y (tptp.aa_opt5369159329878751634on_num (tptp.map_option_num_num tptp.bit0) (tptp.aa_num_option_num (tptp.bit_un7362597486090784418nd_num M5) N5))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M5) _let_1)))))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 M5))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y (tptp.aa_num_option_num tptp.some_num tptp.one)) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (tptp.product_Pair_num_num _let_1 tptp.one))))))))) (=> (forall ((M5 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M5)) (forall ((N5 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 N5))) (=> (= Xa2 _let_1) (=> (= Y (tptp.aa_opt5369159329878751634on_num (tptp.map_option_num_num tptp.bit0) (tptp.aa_num_option_num (tptp.bit_un7362597486090784418nd_num M5) N5))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M5) _let_1)))))))))) (not (forall ((M5 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M5)) (forall ((N5 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N5))) (=> (= Xa2 _let_1) (=> (= Y (tptp.aa_opt5369159329878751634on_num (tptp.case_o6005452278849405969um_num (tptp.aa_num_option_num tptp.some_num tptp.one) tptp.aTP_Lamm_amo) (tptp.aa_num_option_num (tptp.bit_un7362597486090784418nd_num M5) N5))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M5) _let_1)))))))))))))))))))))))) (forall ((X tptp.num) (Xa2 tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X tptp.one))) (let ((_let_2 (tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel))) (=> (= (tptp.aa_num_option_num (tptp.bit_un2480387367778600638or_num X) Xa2) Y) (=> (tptp.pp (tptp.aa_Pro762926636801165566m_bool _let_2 (tptp.product_Pair_num_num X Xa2))) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y tptp.none_num) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool _let_2 (tptp.product_Pair_num_num tptp.one tptp.one))))))) (=> (=> _let_1 (forall ((N5 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 N5))) (=> (= Xa2 _let_1) (=> (= Y (tptp.aa_num_option_num tptp.some_num (tptp.aa_num_num tptp.bit1 N5))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (tptp.product_Pair_num_num tptp.one _let_1))))))))) (=> (=> _let_1 (forall ((N5 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N5))) (=> (= Xa2 _let_1) (=> (= Y (tptp.aa_num_option_num tptp.some_num (tptp.aa_num_num tptp.bit0 N5))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (tptp.product_Pair_num_num tptp.one _let_1))))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 M5))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y (tptp.aa_num_option_num tptp.some_num (tptp.aa_num_num tptp.bit1 M5))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (tptp.product_Pair_num_num _let_1 tptp.one))))))))) (=> (forall ((M5 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M5)) (forall ((N5 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 N5))) (=> (= Xa2 _let_1) (=> (= Y (tptp.aa_opt5369159329878751634on_num (tptp.map_option_num_num tptp.bit0) (tptp.aa_num_option_num (tptp.bit_un2480387367778600638or_num M5) N5))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M5) _let_1)))))))))) (=> (forall ((M5 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 M5)) (forall ((N5 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N5))) (=> (= Xa2 _let_1) (=> (= Y (tptp.aa_num_option_num tptp.some_num (tptp.aa_option_num_num (tptp.case_option_num_num tptp.one tptp.bit1) (tptp.aa_num_option_num (tptp.bit_un2480387367778600638or_num M5) N5)))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M5) _let_1)))))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 M5))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y (tptp.aa_num_option_num tptp.some_num (tptp.aa_num_num tptp.bit0 M5))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (tptp.product_Pair_num_num _let_1 tptp.one))))))))) (=> (forall ((M5 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M5)) (forall ((N5 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 N5))) (=> (= Xa2 _let_1) (=> (= Y (tptp.aa_num_option_num tptp.some_num (tptp.aa_option_num_num (tptp.case_option_num_num tptp.one tptp.bit1) (tptp.aa_num_option_num (tptp.bit_un2480387367778600638or_num M5) N5)))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M5) _let_1)))))))))) (not (forall ((M5 tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 M5)) (forall ((N5 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N5))) (=> (= Xa2 _let_1) (=> (= Y (tptp.aa_opt5369159329878751634on_num (tptp.map_option_num_num tptp.bit0) (tptp.aa_num_option_num (tptp.bit_un2480387367778600638or_num M5) N5))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M5) _let_1)))))))))))))))))))))))) (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ Xa2)) (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ X)) (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ (tptp.aa_Pro262675715343573244at_nat (tptp.aa_Pro8023792847356852296at_nat (tptp.aa_fun6875833325056119164at_nat tptp.produc4528391901023682385at_nat tptp.aTP_Lamm_amr) Xa2) X)))) (forall ((Z tptp.int)) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (not (= Z (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat X3) Y3))))))) (= tptp.zero_zero_int (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ _let_21)) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2) (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat N2) tptp.zero_zero_nat)))) (forall ((X tptp.product_prod_nat_nat)) (= (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ X)) (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ (tptp.aa_Pro262675715343573244at_nat (tptp.produc2626176000494625587at_nat tptp.aTP_Lamm_ams) X)))) (= tptp.one_one_int (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ _let_18)) (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ Xa2)) (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ X))) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool (tptp.aa_fun174371099813217148t_bool tptp.produc5023667602222594023t_bool tptp.aTP_Lamm_amu) Xa2) X)))) (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ Xa2)) (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ X))) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool (tptp.aa_fun174371099813217148t_bool tptp.produc5023667602222594023t_bool tptp.aTP_Lamm_amw) Xa2) X)))) (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ Xa2)) (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ X)) (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ (tptp.aa_Pro262675715343573244at_nat (tptp.aa_Pro8023792847356852296at_nat (tptp.aa_fun6875833325056119164at_nat tptp.produc4528391901023682385at_nat tptp.aTP_Lamm_amy) Xa2) X)))) (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ Xa2)) (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ X)) (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ (tptp.aa_Pro262675715343573244at_nat (tptp.aa_Pro8023792847356852296at_nat (tptp.aa_fun6875833325056119164at_nat tptp.produc4528391901023682385at_nat tptp.aTP_Lamm_ana) Xa2) X)))) (forall ((X tptp.int) (Xa2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Xa2)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool (tptp.aa_fun174371099813217148t_bool tptp.produc5023667602222594023t_bool tptp.aTP_Lamm_amw) (tptp.aa_int1417691210696471063at_nat tptp.rep_Integ X)) (tptp.aa_int1417691210696471063at_nat tptp.rep_Integ Xa2))))) (forall ((X tptp.int) (Xa2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Xa2)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool (tptp.aa_fun174371099813217148t_bool tptp.produc5023667602222594023t_bool tptp.aTP_Lamm_amu) (tptp.aa_int1417691210696471063at_nat tptp.rep_Integ X)) (tptp.aa_int1417691210696471063at_nat tptp.rep_Integ Xa2))))) (= tptp.uminus_uminus_int (tptp.aa_fun8399641135911395862nt_int _let_36 _let_20)) (= tptp.pred_nat (tptp.collec3392354462482085612at_nat (tptp.produc8955392012077580105t_bool tptp.aTP_Lamm_anb))) (= tptp.times_times_int (tptp.map_fu8294830438409148311nt_int tptp.rep_Integ _let_36 _let_22)) (= tptp.minus_minus_int (tptp.map_fu8294830438409148311nt_int tptp.rep_Integ _let_36 _let_14)) (= tptp.plus_plus_int (tptp.map_fu8294830438409148311nt_int tptp.rep_Integ _let_36 _let_12)) (forall ((M6 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat M6)) (= (tptp.aa_set_nat_nat tptp.gcd_Gcd_nat M6) (tptp.aa_set_nat_nat tptp.gcd_Gcd_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat M6) (tptp.insert_nat tptp.zero_zero_nat tptp.bot_bot_set_nat)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_num tptp.num_of_nat (tptp.aa_nat_nat tptp.suc N2)))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (and (=> _let_2 (= _let_1 (tptp.aa_num_num tptp.inc (tptp.aa_nat_num tptp.num_of_nat N2)))) (=> (not _let_2) (= _let_1 tptp.one)))))) (forall ((M6 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat M6)) (=> (not (= M6 tptp.bot_bot_set_nat)) (=> (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) M6))) (= (tptp.aa_set_nat_nat tptp.gcd_Gcd_nat M6) (tptp.aa_set_nat_nat tptp.lattic8265883725875713057ax_nat (tptp.comple7806235888213564991et_nat (tptp.image_nat_set_nat tptp.aTP_Lamm_anc M6)))))))) (forall ((K5 tptp.set_int)) (= (tptp.gcd_Gcd_int (tptp.image_int_int tptp.abs_abs_int K5)) (tptp.gcd_Gcd_int K5))) (forall ((K5 tptp.set_int)) (= (tptp.aa_set_nat_nat tptp.gcd_Gcd_nat (tptp.image_int_nat tptp.aTP_Lamm_and K5)) (tptp.aa_int_nat tptp.nat2 (tptp.gcd_Gcd_int K5)))) (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (= (tptp.aa_set_nat_nat tptp.lattic8265883725875713057ax_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_adt N2))) N2))) (forall ((N7 tptp.set_nat)) (= (tptp.gcd_Gcd_int (tptp.image_nat_int tptp.semiri1314217659103216013at_int N7)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_set_nat_nat tptp.gcd_Gcd_nat N7)))) (forall ((K5 tptp.set_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.gcd_Gcd_int K5)))) (forall ((X6 tptp.set_nat)) (let ((_let_1 (tptp.aa_set_nat_nat tptp.complete_Sup_Sup_nat X6))) (let ((_let_2 (= X6 tptp.bot_bot_set_nat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (tptp.aa_set_nat_nat tptp.lattic8265883725875713057ax_nat X6))))))) (forall ((S tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat tptp.finite_card_nat S)) (tptp.aa_nat_nat tptp.suc (tptp.aa_set_nat_nat tptp.lattic8265883725875713057ax_nat S)))))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (tptp.aa_set_nat_nat tptp.lattic8265883725875713057ax_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_ane N2) M))))))))) (forall ((K5 tptp.set_int)) (= (tptp.gcd_Gcd_int K5) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_set_nat_nat tptp.gcd_Gcd_nat (tptp.image_int_nat (tptp.comp_int_nat_int tptp.nat2 tptp.abs_abs_int) K5))))) (= (tptp.comple7806235888213564991et_nat (tptp.image_nat_set_nat tptp.set_or1210151606488870762an_nat tptp.top_top_set_nat)) tptp.bot_bot_set_nat) (forall ((N2 tptp.int)) (=> (not (= N2 tptp.zero_zero_int)) (= (tptp.lattic8263393255366662781ax_int (tptp.collect_int (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_adv N2))) (tptp.aa_int_int tptp.abs_abs_int N2)))) (forall ((K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_nat_set_nat tptp.set_or1210151606488870762an_nat _let_1) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat (tptp.aa_nat_set_nat tptp.set_or1210151606488870762an_nat K)) (tptp.insert_nat _let_1 tptp.bot_bot_set_nat))))) (tptp.order_mono_nat_nat tptp.suc) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (tptp.order_mono_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2)))) (forall ((K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) K)) (tptp.order_mono_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_anf K)))) (forall ((N2 tptp.nat) (K tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N2) K) (tptp.finite_card_set_nat (tptp.collect_set_nat (tptp.aa_nat8857836526276733660t_bool (tptp.aTP_Lamm_ang N2) K))))) (forall ((J tptp.int) (I2 tptp.int) (Js tptp.list_int)) (let ((_let_1 (tptp.upto_aux I2 J Js))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int J) I2)))) (and (=> _let_2 (= _let_1 Js)) (=> (not _let_2) (= _let_1 (tptp.upto_aux I2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int J) tptp.one_one_int) (tptp.cons_int J Js)))))))) (forall ((I2 tptp.int) (J tptp.int)) (let ((_let_1 (tptp.upto I2 J))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I2) J)))) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int I2) J))) (and (=> _let_2 (= _let_1 (tptp.cons_int I2 (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I2) tptp.one_one_int) J)))) (=> (not _let_2) (= _let_1 tptp.nil_int))))))) (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.list_int)) (let ((_let_1 (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X) Xa2))))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Xa2)))) (=> (= (tptp.upto X Xa2) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y (tptp.cons_int X (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) tptp.one_one_int) Xa2)))) (=> (not _let_2) (= Y tptp.nil_int))) (not _let_1)))))))) (forall ((I2 tptp.int) (J tptp.int)) (let ((_let_1 (tptp.upto I2 J))) (= (tptp.linord1735203802627413978nt_int tptp.aTP_Lamm_fv _let_1) _let_1))) (forall ((I2 tptp.int) (J tptp.int)) (= (= (tptp.upto I2 J) tptp.nil_int) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int J) I2)))) (forall ((I2 tptp.int) (J tptp.int)) (= (= tptp.nil_int (tptp.upto I2 J)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int J) I2)))) (forall ((J tptp.int) (I2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int J) I2)) (= (tptp.upto I2 J) tptp.nil_int))) (forall ((I2 tptp.int) (K tptp.nat) (J tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I2) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int K)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_1) J)) (= (tptp.aa_nat_int (tptp.nth_int (tptp.upto I2 J)) K) _let_1)))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N2))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int M))) (let ((_let_3 (tptp.upto _let_2 _let_1))) (let ((_let_4 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_2) _let_1)))) (and (=> _let_4 (= _let_3 (tptp.cons_int _let_2 (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_2) tptp.one_one_int) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N2)))) (let ((_let_2 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M)))) (let ((_let_3 (tptp.upto _let_2 _let_1))) (let ((_let_4 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_2) _let_1)))) (and (=> _let_4 (= _let_3 (tptp.cons_int _let_2 (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_2) tptp.one_one_int) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N2))) (let ((_let_2 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M)))) (let ((_let_3 (tptp.upto _let_2 _let_1))) (let ((_let_4 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_2) _let_1)))) (and (=> _let_4 (= _let_3 (tptp.cons_int _let_2 (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_2) tptp.one_one_int) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N2)))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int M))) (let ((_let_3 (tptp.upto _let_2 _let_1))) (let ((_let_4 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_2) _let_1)))) (and (=> _let_4 (= _let_3 (tptp.cons_int _let_2 (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_2) tptp.one_one_int) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))) (forall ((M tptp.int) (N2 tptp.int)) (tptp.sorted_wrt_int tptp.ord_less_eq_int (tptp.upto M N2))) (forall ((I2 tptp.int) (J tptp.int)) (tptp.sorted_wrt_int tptp.ord_less_int (tptp.upto I2 J))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I2) J)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int J) K)) (= (tptp.upto I2 K) (tptp.append_int (tptp.upto I2 J) (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) tptp.one_one_int) K)))))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I2) J)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int J) K)) (= (tptp.upto I2 K) (tptp.append_int (tptp.upto I2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int J) tptp.one_one_int)) (tptp.upto J K)))))) (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.list_int)) (let ((_let_1 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Xa2)))) (=> (= (tptp.upto X Xa2) Y) (and (=> _let_1 (= Y (tptp.cons_int X (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) tptp.one_one_int) Xa2)))) (=> (not _let_1) (= Y tptp.nil_int)))))) (forall ((I2 tptp.int) (J tptp.int)) (let ((_let_1 (tptp.upto I2 J))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I2) J)))) (and (=> _let_2 (= _let_1 (tptp.cons_int I2 (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I2) tptp.one_one_int) J)))) (=> (not _let_2) (= _let_1 tptp.nil_int)))))) (forall ((I2 tptp.int) (J tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I2) J)) (= (tptp.upto I2 J) (tptp.cons_int I2 (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I2) tptp.one_one_int) J))))) (forall ((I2 tptp.int) (J tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I2) J)) (= (tptp.upto I2 J) (tptp.append_int (tptp.upto I2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int J) tptp.one_one_int)) (tptp.cons_int J tptp.nil_int))))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I2) J)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int J) K)) (= (tptp.upto I2 K) (tptp.append_int (tptp.upto I2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int J) tptp.one_one_int)) (tptp.cons_int J (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) tptp.one_one_int) K))))))) (forall ((M tptp.nat) (N7 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) M)) (= (tptp.finite_card_list_nat (tptp.collect_list_nat (tptp.aa_nat2079453845469346690t_bool (tptp.aTP_Lamm_anh M) N7))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.finite_card_list_nat (tptp.collect_list_nat (tptp.aa_nat2079453845469346690t_bool (tptp.aTP_Lamm_ani M) N7)))) (tptp.finite_card_list_nat (tptp.collect_list_nat (tptp.aa_nat2079453845469346690t_bool (tptp.aTP_Lamm_anj M) N7))))))) (forall ((M tptp.nat) (N7 tptp.nat)) (= (tptp.finite_card_list_nat (tptp.collect_list_nat (tptp.aa_nat2079453845469346690t_bool (tptp.aTP_Lamm_anh M) N7))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N7) M)) tptp.one_one_nat)) N7))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_list_nat (tptp.upt M) N2))) (= (tptp.linord738340561235409698at_nat tptp.aTP_Lamm_fu _let_1) _let_1))) (forall ((J tptp.nat)) (= (= (tptp.aa_nat_list_nat (tptp.upt tptp.zero_zero_nat) J) tptp.nil_nat) (= J tptp.zero_zero_nat))) (forall ((I2 tptp.nat) (J tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) J)) (= (tptp.aa_list_nat_nat tptp.hd_nat (tptp.aa_nat_list_nat (tptp.upt I2) J)) I2))) (forall ((J tptp.nat) (I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat J) I2)) (= (tptp.aa_nat_list_nat (tptp.upt I2) J) tptp.nil_nat))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.upt I2))) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) J)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat J) K))) (= (tptp.append_nat (tptp.aa_nat_list_nat _let_1 J) (tptp.aa_nat_list_nat (tptp.upt J) K)) (tptp.aa_nat_list_nat _let_1 K))))) (forall ((I2 tptp.nat) (J tptp.nat)) (= (= (tptp.aa_nat_list_nat (tptp.upt I2) J) tptp.nil_nat) (or (= J tptp.zero_zero_nat) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat J) I2))))) (forall ((I2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) M))) (let ((_let_2 (tptp.upt I2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) N2)) (= (tptp.take_nat M (tptp.aa_nat_list_nat _let_2 N2)) (tptp.aa_nat_list_nat _let_2 _let_1)))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N2))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (let ((_let_3 (tptp.aa_nat_list_nat (tptp.upt _let_2) _let_1))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_2) _let_1)))) (and (=> _let_4 (= _let_3 (tptp.cons_nat _let_2 (tptp.aa_nat_list_nat (tptp.upt (tptp.aa_nat_nat tptp.suc _let_2)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_nat)))))))) (forall ((I2 tptp.nat) (J tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) J)) (= (tptp.aa_list_nat_nat tptp.last_nat (tptp.aa_nat_list_nat (tptp.upt I2) J)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) tptp.one_one_nat)))) (forall ((I2 tptp.nat) (K tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) J)) (= (tptp.aa_nat_nat (tptp.nth_nat (tptp.aa_nat_list_nat (tptp.upt I2) J)) K) _let_1)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_list_nat_nat tptp.groups4561878855575611511st_nat (tptp.aa_nat_list_nat (tptp.upt M) N2)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat tptp.aTP_Lamm_fu) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat M) N2))))) (forall ((Ofs tptp.nat) (A tptp.nat) (B tptp.nat)) (= (tptp.map_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_hu Ofs) (tptp.aa_nat_list_nat (tptp.upt A) B)) (tptp.aa_nat_list_nat (tptp.upt (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) Ofs)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) Ofs)))) (forall ((I2 tptp.nat) (J tptp.nat) (Xs tptp.list_nat) (Ys2 tptp.list_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) J)) (= (= (tptp.aa_nat_list_nat (tptp.upt I2) J) (tptp.append_nat Xs Ys2)) (exists ((K3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) K3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K3) J)) (= (tptp.aa_nat_list_nat (tptp.upt I2) K3) Xs) (= (tptp.aa_nat_list_nat (tptp.upt K3) J) Ys2)))))) (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.upt tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) J)) (= (tptp.append_nat (tptp.aa_nat_list_nat _let_1 I2) (tptp.aa_nat_list_nat (tptp.upt I2) J)) (tptp.aa_nat_list_nat _let_1 J))))) (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.aa_nat_list_nat (tptp.upt I2) J))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) J)))) (and (=> _let_2 (= _let_1 (tptp.cons_nat I2 (tptp.aa_nat_list_nat (tptp.upt (tptp.aa_nat_nat tptp.suc I2)) J)))) (=> (not _let_2) (= _let_1 tptp.nil_nat)))))) (forall ((I2 tptp.nat) (J tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) J)) (= (tptp.aa_nat_list_nat (tptp.upt I2) J) (tptp.cons_nat I2 (tptp.aa_nat_list_nat (tptp.upt (tptp.aa_nat_nat tptp.suc I2)) J))))) (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.upt I2))) (let ((_let_2 (tptp.aa_nat_list_nat _let_1 (tptp.aa_nat_nat tptp.suc J)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) J)))) (and (=> _let_3 (= _let_2 (tptp.append_nat (tptp.aa_nat_list_nat _let_1 J) (tptp.cons_nat J tptp.nil_nat)))) (=> (not _let_3) (= _let_2 tptp.nil_nat))))))) (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.upt I2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) J)) (= (tptp.aa_nat_list_nat _let_1 (tptp.aa_nat_nat tptp.suc J)) (tptp.append_nat (tptp.aa_nat_list_nat _let_1 J) (tptp.cons_nat J tptp.nil_nat)))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) K))) (let ((_let_2 (tptp.upt I2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) J)) (= (tptp.aa_nat_list_nat _let_2 _let_1) (tptp.append_nat (tptp.aa_nat_list_nat _let_2 J) (tptp.aa_nat_list_nat (tptp.upt J) _let_1))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.upt M))) (= (tptp.butlast_nat (tptp.aa_nat_list_nat _let_1 N2)) (tptp.aa_nat_list_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat))))) (forall ((M tptp.nat) (N2 tptp.nat)) (tptp.pp (tptp.aa_list_nat_bool (tptp.sorted_wrt_nat tptp.ord_less_nat) (tptp.aa_nat_list_nat (tptp.upt M) N2)))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (tptp.map_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_hu N2) (tptp.aa_nat_list_nat (tptp.upt tptp.zero_zero_nat) M)) (tptp.aa_nat_list_nat (tptp.upt N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (tptp.pp (tptp.aa_list_nat_bool (tptp.sorted_wrt_nat tptp.ord_less_eq_nat) (tptp.aa_nat_list_nat (tptp.upt M) N2)))) (forall ((L tptp.nat) (H tptp.nat) (Is1 tptp.list_nat) (I2 tptp.nat) (Is2 tptp.list_nat)) (let ((_let_1 (tptp.upt L))) (= (= (tptp.aa_nat_list_nat _let_1 H) (tptp.append_nat Is1 (tptp.cons_nat I2 Is2))) (and (= Is1 (tptp.aa_nat_list_nat _let_1 I2)) (= Is2 (tptp.aa_nat_list_nat (tptp.upt (tptp.aa_nat_nat tptp.suc I2)) H)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat L) I2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) H)))))) (forall ((I2 tptp.nat) (J tptp.nat) (X tptp.nat) (Xs tptp.list_nat)) (= (= (tptp.aa_nat_list_nat (tptp.upt I2) J) (tptp.cons_nat X Xs)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) J)) (= I2 X) (= (tptp.aa_nat_list_nat (tptp.upt (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) tptp.one_one_nat)) J) Xs)))) (forall ((U tptp.nat) (U2 tptp.nat) (P tptp.fun_nat_bool)) (let ((_let_1 (tptp.upt tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat U) U2)) (=> (forall ((I3 tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat U) I3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) U2))) (not (tptp.pp (tptp.aa_nat_bool P I3))))) (= (tptp.filter_nat2 P (tptp.aa_nat_list_nat _let_1 U)) (tptp.filter_nat2 P (tptp.aa_nat_list_nat _let_1 U2))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.map_nat_nat tptp.aTP_Lamm_ank (tptp.aa_nat_list_nat (tptp.upt (tptp.aa_nat_nat tptp.suc M)) (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_list_nat (tptp.upt M) N2))) (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (tptp.bezw Xa2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X) Xa2)))) (let ((_let_2 (tptp.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int _let_1))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= (tptp.bezw X Xa2) Y) (and (=> _let_3 (= Y (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_3) (= Y (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int _let_2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_Pro6799258434465214121nt_int tptp.product_fst_int_int _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_2) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X) Xa2))))))))))))) (forall ((Y tptp.nat) (X tptp.nat)) (let ((_let_1 (tptp.bezw Y (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X) Y)))) (let ((_let_2 (tptp.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int _let_1))) (let ((_let_3 (tptp.bezw X Y))) (let ((_let_4 (= Y tptp.zero_zero_nat))) (and (=> _let_4 (= _let_3 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_4) (= _let_3 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int _let_2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_Pro6799258434465214121nt_int tptp.product_fst_int_int _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_2) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X) Y))))))))))))) (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.accp_P4275260045618599050at_nat tptp.bezw_rel) (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat X) Xa2))))) (let ((_let_2 (tptp.bezw Xa2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X) Xa2)))) (let ((_let_3 (tptp.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int _let_2))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= (tptp.bezw X Xa2) Y) (=> _let_1 (not (=> (and (=> _let_4 (= Y (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_4) (= Y (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int _let_3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_Pro6799258434465214121nt_int tptp.product_fst_int_int _let_2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_3) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X) Xa2)))))))) (not _let_1)))))))))) (forall ((Y tptp.nat) (X tptp.nat)) (let ((_let_1 (tptp.bezw Y (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X) Y)))) (let ((_let_2 (tptp.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int _let_1))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) Y)) (= (tptp.bezw X Y) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int _let_2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_Pro6799258434465214121nt_int tptp.product_fst_int_int _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_2) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X) Y)))))))))) (forall ((B tptp.bool) (H tptp.produc3658429121746597890et_nat)) (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn (tptp.aa_bool_assn tptp.pure_assn B)) H)) (and (= (tptp.produc8586169260539613262et_nat H) tptp.bot_bot_set_nat) (tptp.pp B)))) (forall ((H tptp.produc3658429121746597890et_nat)) (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn tptp.one_one_assn) H)) (= (tptp.produc8586169260539613262et_nat H) tptp.bot_bot_set_nat))) (forall ((P tptp.assn) (H tptp.produc3658429121746597890et_nat)) (=> (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn P) tptp.top_top_assn)) H)) (not (forall ((H5 tptp.produc3658429121746597890et_nat)) (=> (= (tptp.produc1824681642469235216et_nat H5) (tptp.produc1824681642469235216et_nat H)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat (tptp.produc8586169260539613262et_nat H5)) (tptp.produc8586169260539613262et_nat H))) (not (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn P) H5))))))))) (= tptp.bNF_Ca8459412986667044542atLess _let_11) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat M) N2)) (tptp.transi6264000038957366511cl_nat tptp.pred_nat))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat M) N2)) (tptp.transi2905341329935302413cl_nat tptp.pred_nat))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat N2) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat (tptp.aa_nat_nat tptp.suc M)) (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat M) N2)))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat B) _let_1) _let_1)))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat _let_1) B) _let_1)))) (forall ((M tptp.nat) (N2 tptp.nat) (Q5 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat N2) Q5)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat (tptp.aa_nat_nat _let_1 N2)) (tptp.aa_nat_nat _let_1 Q5))))) (forall ((M tptp.nat) (N2 tptp.nat) (Q5 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat M) N2)) Q5) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) Q5)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) Q5)))) (forall ((M tptp.nat) (I2 tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) I2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) I2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat M) N2)) I2))) (= tptp.inf_inf_nat tptp.ord_min_nat) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat M) (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_nat_nat (tptp.case_nat_nat tptp.zero_zero_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_anl N2)) M))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat (tptp.aa_nat_nat tptp.suc N2)) M) (tptp.aa_nat_nat (tptp.case_nat_nat tptp.zero_zero_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_anm N2)) M))) (= tptp.semiri1316708129612266289at_nat tptp.id_nat) (= tptp.nat2 (tptp.map_fu2345160673673942751at_nat tptp.rep_Integ tptp.id_nat _let_19)) (= tptp.ord_less_int (tptp.map_fu2743658913401090412t_bool tptp.rep_Integ _let_35 _let_17)) (= tptp.ord_less_eq_int (tptp.map_fu2743658913401090412t_bool tptp.rep_Integ _let_35 _let_15)) (= tptp.ord_le3102999989581377725nteger (tptp.map_fu1404520703793252016r_bool tptp.code_int_of_integer _let_34 tptp.ord_less_eq_int)) (= tptp.ord_le6747313008572928689nteger (tptp.map_fu1404520703793252016r_bool tptp.code_int_of_integer _let_34 tptp.ord_less_int)) (forall ((A tptp.nat) (B tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat tptp.zero_zero_nat) A) A)) (forall ((A tptp.nat) (B tptp.nat)) (= (= tptp.zero_zero_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B)) (and (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) tptp.zero_zero_nat) A)) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat tptp.zero_zero_nat) N2) N2)) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat N2) tptp.zero_zero_nat) N2)) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat (tptp.aa_nat_nat tptp.suc M)) (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat) (Q5 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat M) N2)) Q5) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) Q5)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) Q5)))) (forall ((M tptp.nat) (N2 tptp.nat) (Q5 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat N2) Q5)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat (tptp.aa_nat_nat _let_1 N2)) (tptp.aa_nat_nat _let_1 Q5))))) (forall ((M tptp.nat) (N2 tptp.nat) (Q5 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat N2) Q5)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat (tptp.aa_nat_nat _let_1 N2)) (tptp.aa_nat_nat _let_1 Q5))))) (forall ((M tptp.nat) (N2 tptp.nat) (Q5 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat M) N2)) Q5) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) Q5)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) Q5)))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M)) M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat N2) M))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat _let_1) M) (tptp.aa_nat_nat (tptp.case_nat_nat _let_1 (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_ann N2)) M)))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat M) _let_1) (tptp.aa_nat_nat (tptp.case_nat_nat _let_1 (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_ano N2)) M)))) (tptp.semila1623282765462674594er_nat tptp.ord_max_nat tptp.zero_zero_nat tptp.aTP_Lamm_df tptp.aTP_Lamm_dg) (= tptp.sup_sup_nat tptp.ord_max_nat) (forall ((N7 tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.inj_on_nat_nat tptp.suc) N7))) (forall ((N7 tptp.set_nat) (K tptp.nat)) (=> (forall ((N5 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N5) N7)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N5)))) (tptp.pp (tptp.aa_set_nat_bool (tptp.inj_on_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_amp K)) N7)))) (forall ((X tptp.rat)) (= (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X) (tptp.the_int (tptp.aTP_Lamm_anp X)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (= X Y)))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.abs_abs_rat A))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)))) (and (=> _let_2 (= _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat A))) (=> (not _let_2) (= _let_1 A)))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.sgn_sgn_rat A))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)))) (let ((_let_3 (= A tptp.zero_zero_rat))) (and (=> _let_3 (= _let_1 tptp.zero_zero_rat)) (=> (not _let_3) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)))))))))) (forall ((Q5 tptp.int) (P3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Q5) tptp.zero_zero_int)) (= (tptp.aa_Pro6970504127699319548nt_int tptp.normalize (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int P3) Q5)) (tptp.aa_Pro6970504127699319548nt_int tptp.normalize (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int tptp.uminus_uminus_int P3)) (tptp.aa_int_int tptp.uminus_uminus_int Q5)))))) (forall ((P3 tptp.int)) (= (tptp.aa_Pro6970504127699319548nt_int tptp.normalize (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int P3) tptp.zero_zero_int)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))) (forall ((R3 tptp.product_prod_int_int) (P3 tptp.int) (Q5 tptp.int)) (=> (= (tptp.aa_Pro6970504127699319548nt_int tptp.normalize R3) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int P3) Q5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Q5)))) (forall ((Q5 tptp.int) (S2 tptp.int) (P3 tptp.int) (R3 tptp.int)) (=> (not (= Q5 tptp.zero_zero_int)) (=> (not (= S2 tptp.zero_zero_int)) (=> (= (tptp.aa_Pro6970504127699319548nt_int tptp.normalize (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int P3) Q5)) (tptp.aa_Pro6970504127699319548nt_int tptp.normalize (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int R3) S2))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int P3) S2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int R3) Q5)))))) (forall ((P3 tptp.product_prod_int_int)) (let ((_let_1 (tptp.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int P3))) (let ((_let_2 (tptp.aa_Pro6799258434465214121nt_int tptp.product_fst_int_int P3))) (let ((_let_3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int _let_2) _let_1))) (let ((_let_4 (tptp.aa_int_int tptp.uminus_uminus_int _let_3))) (let ((_let_5 (tptp.aa_int_fun_int_int tptp.divide_divide_int _let_1))) (let ((_let_6 (tptp.aa_int_fun_int_int tptp.divide_divide_int _let_2))) (let ((_let_7 (tptp.aa_Pro6970504127699319548nt_int tptp.normalize P3))) (let ((_let_8 (= _let_1 tptp.zero_zero_int))) (let ((_let_9 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) _let_1)))) (and (=> _let_9 (= _let_7 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int _let_6 _let_3)) (tptp.aa_int_int _let_5 _let_3)))) (=> (not _let_9) (and (=> _let_8 (= _let_7 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))) (=> (not _let_8) (= _let_7 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int _let_6 _let_4)) (tptp.aa_int_int _let_5 _let_4))))))))))))))))) (= (tptp.quotient_of _let_33) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int _let_32) tptp.one_one_int)) (forall ((M tptp.int) (N2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int M) N2))) (or (not (= M tptp.zero_zero_int)) (not (= N2 tptp.zero_zero_int))))) (forall ((K tptp.num)) (= (tptp.quotient_of (tptp.aa_num_rat tptp.numeral_numeral_rat K)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_num_int tptp.numeral_numeral_int K)) tptp.one_one_int))) (= (tptp.quotient_of tptp.one_one_rat) _let_27) (= (tptp.quotient_of tptp.zero_zero_rat) _let_26) (forall ((K tptp.num)) (= (tptp.quotient_of (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat K))) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int K))) tptp.one_one_int))) (forall ((X tptp.int) (Y tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int X) Y)))) (forall ((R3 tptp.rat) (N2 tptp.int) (D2 tptp.int)) (=> (= (tptp.quotient_of R3) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int N2) D2)) (= R3 (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat N2)) (tptp.aa_int_rat tptp.ring_1_of_int_rat D2))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int A) B)) A)))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int A) B)) B)))) (forall ((X tptp.int) (Y tptp.int) (P tptp.fun_int_bool)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.gcd_gcd_int X))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int _let_1 Y))))) (let ((_let_3 (tptp.aa_int_int tptp.uminus_uminus_int Y))) (let ((_let_4 (tptp.aa_int_fun_int_int tptp.gcd_gcd_int (tptp.aa_int_int tptp.uminus_uminus_int X)))) (let ((_let_5 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) tptp.zero_zero_int)))) (let ((_let_6 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) tptp.zero_zero_int)))) (let ((_let_7 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_8 (tptp.pp (tptp.aa_int_bool _let_7 Y)))) (let ((_let_9 (tptp.pp (tptp.aa_int_bool _let_7 X)))) (=> (=> _let_9 (=> _let_8 _let_2)) (=> (=> _let_9 (=> _let_5 (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int _let_1 _let_3))))) (=> (=> _let_6 (=> _let_8 (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int _let_4 Y))))) (=> (=> _let_6 (=> _let_5 (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int _let_4 _let_3))))) _let_2)))))))))))))) (forall ((D2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D2))) (= (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) D2)) (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 B)) (forall ((E3 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int E3))) (=> (and (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 B))) (tptp.pp (tptp.aa_int_bool _let_1 D2)))))) (= D2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int A) B))))) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Y)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int X) Y) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int Y) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int X) Y))))) (forall ((R3 tptp.rat) (P3 tptp.int) (Q5 tptp.int)) (=> (= (tptp.quotient_of R3) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int P3) Q5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Q5)))) (forall ((R3 tptp.rat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int (tptp.quotient_of R3))))) (forall ((N2 tptp.int) (M tptp.int)) (=> (not (= N2 tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int M) N2) (tptp.lattic8263393255366662781ax_int (tptp.collect_int (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_anq N2) M)))))) (forall ((P3 tptp.rat)) (= (tptp.quotient_of (tptp.aa_rat_rat tptp.uminus_uminus_rat P3)) (tptp.aa_Pro6970504127699319548nt_int (tptp.aa_fun8026974734089330650nt_int tptp.produc4245557441103728435nt_int tptp.aTP_Lamm_anr) (tptp.quotient_of P3)))) (forall ((P3 tptp.rat) (Q5 tptp.rat)) (= (tptp.quotient_of (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat P3) Q5)) (tptp.aa_Pro6970504127699319548nt_int (tptp.aa_fun8026974734089330650nt_int tptp.produc4245557441103728435nt_int (tptp.aTP_Lamm_ant Q5)) (tptp.quotient_of P3)))) (forall ((P3 tptp.rat) (Q5 tptp.rat)) (= (tptp.quotient_of (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat P3) Q5)) (tptp.aa_Pro6970504127699319548nt_int (tptp.aa_fun8026974734089330650nt_int tptp.produc4245557441103728435nt_int (tptp.aTP_Lamm_anv Q5)) (tptp.quotient_of P3)))) (forall ((P3 tptp.rat) (Q5 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat P3) Q5)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool (tptp.aTP_Lamm_anx Q5)) (tptp.quotient_of P3))))) (forall ((P3 tptp.rat) (Q5 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat P3) Q5)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool (tptp.aTP_Lamm_anz Q5)) (tptp.quotient_of P3))))) (forall ((P3 tptp.rat)) (= (tptp.aa_rat_int tptp.archim3151403230148437115or_rat P3) (tptp.aa_Pro6799258434465214121nt_int (tptp.aa_fun914008879417524284nt_int tptp.produc8211389475949308722nt_int tptp.divide_divide_int) (tptp.quotient_of P3)))) (forall ((P3 tptp.rat)) (= (tptp.quotient_of (tptp.aa_rat_rat tptp.abs_abs_rat P3)) (tptp.aa_Pro6970504127699319548nt_int (tptp.aa_fun8026974734089330650nt_int tptp.produc4245557441103728435nt_int tptp.aTP_Lamm_aoa) (tptp.quotient_of P3)))) (forall ((P3 tptp.rat) (Q5 tptp.rat)) (= (tptp.quotient_of (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat P3) Q5)) (tptp.aa_Pro6970504127699319548nt_int (tptp.aa_fun8026974734089330650nt_int tptp.produc4245557441103728435nt_int (tptp.aTP_Lamm_aoc Q5)) (tptp.quotient_of P3)))) (forall ((P3 tptp.rat) (Q5 tptp.rat)) (= (tptp.quotient_of (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat P3) Q5)) (tptp.aa_Pro6970504127699319548nt_int (tptp.aa_fun8026974734089330650nt_int tptp.produc4245557441103728435nt_int (tptp.aTP_Lamm_aoe Q5)) (tptp.quotient_of P3)))) (forall ((P3 tptp.rat)) (= (tptp.quotient_of (tptp.aa_rat_rat tptp.sgn_sgn_rat P3)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int tptp.sgn_sgn_int (tptp.aa_Pro6799258434465214121nt_int tptp.product_fst_int_int (tptp.quotient_of P3)))) tptp.one_one_int))) (forall ((A tptp.int)) (= (tptp.quotient_of (tptp.aa_int_rat tptp.of_int A)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) tptp.one_one_int))) (forall ((P3 tptp.rat)) (= (tptp.quotient_of (tptp.aa_rat_rat tptp.inverse_inverse_rat P3)) (tptp.aa_Pro6970504127699319548nt_int (tptp.aa_fun8026974734089330650nt_int tptp.produc4245557441103728435nt_int tptp.aTP_Lamm_aof) (tptp.quotient_of P3)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat M) N2))) (or (not (= M tptp.zero_zero_nat)) (not (= N2 tptp.zero_zero_nat))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat A) B)) A)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat A) B)) B)))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M)) N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat M) N2)))) (forall ((A3 tptp.set_nat)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A4) A3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B4) A3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat A4) B4)) A3))))) (=> (not (= A3 tptp.bot_bot_set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat (tptp.aa_set_nat_nat tptp.gcd_Gcd_nat A3)) A3))))) (forall ((B tptp.nat) (A tptp.nat)) (exists ((X3 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat A) B))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (let ((_let_3 (tptp.aa_nat_nat _let_2 Y3))) (let ((_let_4 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B))) (let ((_let_5 (tptp.aa_nat_nat _let_4 X3))) (let ((_let_6 (tptp.aa_nat_nat _let_4 Y3))) (let ((_let_7 (tptp.aa_nat_nat _let_2 X3))) (or (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_6) _let_7)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat _let_7) _let_6) _let_1)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_3) _let_5)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat _let_5) _let_3) _let_1)))))))))))) (tptp.semila1623282765462674594er_nat tptp.gcd_gcd_nat tptp.zero_zero_nat tptp.dvd_dvd_nat tptp.aTP_Lamm_adw) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat M) N2) (tptp.aa_set_nat_nat tptp.lattic8265883725875713057ax_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_aog N2) M)))))) (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.accp_P4275260045618599050at_nat tptp.gcd_nat_rel) (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat X) Xa2))))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y X)) (=> (not _let_2) (= Y (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat Xa2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X) Xa2))))) (not _let_1)))))))) (forall ((K tptp.num)) (= (tptp.frct (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.one_one_int) (tptp.aa_num_int tptp.numeral_numeral_int K))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat tptp.one_one_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat K)))) (forall ((A tptp.int)) (= (tptp.frct (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) tptp.zero_zero_int)) tptp.zero_zero_rat)) (forall ((A tptp.int)) (= (tptp.frct (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) A)) tptp.zero_zero_rat)) (= (tptp.frct _let_27) tptp.one_one_rat) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A))) (= (tptp.frct (tptp.aa_int7462565939943104719nt_int _let_1 (tptp.aa_int_int tptp.uminus_uminus_int B))) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.frct (tptp.aa_int7462565939943104719nt_int _let_1 B)))))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.frct (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.frct (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) B))))) (forall ((K tptp.num)) (= (tptp.frct (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_num_int tptp.numeral_numeral_int K)) tptp.one_one_int)) (tptp.aa_num_rat tptp.numeral_numeral_rat K))) (forall ((K tptp.num) (L tptp.num)) (= (tptp.frct (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_num_int tptp.numeral_numeral_int K)) (tptp.aa_num_int tptp.numeral_numeral_int L))) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_num_rat tptp.numeral_numeral_rat K)) (tptp.aa_num_rat tptp.numeral_numeral_rat L)))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B))) (let ((_let_2 (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat _let_1)) _let_2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_2) (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int)))))))) (forall ((B tptp.int) (D2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) D2))) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D2 tptp.zero_zero_int)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B)) (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract C) D2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) D2)) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B)) _let_1)))))))) (forall ((B tptp.int) (D2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) D2))) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D2 tptp.zero_zero_int)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B)) (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract C) D2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) D2)) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B)) _let_1)))))))) (forall ((A tptp.int) (B tptp.int) (P3 tptp.int) (Q5 tptp.int)) (let ((_let_1 (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B))) (=> (= (tptp.quotient_of _let_1) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int P3) Q5)) (= (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract P3) Q5) _let_1)))) (forall ((P tptp.fun_rat_bool) (Q5 tptp.rat)) (=> (forall ((A4 tptp.int) (B4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B4)) (tptp.pp (tptp.aa_rat_bool P (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A4) B4))))) (tptp.pp (tptp.aa_rat_bool P Q5)))) (forall ((A tptp.int) (B tptp.int) (P3 tptp.int) (Q5 tptp.int)) (=> (= (tptp.aa_Pro6970504127699319548nt_int tptp.normalize (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) B)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int P3) Q5)) (= (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract P3) Q5) (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.quotient_of (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B)) (tptp.aa_Pro6970504127699319548nt_int tptp.normalize (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) B)))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B)) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B))) (tptp.pp (tptp.aa_int_bool _let_1 A)))))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B)) tptp.one_one_rat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B))))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A))))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A))))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B)) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int))))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A))))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B)) tptp.one_one_rat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B))))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_rat_bool tptp.positive (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A) B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B))))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (tptp.pp (tptp.aa_rat_bool tptp.positive (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat Y) X))))) (= tptp.positive (tptp.map_fu5118516228767806217l_bool tptp.rep_Rat tptp.id_bool tptp.aTP_Lamm_aoh)) (forall ((X tptp.rat)) (let ((_let_1 (tptp.aa_rat7754553326175492643nt_int tptp.rep_Rat X))) (= (tptp.pp (tptp.aa_rat_bool tptp.positive X)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_Pro6799258434465214121nt_int tptp.product_fst_int_int _let_1)) (tptp.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int _let_1))))))) (= tptp.plus_plus_rat (tptp.map_fu5968964422797239547at_rat tptp.rep_Rat _let_31 tptp.aTP_Lamm_aoi)) (= tptp.inverse_inverse_rat (tptp.aa_fun7041730090766645614at_rat _let_31 tptp.aTP_Lamm_aoj)) (= tptp.one_one_rat (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat _let_27)) (forall ((Xa2 tptp.int) (X tptp.int)) (= (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract Xa2) X) (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat (tptp.aa_Pro6970504127699319548nt_int (tptp.if_Pro3027730157355071871nt_int (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int X) tptp.zero_zero_int) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Xa2) X))))) (= tptp.zero_zero_rat (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat _let_26)) (= tptp.fract (tptp.map_fu7945985449245211511nt_rat tptp.id_int (tptp.map_fu3424225382358772769nt_rat tptp.id_int tptp.abs_Rat) tptp.aTP_Lamm_aok)) (= tptp.uminus_uminus_rat (tptp.aa_fun7041730090766645614at_rat _let_31 tptp.aTP_Lamm_aol)) (= tptp.times_times_rat (tptp.map_fu5968964422797239547at_rat tptp.rep_Rat _let_31 tptp.aTP_Lamm_aom)) (forall ((Xa2 tptp.product_prod_int_int) (X tptp.product_prod_int_int)) (let ((_let_1 (tptp.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int X))) (let ((_let_2 (tptp.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int Xa2))) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool tptp.ratrel Xa2) Xa2)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool tptp.ratrel X) X)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat Xa2)) (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat X)) (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_Pro6799258434465214121nt_int tptp.product_fst_int_int Xa2)) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_Pro6799258434465214121nt_int tptp.product_fst_int_int X)) _let_2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_2) _let_1))))))))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool tptp.ratrel _let_27) _let_27)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool tptp.ratrel _let_26) _let_26)) (forall ((X5 tptp.product_prod_int_int) (Xa3 tptp.product_prod_int_int)) (let ((_let_1 (tptp.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int X5))) (let ((_let_2 (tptp.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int Xa3))) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool tptp.ratrel X5) Xa3)) (and (not (= _let_1 tptp.zero_zero_int)) (not (= _let_2 tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_Pro6799258434465214121nt_int tptp.product_fst_int_int X5)) _let_2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_Pro6799258434465214121nt_int tptp.product_fst_int_int Xa3)) _let_1))))))) (forall ((X tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool tptp.ratrel X) X)) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat X)) (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_Pro6799258434465214121nt_int tptp.product_fst_int_int X))) (tptp.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int X)))))) (forall ((Xa2 tptp.product_prod_int_int) (X tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool tptp.ratrel Xa2) Xa2)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool tptp.ratrel X) X)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat Xa2)) (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat X)) (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_Pro6799258434465214121nt_int tptp.product_fst_int_int Xa2)) (tptp.aa_Pro6799258434465214121nt_int tptp.product_fst_int_int X))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int Xa2)) (tptp.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int X)))))))) (forall ((X tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool tptp.ratrel X) X)) (= (tptp.pp (tptp.aa_rat_bool tptp.positive (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat X))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_Pro6799258434465214121nt_int tptp.product_fst_int_int X)) (tptp.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int X))))))) (forall ((X tptp.product_prod_int_int)) (let ((_let_1 (tptp.aa_Pro6799258434465214121nt_int tptp.product_fst_int_int X))) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool tptp.ratrel X) X)) (= (tptp.aa_rat_rat tptp.inverse_inverse_rat (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat X)) (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat (tptp.aa_Pro6970504127699319548nt_int (tptp.if_Pro3027730157355071871nt_int (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int _let_1) tptp.zero_zero_int) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int X)) _let_1))))))) (forall ((X5 tptp.product_prod_int_int) (Xa3 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.cr_rat X5) Xa3)) (and (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool tptp.ratrel X5) X5)) (= (tptp.aa_Pro6166618844887768661nt_rat tptp.abs_Rat X5) Xa3)))) (= tptp.code_dup (tptp.map_fu2599414010547811884nteger tptp.code_int_of_integer tptp.code_integer_of_int tptp.aTP_Lamm_aon)) (forall ((X tptp.rat)) (= (tptp.quotient_of X) (tptp.the_Pr4378521158711661632nt_int (tptp.aTP_Lamm_aoo X)))) (forall ((Q5 tptp.int) (P3 tptp.int)) (let ((_let_1 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int P3) Q5))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Q5)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int P3) Q5)) (= (tptp.aa_Pro6970504127699319548nt_int tptp.normalize _let_1) _let_1))))) (forall ((R3 tptp.rat) (P3 tptp.int) (Q5 tptp.int)) (=> (= (tptp.quotient_of R3) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int P3) Q5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int P3) Q5)))) (forall ((R3 tptp.product_prod_int_int) (P3 tptp.int) (Q5 tptp.int)) (=> (= (tptp.aa_Pro6970504127699319548nt_int tptp.normalize R3) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int P3) Q5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int P3) Q5)))) (forall ((P tptp.fun_rat_bool) (Q5 tptp.rat)) (=> (forall ((A4 tptp.int) (B4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int A4) B4)) (tptp.pp (tptp.aa_rat_bool P (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A4) B4)))))) (tptp.pp (tptp.aa_rat_bool P Q5)))) (forall ((Q5 tptp.rat)) (not (forall ((A4 tptp.int) (B4 tptp.int)) (=> (= Q5 (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A4) B4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B4)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int A4) B4)))))))) (forall ((Q5 tptp.rat)) (=> (forall ((A4 tptp.int) (B4 tptp.int)) (=> (= Q5 (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract A4) B4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) B4)) (=> (not (= A4 tptp.zero_zero_int)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int A4) B4))))))) (= Q5 tptp.zero_zero_rat))) (forall ((R3 tptp.rat)) (exists ((X3 tptp.product_prod_int_int)) (let ((_let_1 (tptp.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int X3))) (let ((_let_2 (tptp.aa_Pro6799258434465214121nt_int tptp.product_fst_int_int X3))) (and (= R3 (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract _let_2) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int _let_2) _let_1)) (forall ((Y4 tptp.product_prod_int_int)) (let ((_let_1 (tptp.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int Y4))) (let ((_let_2 (tptp.aa_Pro6799258434465214121nt_int tptp.product_fst_int_int Y4))) (=> (and (= R3 (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract _let_2) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int _let_2) _let_1))) (= Y4 X3)))))))))) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.algebr934650988132801477me_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat)) N2)))) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.algebr934650988132801477me_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat))))) (tptp.bNF_re1394333895916556125l_bool tptp.ratrel tptp.fequal_bool tptp.aTP_Lamm_aoh tptp.aTP_Lamm_aoh) (tptp.bNF_re6378542964492772123um_int tptp.fequal_num (tptp.bNF_re1822329894187522285nt_int tptp.fequal_num tptp.fequal_int) tptp.aTP_Lamm_aop tptp.aTP_Lamm_aop) (tptp.bNF_re4808202430149235895nt_int tptp.fequal_int (tptp.bNF_re6250860962936578807nt_int tptp.fequal_int tptp.ratrel) tptp.aTP_Lamm_aok tptp.aTP_Lamm_aok) (tptp.bNF_re4712519889275205905nt_int tptp.fequal_int tptp.fequal_int tptp.aTP_Lamm_aon tptp.aTP_Lamm_aon) (tptp.bNF_re5780769757191362231t_bool tptp.fequal_int _let_29 tptp.ord_less_eq_int tptp.ord_less_eq_int) (tptp.bNF_re1480548845665215743t_bool tptp.fequal_nat _let_30 tptp.ord_less_eq_nat tptp.ord_less_eq_nat) (tptp.bNF_re1480548845665215743t_bool tptp.fequal_nat _let_30 tptp.ord_less_nat tptp.ord_less_nat) (tptp.bNF_re5780769757191362231t_bool tptp.fequal_int _let_29 tptp.ord_less_int tptp.ord_less_int) (tptp.bNF_re4734134812813710757nt_int tptp.ratrel _let_28 tptp.aTP_Lamm_aom tptp.aTP_Lamm_aom) (tptp.bNF_re4734134812813710757nt_int tptp.ratrel _let_28 tptp.aTP_Lamm_aoi tptp.aTP_Lamm_aoi) (tptp.pp (tptp.aa_fun1403452029515102102t_bool (tptp.aa_fun8298786006102058668t_bool _let_28 tptp.aTP_Lamm_aol) tptp.aTP_Lamm_aol)) (tptp.pp (tptp.aa_fun1403452029515102102t_bool (tptp.aa_fun8298786006102058668t_bool _let_28 tptp.aTP_Lamm_aoj) tptp.aTP_Lamm_aoj)) (tptp.bNF_re6323452265856231590at_rat tptp.pcr_rat _let_25 tptp.aTP_Lamm_aoi tptp.plus_plus_rat) (tptp.pp (tptp.aa_rat_bool (tptp.aa_Pro6332413336323567195t_bool tptp.pcr_rat _let_27) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_Pro6332413336323567195t_bool tptp.pcr_rat _let_26) tptp.zero_zero_rat)) (tptp.bNF_re2486238095283335024nt_rat tptp.fequal_int (tptp.bNF_re2214769303045360666nt_rat tptp.fequal_int tptp.pcr_rat) tptp.aTP_Lamm_aok tptp.fract) (tptp.pp (tptp.aa_fun_rat_rat_bool (tptp.aa_fun2103967415933125506t_bool _let_25 tptp.aTP_Lamm_aol) tptp.uminus_uminus_rat)) (tptp.bNF_re6323452265856231590at_rat tptp.pcr_rat _let_25 tptp.aTP_Lamm_aom tptp.times_times_rat) (tptp.bNF_re3535474257078034868l_bool tptp.pcr_rat tptp.fequal_bool tptp.aTP_Lamm_aoh tptp.positive) (tptp.pp (tptp.aa_fun_rat_rat_bool (tptp.aa_fun2103967415933125506t_bool _let_25 tptp.aTP_Lamm_aoj) tptp.inverse_inverse_rat)) (tptp.bNF_re8869769828555196650nt_int tptp.pcr_int _let_23 _let_22 tptp.times_times_int) (tptp.pp (tptp.aa_int_bool (tptp.aa_Pro2928840338864870335t_bool tptp.pcr_int _let_21) tptp.zero_zero_int)) (tptp.bNF_re6830278522597306478at_int tptp.fequal_nat tptp.pcr_int tptp.aTP_Lamm_aoq tptp.semiri1314217659103216013at_int) (tptp.pp (tptp.aa_fun_int_int_bool (tptp.aa_fun7527181275634263258t_bool _let_23 _let_20) tptp.uminus_uminus_int)) (tptp.bNF_re4555766996558763186at_nat tptp.pcr_int tptp.fequal_nat _let_19 tptp.nat2) (tptp.pp (tptp.aa_int_bool (tptp.aa_Pro2928840338864870335t_bool tptp.pcr_int _let_18) tptp.one_one_int)) (tptp.bNF_re2632563231991741785t_bool tptp.pcr_int _let_24 _let_17 tptp.ord_less_int) (tptp.bNF_re2632563231991741785t_bool tptp.pcr_int _let_24 _let_15 tptp.ord_less_eq_int) (tptp.bNF_re8869769828555196650nt_int tptp.pcr_int _let_23 _let_12 tptp.plus_plus_int) (tptp.bNF_re8869769828555196650nt_int tptp.pcr_int _let_23 _let_14 tptp.minus_minus_int) (forall ((X6 tptp.set_int)) (= (tptp.complete_Sup_Sup_int X6) (tptp.the_int (tptp.aTP_Lamm_aor X6)))) (tptp.bNF_re6214786843070381989at_nat tptp.intrel _let_13 _let_22 _let_22) (forall ((X tptp.nat) (Y tptp.nat) (U tptp.nat) (V tptp.nat)) (= (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool tptp.intrel (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat X) Y)) (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat U) V))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) V) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat U) Y)))) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool tptp.intrel _let_21) _let_21)) (tptp.pp (tptp.aa_fun4519828053337421206t_bool (tptp.aa_fun2399787666232550060t_bool _let_13 _let_20) _let_20)) (tptp.bNF_re8246922863344978751at_nat tptp.intrel tptp.fequal_nat _let_19 _let_19) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool tptp.intrel _let_18) _let_18)) (= tptp.intrel (tptp.aa_fun174371099813217148t_bool tptp.produc5023667602222594023t_bool tptp.aTP_Lamm_aot)) (tptp.bNF_re2219331435504962769t_bool tptp.intrel _let_16 _let_17 _let_17) (tptp.bNF_re2219331435504962769t_bool tptp.intrel _let_16 _let_15 _let_15) (tptp.bNF_re6214786843070381989at_nat tptp.intrel _let_13 _let_14 _let_14) (tptp.bNF_re6214786843070381989at_nat tptp.intrel _let_13 _let_12 _let_12) (forall ((P tptp.fun_nat_bool) (K tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P K)) (=> (forall ((Y3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P Y3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y3) B)))) (tptp.pp (tptp.aa_nat_bool P (tptp.order_Greatest_nat P)))))) (forall ((P tptp.fun_nat_bool) (K tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P K)) (=> (forall ((Y3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P Y3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y3) B)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) (tptp.order_Greatest_nat P)))))) (forall ((P tptp.fun_nat_bool) (B tptp.nat)) (=> (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool P X_13))) (=> (forall ((Y3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P Y3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y3) B)))) (tptp.pp (tptp.aa_nat_bool P (tptp.order_Greatest_nat P)))))) (forall ((N2 tptp.nat)) (= (tptp.field_nat (tptp.collec3392354462482085612at_nat (tptp.produc8955392012077580105t_bool (tptp.aTP_Lamm_aou N2)))) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_dg N2)))) (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.wf_nat _let_11)) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat X) Y)) tptp.less_than)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)))) (forall ((N2 tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) (tptp.aa_nat_nat tptp.suc I2)))) (= (tptp.aa_nat_nat (tptp.nth_nat (tptp.linord2614967742042102400et_nat (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or5834768355832116004an_nat I2) J))) N2) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) N2))))) (forall ((S tptp.set_nat) (N2 tptp.nat)) (=> (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) (tptp.aa_nat_nat (tptp.infini8530281810654367211te_nat S) N2))))) (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc I2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) J)) (= (tptp.linord2614967742042102400et_nat (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or5834768355832116004an_nat I2) J)) (tptp.cons_nat _let_1 (tptp.linord2614967742042102400et_nat (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or5834768355832116004an_nat _let_1) J))))))) (forall ((S tptp.set_nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_set_nat_nat tptp.finite_card_nat S))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) (tptp.aa_nat_nat (tptp.infini8530281810654367211te_nat S) N2)))))) (forall ((N2 tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) I2))) (= (tptp.aa_nat_nat (tptp.nth_nat (tptp.linord2614967742042102400et_nat (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or6659071591806873216st_nat I2) J))) N2) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) N2))))) (forall ((P tptp.fun_nat_bool)) (=> (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat)) (= (tptp.ord_Least_nat P) tptp.zero_zero_nat))) (forall ((L tptp.code_integer) (U tptp.code_integer)) (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.set_or4266950643985792945nteger L U)))) (forall ((X6 tptp.set_nat)) (= (tptp.aa_set_nat_nat tptp.complete_Inf_Inf_nat X6) (tptp.ord_Least_nat (tptp.aTP_Lamm_ae X6)))) (forall ((P tptp.fun_nat_bool) (N2 tptp.nat) (Q tptp.fun_nat_bool) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P N2)) (=> (tptp.pp (tptp.aa_nat_bool Q M)) (=> (not (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat))) (=> (forall ((K2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc K2))) (tptp.pp (tptp.aa_nat_bool Q K2)))) (= (tptp.ord_Least_nat P) (tptp.aa_nat_nat tptp.suc (tptp.ord_Least_nat Q)))))))) (forall ((P tptp.fun_nat_bool) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P N2)) (=> (not (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat))) (= (tptp.ord_Least_nat P) (tptp.aa_nat_nat tptp.suc (tptp.ord_Least_nat (tptp.aTP_Lamm_aov P))))))) (forall ((L tptp.code_integer) (U tptp.code_integer)) (= (tptp.set_or8404916559141939852nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger L) tptp.one_one_Code_integer) U) (tptp.set_or4266950643985792945nteger L U))) (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc I2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) J)) (= (tptp.linord2614967742042102400et_nat (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or6659071591806873216st_nat I2) J)) (tptp.cons_nat _let_1 (tptp.linord2614967742042102400et_nat (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or6659071591806873216st_nat _let_1) J))))))) (forall ((L tptp.code_integer) (U tptp.code_integer)) (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger (tptp.set_or2715278749043346189nteger L U)))) (forall ((L tptp.code_integer) (U tptp.code_integer)) (= (tptp.set_or189985376899183464nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger L) tptp.one_one_Code_integer) U) (tptp.set_or2715278749043346189nteger L U))) (forall ((K tptp.nat)) (= (tptp.aa_nat_set_nat tptp.set_ord_atLeast_nat (tptp.aa_nat_nat tptp.suc K)) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat (tptp.aa_nat_set_nat tptp.set_ord_atLeast_nat K)) (tptp.insert_nat K tptp.bot_bot_set_nat)))) (= (tptp.comple7399068483239264473et_nat (tptp.image_nat_set_nat tptp.set_ord_atLeast_nat tptp.top_top_set_nat)) tptp.top_top_set_nat) (tptp.filter3212408913953519116et_nat tptp.set_ord_atMost_nat _let_10 tptp.at_top_nat) (tptp.filter3212408913953519116et_nat tptp.set_ord_lessThan_nat _let_10 tptp.at_top_nat) (tptp.filterlim_nat_nat tptp.suc tptp.at_top_nat tptp.at_top_nat) (not (= tptp.at_top_nat tptp.bot_bot_filter_nat)) (forall ((M6 tptp.set_nat) (N7 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool (tptp.bij_betw_nat_nat tptp.suc) M6) N7)) (= (tptp.image_nat_nat tptp.suc M6) N7))) (forall ((X tptp.product_unit)) (tptp.pp (tptp.member_bool (tptp.aa_Product_unit_bool tptp.product_Rep_unit X) (tptp.insert_bool tptp.fTrue tptp.bot_bot_set_bool)))) (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (= (tptp.pp (tptp.aa_Product_unit_bool tptp.product_Rep_unit X)) (tptp.pp (tptp.aa_Product_unit_bool tptp.product_Rep_unit Y))) (= X Y))) (forall ((Y tptp.bool) (P tptp.fun_bool_bool)) (=> (tptp.pp (tptp.member_bool Y (tptp.insert_bool tptp.fTrue tptp.bot_bot_set_bool))) (=> (forall ((X3 tptp.product_unit)) (tptp.pp (tptp.aa_bool_bool P (tptp.aa_Product_unit_bool tptp.product_Rep_unit X3)))) (tptp.pp (tptp.aa_bool_bool P Y))))) (forall ((Y tptp.bool)) (=> (tptp.pp (tptp.member_bool Y (tptp.insert_bool tptp.fTrue tptp.bot_bot_set_bool))) (not (forall ((X3 tptp.product_unit)) (= (tptp.pp Y) (not (tptp.pp (tptp.aa_Product_unit_bool tptp.product_Rep_unit X3)))))))) (tptp.type_d5772988228442255350t_bool tptp.product_Rep_unit tptp.product_Abs_unit _let_9) (forall ((Y tptp.bool)) (=> (tptp.pp (tptp.member_bool Y (tptp.insert_bool tptp.fTrue tptp.bot_bot_set_bool))) (= (tptp.pp (tptp.aa_Product_unit_bool tptp.product_Rep_unit (tptp.aa_bool_Product_unit tptp.product_Abs_unit Y))) (tptp.pp Y)))) (forall ((X tptp.product_unit)) (= (tptp.aa_bool_Product_unit tptp.product_Abs_unit (tptp.aa_Product_unit_bool tptp.product_Rep_unit X)) X)) (forall ((X tptp.product_unit)) (not (forall ((Y3 tptp.bool)) (=> (= X (tptp.aa_bool_Product_unit tptp.product_Abs_unit Y3)) (not (tptp.pp (tptp.member_bool Y3 (tptp.insert_bool tptp.fTrue tptp.bot_bot_set_bool)))))))) (forall ((P tptp.fun_Pr1572506220757514509t_bool) (X tptp.product_unit)) (=> (forall ((Y3 tptp.bool)) (=> (tptp.pp (tptp.member_bool Y3 (tptp.insert_bool tptp.fTrue tptp.bot_bot_set_bool))) (tptp.pp (tptp.aa_Product_unit_bool P (tptp.aa_bool_Product_unit tptp.product_Abs_unit Y3))))) (tptp.pp (tptp.aa_Product_unit_bool P X)))) (forall ((X tptp.bool) (Y tptp.bool)) (let ((_let_1 (tptp.insert_bool tptp.fTrue tptp.bot_bot_set_bool))) (=> (tptp.pp (tptp.member_bool X _let_1)) (=> (tptp.pp (tptp.member_bool Y _let_1)) (= (= (tptp.aa_bool_Product_unit tptp.product_Abs_unit X) (tptp.aa_bool_Product_unit tptp.product_Abs_unit Y)) (= (tptp.pp X) (tptp.pp Y))))))) (forall ((P tptp.fun_nat_bool)) (= (tptp.eventually_nat (tptp.aTP_Lamm_aov P) tptp.at_top_nat) (tptp.eventually_nat P tptp.at_top_nat))) (forall ((P tptp.fun_nat_bool) (K tptp.nat)) (= (tptp.eventually_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_aow P) K) tptp.at_top_nat) (tptp.eventually_nat P tptp.at_top_nat))) (forall ((F3 tptp.filter_nat)) (= (tptp.ord_le2510731241096832064er_nat F3 tptp.at_top_nat) (forall ((N9 tptp.nat)) (tptp.eventually_nat (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N9) F3)))) (forall ((C tptp.nat) (P tptp.fun_nat_bool)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) X3)) (tptp.pp (tptp.aa_nat_bool P X3)))) (tptp.eventually_nat P tptp.at_top_nat))) (forall ((P tptp.fun_nat_bool)) (= (tptp.eventually_nat P tptp.at_top_nat) (exists ((N9 tptp.nat)) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N9) N)) (tptp.pp (tptp.aa_nat_bool P N))))))) (not (tptp.eventually_nat tptp.aTP_Lamm_bg tptp.at_top_nat)) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.bNF_We3818239936649020644el_nat (tptp.collec3392354462482085612at_nat (tptp.produc8955392012077580105t_bool (tptp.aTP_Lamm_aou N2)))))) (= tptp.top_to1996260823553986621t_unit _let_6) (= tptp.bot_bot_Product_unit tptp.product_Unity) (= tptp.product_Unity (tptp.aa_bool_Product_unit tptp.product_Abs_unit tptp.fTrue)) (forall ((Uu tptp.product_unit) (Uv tptp.product_unit)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.sup_sup_Product_unit Uu) Uv) tptp.product_Unity)) (forall ((Uu tptp.set_Product_unit)) (= (tptp.comple2584293577114468500t_unit Uu) tptp.product_Unity)) (forall ((Y tptp.product_unit)) (= Y tptp.product_Unity)) (= tptp.top_top_Product_unit tptp.product_Unity) (forall ((Uu tptp.product_unit)) (= (tptp.uminus2952777764628376836t_unit Uu) tptp.product_Unity)) (forall ((Uu tptp.set_Product_unit)) (= (tptp.comple4687483117567863418t_unit Uu) tptp.product_Unity)) (forall ((Uu tptp.product_unit) (Uv tptp.product_unit)) (= (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit Uu) Uv) tptp.product_Unity)) (forall ((N2 tptp.nat)) (= (tptp.heap_Time_wait N2) (tptp.heap_T6183433275982383450t_unit (tptp.aTP_Lamm_aox N2)))) (= tptp.defaul566961228789861419t_unit tptp.product_Unity) (forall ((B tptp.code_natural) (I2 tptp.code_natural)) (let ((_let_1 (tptp.log B I2))) (let ((_let_2 (or (tptp.pp (tptp.aa_Code_natural_bool (tptp.aa_Cod6910080592713026658l_bool tptp.ord_le1926595141338095240atural B) tptp.one_one_Code_natural)) (tptp.pp (tptp.aa_Code_natural_bool (tptp.aa_Cod6910080592713026658l_bool tptp.ord_le5570908160329646204atural I2) B))))) (and (=> _let_2 (= _let_1 tptp.one_one_Code_natural)) (=> (not _let_2) (= _let_1 (tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural (tptp.log B (tptp.divide5121882707175180666atural I2 B))))))))) (forall ((X tptp.code_natural) (Xa2 tptp.code_natural) (Y tptp.code_natural)) (let ((_let_1 (or (tptp.pp (tptp.aa_Code_natural_bool (tptp.aa_Cod6910080592713026658l_bool tptp.ord_le1926595141338095240atural X) tptp.one_one_Code_natural)) (tptp.pp (tptp.aa_Code_natural_bool (tptp.aa_Cod6910080592713026658l_bool tptp.ord_le5570908160329646204atural Xa2) X))))) (=> (= (tptp.log X Xa2) Y) (and (=> _let_1 (= Y tptp.one_one_Code_natural)) (=> (not _let_1) (= Y (tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural (tptp.log X (tptp.divide5121882707175180666atural Xa2 X))))))))) (forall ((X tptp.code_natural) (Xa2 tptp.code_natural) (Y tptp.code_natural)) (let ((_let_1 (tptp.accp_P8126237942716283194atural tptp.log_rel (tptp.produc3574140220909816553atural X Xa2)))) (let ((_let_2 (or (tptp.pp (tptp.aa_Code_natural_bool (tptp.aa_Cod6910080592713026658l_bool tptp.ord_le1926595141338095240atural X) tptp.one_one_Code_natural)) (tptp.pp (tptp.aa_Code_natural_bool (tptp.aa_Cod6910080592713026658l_bool tptp.ord_le5570908160329646204atural Xa2) X))))) (=> (= (tptp.log X Xa2) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y tptp.one_one_Code_natural)) (=> (not _let_2) (= Y (tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural (tptp.log X (tptp.divide5121882707175180666atural Xa2 X)))))) (not _let_1)))))))) (forall ((K tptp.code_natural) (L tptp.code_natural) (R3 tptp.code_natural)) (let ((_let_1 (tptp.minus_shift R3 K L))) (let ((_let_2 (tptp.pp (tptp.aa_Code_natural_bool (tptp.aa_Cod6910080592713026658l_bool tptp.ord_le5570908160329646204atural K) L)))) (and (=> _let_2 (= _let_1 (tptp.minus_7197305767214868737atural (tptp.plus_p4538020629002901425atural R3 K) L))) (=> (not _let_2) (= _let_1 (tptp.minus_7197305767214868737atural K L))))))) (forall ((X tptp.produc6284619029570389740atural)) (not (forall ((F2 tptp.fun_Co621691207274083130e_term) (D tptp.code_natural) (I3 tptp.code_natural)) (not (= X (tptp.produc1507819840854600734atural F2 (tptp.produc3574140220909816553atural D I3))))))) (forall ((X tptp.produc651309673056299192atural)) (not (forall ((F2 tptp.fun_Pr8336614522058983534e_term) (D tptp.code_natural) (I3 tptp.code_natural)) (not (= X (tptp.produc2566709293081654762atural F2 (tptp.produc3574140220909816553atural D I3))))))) (forall ((X tptp.produc7822875418678951345atural)) (not (forall ((B4 tptp.code_natural) (I3 tptp.code_natural)) (not (= X (tptp.produc3574140220909816553atural B4 I3)))))) (forall ((V tptp.code_natural) (W2 tptp.code_natural)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 tptp.one))) (let ((_let_2 (tptp.aa_num_num tptp.bit1 _let_1))) (let ((_let_3 (tptp.aa_num_num tptp.bit0 _let_1))) (let ((_let_4 (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 _let_3)))))))))))))))) (let ((_let_5 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_6 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 _let_5)))))) (let ((_let_7 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 _let_2)))))))))))))))))))))) (let ((_let_8 (tptp.minus_shift (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 _let_7))))))))) (tptp.times_2397367101498566445atural (tptp.modulo8411746178871703098atural W2 _let_4) (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 _let_6)))))))))))) (tptp.times_2397367101498566445atural (tptp.divide5121882707175180666atural W2 _let_4) (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 _let_2)))))))))))))) (let ((_let_9 (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 _let_3)))))))))))))))) (let ((_let_10 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 _let_7))))))))) (let ((_let_11 (tptp.minus_shift (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit1 _let_10)) (tptp.times_2397367101498566445atural (tptp.modulo8411746178871703098atural V _let_9) (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 _let_6)))))))))))) (tptp.times_2397367101498566445atural (tptp.divide5121882707175180666atural V _let_9) (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 _let_5))))))))))))))))) (= (tptp.aa_Pro7165575656943818355atural tptp.next (tptp.produc3574140220909816553atural V W2)) (tptp.aa_Pro7165575656943818355atural (tptp.produc6639722614265839536atural (tptp.plus_p4538020629002901425atural (tptp.minus_shift (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 _let_10)) _let_11 (tptp.plus_p4538020629002901425atural _let_8 tptp.one_one_Code_natural)) tptp.one_one_Code_natural)) (tptp.produc3574140220909816553atural _let_11 _let_8))))))))))))))) (forall ((S2 tptp.produc7822875418678951345atural)) (= (tptp.split_seed S2) (tptp.produc8282080750456430313atural (tptp.aTP_Lamm_aoz S2) S2))) (forall ((K tptp.code_natural)) (= (tptp.range K) (tptp.produc5538323210962509403atural (tptp.iterat8892046348760725948atural (tptp.log (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 tptp.one))))))))))))))))))))))))))))))) K) tptp.aTP_Lamm_apb tptp.one_one_Code_natural) (tptp.aTP_Lamm_apc K)))) (forall ((K tptp.code_natural) (S2 tptp.produc7822875418678951345atural)) (=> (tptp.pp (tptp.aa_Code_natural_bool (tptp.aa_Cod6910080592713026658l_bool tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) K)) (tptp.pp (tptp.aa_Code_natural_bool (tptp.aa_Cod6910080592713026658l_bool tptp.ord_le5570908160329646204atural (tptp.produc497848011034438852atural (tptp.aa_Pro7165575656943818355atural (tptp.range K) S2))) K)))) (forall ((Xa2 tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_Code_natural_bool (tptp.aa_Cod6910080592713026658l_bool tptp.ord_le5570908160329646204atural (tptp.aa_nat_Code_natural tptp.code_natural_of_nat Xa2)) (tptp.aa_nat_Code_natural tptp.code_natural_of_nat X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Xa2) X)))) (forall ((Xa2 tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_Code_natural_bool (tptp.aa_Cod6910080592713026658l_bool tptp.ord_le1926595141338095240atural (tptp.aa_nat_Code_natural tptp.code_natural_of_nat Xa2)) (tptp.aa_nat_Code_natural tptp.code_natural_of_nat X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Xa2) X)))) (forall ((X tptp.code_natural) (Xa2 tptp.code_natural)) (= (tptp.pp (tptp.aa_Code_natural_bool (tptp.aa_Cod6910080592713026658l_bool tptp.ord_le1926595141338095240atural X) Xa2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_Code_natural_nat tptp.code_nat_of_natural X)) (tptp.aa_Code_natural_nat tptp.code_nat_of_natural Xa2))))) (forall ((X tptp.code_natural) (Xa2 tptp.code_natural)) (= (tptp.pp (tptp.aa_Code_natural_bool (tptp.aa_Cod6910080592713026658l_bool tptp.ord_le5570908160329646204atural X) Xa2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_Code_natural_nat tptp.code_nat_of_natural X)) (tptp.aa_Code_natural_nat tptp.code_nat_of_natural Xa2))))) (= tptp.ord_le5570908160329646204atural (tptp.map_fu675752389954593592l_bool tptp.code_nat_of_natural _let_8 tptp.ord_less_nat)) (= tptp.ord_le1926595141338095240atural (tptp.map_fu675752389954593592l_bool tptp.code_nat_of_natural _let_8 tptp.ord_less_eq_nat)) (forall ((N2 tptp.code_natural)) (let ((_let_1 (tptp.aa_Code_natural_nat tptp.code_nat_of_natural N2))) (=> (not (= N2 tptp.zero_z2226904508553997617atural)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat _let_1) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) _let_1))))) (forall ((M tptp.nat) (K tptp.int) (L tptp.int) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.bit_concat_bit M) K) L)) N2)) (or (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N2))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int L) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M))))))) (forall ((N2 tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.bit_concat_bit N2) K) L))) (tptp.pp (tptp.aa_int_bool _let_1 L))))) (forall ((N2 tptp.nat) (K tptp.int) (L tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.bit_concat_bit N2) K) L)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int L) tptp.zero_zero_int)))) (forall ((A tptp.nat) (B tptp.nat) (S2 tptp.nat) (T5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat S2) T5)) (tptp.member8206827879206165904at_nat (tptp.produc6161850002892822231at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat A) S2) (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat B) T5)) tptp.fun_pair_less)))) (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (tptp.total_3592101749530773125at_nat A3 tptp.fun_pair_less)) (tptp.trans_4347625901269045472at_nat tptp.fun_pair_less) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat X))) (= (tptp.member8206827879206165904at_nat (tptp.produc6161850002892822231at_nat (tptp.aa_nat7603221163087113075at_nat _let_1 Y) (tptp.aa_nat7603221163087113075at_nat _let_1 Z)) tptp.fun_pair_less) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) Z))))) (= tptp.fun_pair_less (tptp.lex_prod_nat_nat tptp.less_than tptp.less_than)) (tptp.wf_Pro7803398752247294826at_nat tptp.fun_pair_less) (forall ((A tptp.nat) (B tptp.nat) (S2 tptp.nat) (T5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (tptp.member8206827879206165904at_nat (tptp.produc6161850002892822231at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat A) S2) (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat B) T5)) tptp.fun_pair_less))) (forall ((X tptp.product_prod_nat_nat) (XS tptp.set_Pr1261947904930325089at_nat) (Y tptp.product_prod_nat_nat) (YS tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat X) XS)) (=> (tptp.member8206827879206165904at_nat (tptp.produc6161850002892822231at_nat X Y) tptp.fun_pair_less) (=> (tptp.member8757157785044589968at_nat (tptp.produc2922128104949294807at_nat XS YS) tptp.fun_min_strict) (tptp.member8757157785044589968at_nat (tptp.produc2922128104949294807at_nat XS (tptp.insert8211810215607154385at_nat Y YS)) tptp.fun_min_strict))))) (forall ((A tptp.nat) (B tptp.nat) (S2 tptp.nat) (T5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat S2) T5)) (tptp.member8206827879206165904at_nat (tptp.produc6161850002892822231at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat A) S2) (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat B) T5)) tptp.fun_pair_leq)))) (= tptp.fun_pair_leq (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat tptp.fun_pair_less) tptp.id_Pro2258643101195443293at_nat)) (forall ((X6 tptp.set_Pr1261947904930325089at_nat)) (=> (not (= X6 tptp.bot_bo2099793752762293965at_nat)) (tptp.member8757157785044589968at_nat (tptp.produc2922128104949294807at_nat X6 tptp.bot_bo2099793752762293965at_nat) tptp.fun_min_strict))) (= tptp.fun_min_strict (tptp.min_ex6901939911449802026at_nat tptp.fun_pair_less)) (forall ((A tptp.nat) (B tptp.nat) (S2 tptp.nat) (T5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (tptp.member8206827879206165904at_nat (tptp.produc6161850002892822231at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat A) S2) (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat B) T5)) tptp.fun_pair_leq))) (forall ((Y tptp.product_prod_nat_nat) (YS tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (XS tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat Y) YS)) (=> (tptp.member8206827879206165904at_nat (tptp.produc6161850002892822231at_nat X Y) tptp.fun_pair_leq) (=> (tptp.member8757157785044589968at_nat (tptp.produc2922128104949294807at_nat XS YS) tptp.fun_max_weak) (tptp.member8757157785044589968at_nat (tptp.produc2922128104949294807at_nat (tptp.insert8211810215607154385at_nat X XS) YS) tptp.fun_max_weak))))) (forall ((X tptp.product_prod_nat_nat) (XS tptp.set_Pr1261947904930325089at_nat) (Y tptp.product_prod_nat_nat) (YS tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat X) XS)) (=> (tptp.member8206827879206165904at_nat (tptp.produc6161850002892822231at_nat X Y) tptp.fun_pair_leq) (=> (tptp.member8757157785044589968at_nat (tptp.produc2922128104949294807at_nat XS YS) tptp.fun_min_weak) (tptp.member8757157785044589968at_nat (tptp.produc2922128104949294807at_nat XS (tptp.insert8211810215607154385at_nat Y YS)) tptp.fun_min_weak))))) (forall ((X6 tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat X6)) (tptp.member8757157785044589968at_nat (tptp.produc2922128104949294807at_nat tptp.bot_bo2099793752762293965at_nat X6) tptp.fun_max_weak))) (forall ((X6 tptp.set_Pr1261947904930325089at_nat)) (tptp.member8757157785044589968at_nat (tptp.produc2922128104949294807at_nat X6 tptp.bot_bo2099793752762293965at_nat) tptp.fun_min_weak)) (tptp.fun_re2478310338295953701at_nat (tptp.produc9060074326276436823at_nat tptp.fun_min_strict tptp.fun_min_weak)) (= tptp.fun_min_weak (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat (tptp.min_ex6901939911449802026at_nat tptp.fun_pair_leq)) _let_7)) (= tptp.fun_max_weak (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat (tptp.max_ex8135407076693332796at_nat tptp.fun_pair_leq)) _let_7)) (forall ((Y tptp.product_prod_nat_nat) (Y6 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (X6 tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat Y) Y6)) (=> (tptp.member8206827879206165904at_nat (tptp.produc6161850002892822231at_nat X Y) tptp.fun_pair_less) (=> (tptp.member8757157785044589968at_nat (tptp.produc2922128104949294807at_nat X6 Y6) tptp.fun_max_strict) (tptp.member8757157785044589968at_nat (tptp.produc2922128104949294807at_nat (tptp.insert8211810215607154385at_nat X X6) Y6) tptp.fun_max_strict))))) (= tptp.fun_max_strict (tptp.max_ex8135407076693332796at_nat tptp.fun_pair_less)) (tptp.fun_re2478310338295953701at_nat (tptp.produc9060074326276436823at_nat tptp.fun_max_strict tptp.fun_max_weak)) (forall ((Y6 tptp.set_Pr1261947904930325089at_nat)) (=> (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat Y6)) (=> (not (= Y6 tptp.bot_bo2099793752762293965at_nat)) (tptp.member8757157785044589968at_nat (tptp.produc2922128104949294807at_nat tptp.bot_bo2099793752762293965at_nat Y6) tptp.fun_max_strict)))) (forall ((K tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.euclid3395696857347342551nt_int K))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))))))) (forall ((A3 tptp.multis2468970476368604999at_nat) (B3 tptp.multis2468970476368604999at_nat) (Z3 tptp.multis2468970476368604999at_nat)) (let ((_let_1 (tptp.plus_p7104986032573967614at_nat Z3))) (=> (or (tptp.member8757157785044589968at_nat (tptp.produc2922128104949294807at_nat (tptp.set_ms8126754132646256062at_nat A3) (tptp.set_ms8126754132646256062at_nat B3)) tptp.fun_max_strict) (and (= A3 tptp.zero_z1048942125864253310at_nat) (= B3 tptp.zero_z1048942125864253310at_nat))) (tptp.member6689249552917799696at_nat (tptp.produc4348348721325984599at_nat (tptp.aa_mul5754855110707352700at_nat _let_1 A3) (tptp.aa_mul5754855110707352700at_nat _let_1 B3)) tptp.ms_weak)))) (forall ((A3 tptp.multis2468970476368604999at_nat) (B3 tptp.multis2468970476368604999at_nat) (Z3 tptp.multis2468970476368604999at_nat)) (let ((_let_1 (tptp.plus_p7104986032573967614at_nat Z3))) (=> (tptp.member8757157785044589968at_nat (tptp.produc2922128104949294807at_nat (tptp.set_ms8126754132646256062at_nat A3) (tptp.set_ms8126754132646256062at_nat B3)) tptp.fun_max_strict) (tptp.member6689249552917799696at_nat (tptp.produc4348348721325984599at_nat (tptp.aa_mul5754855110707352700at_nat _let_1 A3) (tptp.aa_mul5754855110707352700at_nat _let_1 B3)) tptp.ms_strict)))) (tptp.fun_re7357418987779152907at_nat (tptp.produc5245064249948416855at_nat tptp.ms_strict tptp.ms_weak)) (= tptp.ms_weak (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat tptp.ms_strict) tptp.id_mul2649389997224486051at_nat)) (forall ((Z3 tptp.multis2468970476368604999at_nat) (Z7 tptp.multis2468970476368604999at_nat) (A3 tptp.multis2468970476368604999at_nat) (B3 tptp.multis2468970476368604999at_nat)) (=> (tptp.pw_leq Z3 Z7) (=> (tptp.member8757157785044589968at_nat (tptp.produc2922128104949294807at_nat (tptp.set_ms8126754132646256062at_nat A3) (tptp.set_ms8126754132646256062at_nat B3)) tptp.fun_max_strict) (tptp.member6689249552917799696at_nat (tptp.produc4348348721325984599at_nat (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat Z3) A3) (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat Z7) B3)) tptp.ms_strict)))) (forall ((Z3 tptp.multis2468970476368604999at_nat) (Z7 tptp.multis2468970476368604999at_nat) (A3 tptp.multis2468970476368604999at_nat) (B3 tptp.multis2468970476368604999at_nat)) (=> (tptp.pw_leq Z3 Z7) (=> (tptp.member8757157785044589968at_nat (tptp.produc2922128104949294807at_nat (tptp.set_ms8126754132646256062at_nat A3) (tptp.set_ms8126754132646256062at_nat B3)) tptp.fun_max_strict) (tptp.member6689249552917799696at_nat (tptp.produc4348348721325984599at_nat (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat Z3) A3) (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat Z7) B3)) tptp.ms_weak)))) (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (=> (tptp.member8206827879206165904at_nat (tptp.produc6161850002892822231at_nat X Y) tptp.fun_pair_leq) (tptp.pw_leq (tptp.add_ms2612439473150266591at_nat X tptp.zero_z1048942125864253310at_nat) (tptp.add_ms2612439473150266591at_nat Y tptp.zero_z1048942125864253310at_nat)))) (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat) (X6 tptp.multis2468970476368604999at_nat) (Y6 tptp.multis2468970476368604999at_nat)) (=> (tptp.member8206827879206165904at_nat (tptp.produc6161850002892822231at_nat X Y) tptp.fun_pair_leq) (=> (tptp.pw_leq X6 Y6) (tptp.pw_leq (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat (tptp.add_ms2612439473150266591at_nat X tptp.zero_z1048942125864253310at_nat)) X6) (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat (tptp.add_ms2612439473150266591at_nat Y tptp.zero_z1048942125864253310at_nat)) Y6))))) (forall ((A1 tptp.multis2468970476368604999at_nat) (A22 tptp.multis2468970476368604999at_nat)) (= (tptp.pw_leq A1 A22) (or (and (= A1 tptp.zero_z1048942125864253310at_nat) (= A22 tptp.zero_z1048942125864253310at_nat)) (exists ((X4 tptp.product_prod_nat_nat) (Y5 tptp.product_prod_nat_nat) (X9 tptp.multis2468970476368604999at_nat) (Y7 tptp.multis2468970476368604999at_nat)) (and (= A1 (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat (tptp.add_ms2612439473150266591at_nat X4 tptp.zero_z1048942125864253310at_nat)) X9)) (= A22 (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat (tptp.add_ms2612439473150266591at_nat Y5 tptp.zero_z1048942125864253310at_nat)) Y7)) (tptp.member8206827879206165904at_nat (tptp.produc6161850002892822231at_nat X4 Y5) tptp.fun_pair_leq) (tptp.pw_leq X9 Y7)))))) (forall ((A1 tptp.multis2468970476368604999at_nat) (A22 tptp.multis2468970476368604999at_nat)) (=> (tptp.pw_leq A1 A22) (=> (=> (= A1 tptp.zero_z1048942125864253310at_nat) (not (= A22 tptp.zero_z1048942125864253310at_nat))) (not (forall ((X3 tptp.product_prod_nat_nat) (Y3 tptp.product_prod_nat_nat) (X10 tptp.multis2468970476368604999at_nat)) (=> (= A1 (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat (tptp.add_ms2612439473150266591at_nat X3 tptp.zero_z1048942125864253310at_nat)) X10)) (forall ((Y8 tptp.multis2468970476368604999at_nat)) (=> (= A22 (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat (tptp.add_ms2612439473150266591at_nat Y3 tptp.zero_z1048942125864253310at_nat)) Y8)) (=> (tptp.member8206827879206165904at_nat (tptp.produc6161850002892822231at_nat X3 Y3) tptp.fun_pair_leq) (not (tptp.pw_leq X10 Y8))))))))))) (forall ((Z3 tptp.multis2468970476368604999at_nat) (Z7 tptp.multis2468970476368604999at_nat)) (=> (tptp.pw_leq Z3 Z7) (tptp.member6689249552917799696at_nat (tptp.produc4348348721325984599at_nat (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat Z3) tptp.zero_z1048942125864253310at_nat) (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat Z7) tptp.zero_z1048942125864253310at_nat)) tptp.ms_weak))) (forall ((X6 tptp.multis2468970476368604999at_nat) (Y6 tptp.multis2468970476368604999at_nat)) (=> (tptp.pw_leq X6 Y6) (exists ((A6 tptp.multis2468970476368604999at_nat) (B9 tptp.multis2468970476368604999at_nat) (Z8 tptp.multis2468970476368604999at_nat)) (and (= X6 (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat A6) Z8)) (= Y6 (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat B9) Z8)) (or (tptp.member8757157785044589968at_nat (tptp.produc2922128104949294807at_nat (tptp.set_ms8126754132646256062at_nat A6) (tptp.set_ms8126754132646256062at_nat B9)) tptp.fun_max_strict) (and (= B9 tptp.zero_z1048942125864253310at_nat) (= A6 tptp.zero_z1048942125864253310at_nat))))))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.order_2888998067076097458on_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_dg N2))) (tptp.collec3392354462482085612at_nat (tptp.produc8955392012077580105t_bool (tptp.aTP_Lamm_aou N2)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.collec3392354462482085612at_nat (tptp.produc8955392012077580105t_bool (tptp.aTP_Lamm_aou N2))))) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.order_2888998067076097458on_nat (tptp.field_nat _let_1)) _let_1)))) (= tptp.bNF_Cardinal_cone (tptp.bNF_Ca7083678892733797993t_unit _let_6)) (and (not (tptp.member1730920086087385872l_bool (tptp.produc5355662241087601495l_bool tptp.bNF_Cardinal_ctwo tptp.bNF_Ca1500629177841160323o_bool) tptp.bNF_We9067914441000329236l_bool)) (tptp.bNF_Ca3869711322664823701n_bool (tptp.field_bool tptp.bNF_Cardinal_ctwo) tptp.bNF_Cardinal_ctwo)) (tptp.member3042533333095794346at_nat (tptp.produc4079257842390172913at_nat tptp.bNF_Cardinal_ctwo tptp.bNF_Ca8665028551170535155natLeq) tptp.bNF_We6144460630316186525ol_nat) (= tptp.bNF_Ca8665028551170535155natLeq (tptp.collec3392354462482085612at_nat (tptp.produc8955392012077580105t_bool tptp.ord_less_eq_nat))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_set_nat (tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N2) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_dg N2)))) (forall ((N2 tptp.nat)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat tptp.bNF_Ca8665028551170535155natLeq) (tptp.produc457027306803732586at_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_dg N2)) (tptp.aa_nat1818925681583257441et_nat tptp.aTP_Lamm_apd N2))) (tptp.collec3392354462482085612at_nat (tptp.produc8955392012077580105t_bool (tptp.aTP_Lamm_aou N2))))) (forall ((Uu tptp.product_prod_int_int)) (let ((_let_1 (tptp.aa_Pro6799258434465214121nt_int tptp.product_fst_int_int Uu))) (= (tptp.aa_Pro6970504127699319548nt_int tptp.aTP_Lamm_aoj Uu) (tptp.aa_Pro6970504127699319548nt_int (tptp.if_Pro3027730157355071871nt_int (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int _let_1) tptp.zero_zero_int) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int Uu)) _let_1))))) (forall ((Uu tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool tptp.aTP_Lamm_ag Uu)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uu) (tptp.lim_Product_unit tptp.h2))) (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uu) tptp.as1)))))) (forall ((Uu tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool tptp.aTP_Lamm_ah Uu)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uu) (tptp.lim_Product_unit tptp.h2))) (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uu) tptp.as)))))) (forall ((Uu tptp.product_prod_int_int)) (= (tptp.aa_Pro6970504127699319548nt_int tptp.aTP_Lamm_aol Uu) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_Pro6799258434465214121nt_int tptp.product_fst_int_int Uu))) (tptp.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int Uu)))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_nat tptp.aTP_Lamm_ank Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (forall ((Uu tptp.int)) (= (tptp.aa_int_int tptp.aTP_Lamm_aon Uu) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Uu) Uu))) (forall ((Uu tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.aTP_Lamm_gf Uu) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger Uu) tptp.one_one_Code_integer))) (forall ((Uu tptp.rat)) (= (tptp.aa_rat_rat tptp.aTP_Lamm_gc Uu) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Uu) tptp.one_one_rat))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_nat tptp.aTP_Lamm_ge Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) tptp.one_one_nat))) (forall ((Uu tptp.int)) (= (tptp.aa_int_int tptp.aTP_Lamm_gd Uu) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Uu) tptp.one_one_int))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat7603221163087113075at_nat tptp.aTP_Lamm_aoq Uu) (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat Uu) tptp.zero_zero_nat))) (forall ((Uu tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool tptp.aTP_Lamm_aoh Uu)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_Pro6799258434465214121nt_int tptp.product_fst_int_int Uu)) (tptp.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int Uu)))))) (forall ((Uu tptp.code_natural)) (= (tptp.aa_Cod6352003912080677724atural tptp.aTP_Lamm_apb Uu) (tptp.produc5538323210962509403atural tptp.next (tptp.aTP_Lamm_apa Uu)))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_set_nat tptp.aTP_Lamm_anc Uu) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_adt Uu)))) (forall ((Uu tptp.num)) (= (tptp.aa_num_option_num tptp.aTP_Lamm_amo Uu) (tptp.aa_num_option_num tptp.some_num (tptp.aa_num_num tptp.bit1 Uu)))) (forall ((Uu tptp.num)) (= (tptp.aa_num_option_num tptp.aTP_Lamm_agv Uu) (tptp.aa_num_option_num tptp.some_num (tptp.aa_num_num tptp.bit0 Uu)))) (forall ((Uu tptp.int)) (= (tptp.aa_int2565445551602696444nt_int tptp.aTP_Lamm_anr Uu) (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int tptp.uminus_uminus_int Uu)))) (forall ((Uu tptp.int)) (= (tptp.aa_int2565445551602696444nt_int tptp.aTP_Lamm_aoa Uu) (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int tptp.abs_abs_int Uu)))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat8803788312118491388at_nat tptp.aTP_Lamm_agq Uu) (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat (tptp.aa_nat_nat tptp.suc Uu)))) (forall ((Uu tptp.int)) (= (tptp.aa_int_nat tptp.aTP_Lamm_and Uu) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.abs_abs_int Uu)))) (forall ((Uu tptp.num) (Uua tptp.nat)) (= (tptp.aa_nat_option_num (tptp.aTP_Lamm_ajg Uu) Uua) (tptp.aa_num_option_num (tptp.case_num_option_num (tptp.aa_num_option_num tptp.some_num tptp.one) (tptp.aTP_Lamm_aje Uua) (tptp.aTP_Lamm_ajf Uua)) Uu))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aTP_Lamm_ads Uu) Uua) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))) tptp.zero_z3403309356797280102nteger))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_adq Uu) Uua) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))) tptp.zero_zero_rat))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int tptp.aTP_Lamm_adr Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.if_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))) tptp.zero_zero_int))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_Code_integer_int tptp.code_int_of_integer Uu)))) (= (tptp.aa_Code_integer_int (tptp.aa_Cod1242632294114111009er_int tptp.aTP_Lamm_amg Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.if_int (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer Uua) tptp.zero_z3403309356797280102nteger)) _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int))))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer)) (let ((_let_1 (tptp.code_num_of_integer Uu))) (let ((_let_2 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num _let_1) _let_1))) (= (tptp.aa_Code_integer_num (tptp.aa_Cod6128727250572145423er_num tptp.aTP_Lamm_amf Uu) Uua) (tptp.aa_num_num (tptp.aa_num_fun_num_num (tptp.if_num (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer Uua) tptp.zero_z3403309356797280102nteger)) _let_2) (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num _let_2) tptp.one)))))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer)) (let ((_let_1 (tptp.aa_Code_integer_nat tptp.code_nat_of_integer Uu))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) _let_1))) (= (tptp.aa_Code_integer_nat (tptp.aa_Cod5420483313623307717er_nat tptp.aTP_Lamm_amj Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer Uua) tptp.zero_z3403309356797280102nteger)) _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_2) tptp.one_one_nat)))))) (forall ((Uu tptp.int) (Uua tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.aTP_Lamm_aof Uu) Uua) (tptp.aa_Pro6970504127699319548nt_int (tptp.if_Pro3027730157355071871nt_int (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int Uu) tptp.zero_zero_int) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.sgn_sgn_int Uu)) Uua)) (tptp.aa_int_int tptp.abs_abs_int Uu))))) (forall ((Uu tptp.int) (Uua tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.aTP_Lamm_aok Uu) Uua) (tptp.aa_Pro6970504127699319548nt_int (tptp.if_Pro3027730157355071871nt_int (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int Uua) tptp.zero_zero_int) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aTP_Lamm_adp Uu) Uua) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_bool_bool tptp.fNot (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))) tptp.zero_z3403309356797280102nteger))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_adn Uu) Uua) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.aa_bool_bool tptp.fNot (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))) tptp.zero_zero_rat))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int tptp.aTP_Lamm_ado Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.if_int (tptp.aa_bool_bool tptp.fNot (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))) tptp.zero_zero_int))) (forall ((Uu tptp.option8963830502488799655at_nat) (Uua tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set2934564513904597954at_nat (tptp.aTP_Lamm_en Uu) Uua) (tptp.case_o311359030874850053at_nat tptp.none_s625347054029921090at_nat (tptp.aTP_Lamm_em Uua) Uu))) (forall ((Uu tptp.option_Product_unit) (Uua tptp.product_unit)) (= (tptp.aa_Pro7616171890175246658t_unit (tptp.aTP_Lamm_el Uu) Uua) (tptp.case_o2985186191577459077t_unit tptp.none_Product_unit (tptp.aTP_Lamm_ek Uua) Uu))) (forall ((Uu tptp.option_nat) (Uua tptp.nat)) (= (tptp.aa_nat_option_nat (tptp.aTP_Lamm_ej Uu) Uua) (tptp.case_o7429725398727453821at_nat tptp.none_nat (tptp.aTP_Lamm_ei Uua) Uu))) (forall ((Uu tptp.option_assn) (Uua tptp.assn)) (= (tptp.aa_assn_option_assn (tptp.aTP_Lamm_eh Uu) Uua) (tptp.case_o4484465799723439917n_assn tptp.none_assn (tptp.aTP_Lamm_eg Uua) Uu))) (forall ((Uu tptp.option_set_nat) (Uua tptp.set_nat)) (= (tptp.aa_set6119337032432945050et_nat (tptp.aTP_Lamm_ef Uu) Uua) (tptp.case_o4054078431260844265et_nat tptp.none_set_nat (tptp.aTP_Lamm_ee Uua) Uu))) (forall ((Uu tptp.option_num) (Uua tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aTP_Lamm_fc Uu) Uua)) (tptp.pp (tptp.aa_option_num_bool (tptp.case_option_bool_num tptp.fTrue (tptp.aa_num_fun_num_bool tptp.aTP_Lamm_fb Uua)) Uu)))) (forall ((Uu tptp.option_int) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aTP_Lamm_fe Uu) Uua)) (tptp.case_option_bool_int tptp.fTrue (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_dk Uua) Uu))) (forall ((Uu tptp.option_rat) (Uua tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aTP_Lamm_fa Uu) Uua)) (tptp.case_option_bool_rat tptp.fTrue (tptp.aa_rat_fun_rat_bool tptp.aTP_Lamm_di Uua) Uu))) (forall ((Uu tptp.option_nat) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aTP_Lamm_fd Uu) Uua)) (tptp.case_option_bool_nat tptp.fTrue (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_dg Uua) Uu))) (forall ((Uu tptp.option_assn) (Uua tptp.assn)) (= (tptp.pp (tptp.aa_assn_bool (tptp.aTP_Lamm_ez Uu) Uua)) (tptp.case_o1042097560232087540l_assn tptp.fTrue (tptp.aa_ass5323576183532441186n_bool tptp.aTP_Lamm_dc Uua) Uu))) (forall ((Uu tptp.nat) (Uua tptp.num)) (= (tptp.aa_num_option_num (tptp.aa_nat3713591252005393295on_num tptp.aTP_Lamm_ajh Uu) Uua) (tptp.aa_nat_option_num (tptp.case_nat_option_num tptp.none_num (tptp.aTP_Lamm_ajg Uua)) Uu))) (forall ((Uu tptp.option_set_int) (Uua tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aTP_Lamm_eu Uu) Uua)) (tptp.case_o8226980026459171502et_int tptp.fFalse (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int Uua) Uu))) (forall ((Uu tptp.option_rat) (Uua tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aTP_Lamm_ev Uu) Uua)) (tptp.case_option_bool_rat tptp.fFalse (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Uua) Uu))) (forall ((Uu tptp.option_num) (Uua tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aTP_Lamm_ew Uu) Uua)) (tptp.pp (tptp.aa_option_num_bool (tptp.case_option_bool_num tptp.fFalse (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Uua)) Uu)))) (forall ((Uu tptp.option_nat) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aTP_Lamm_ex Uu) Uua)) (tptp.case_option_bool_nat tptp.fFalse (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Uua) Uu))) (forall ((Uu tptp.option_int) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aTP_Lamm_ey Uu) Uua)) (tptp.case_option_bool_int tptp.fFalse (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Uua) Uu))) (forall ((Uu tptp.nat) (Uua tptp.num)) (= (tptp.aa_num_option_num (tptp.aTP_Lamm_aje Uu) Uua) (tptp.aa_opt5369159329878751634on_num (tptp.case_o6005452278849405969um_num tptp.none_num tptp.aTP_Lamm_agv) (tptp.aa_num_option_num (tptp.bit_take_bit_num Uu) Uua)))) (forall ((Uu tptp.fun_nat_fun_nat_int) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aTP_Lamm_ahc Uu) Uua) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_ahb Uu) Uua)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat Uua)))) (forall ((Uu tptp.fun_nat_fun_nat_nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aTP_Lamm_aha Uu) Uua) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_agy Uu) Uua)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat Uua)))) (forall ((Uu tptp.fun_nat_fun_nat_nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aTP_Lamm_agz Uu) Uua) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_agy Uu) Uua)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat Uua)))) (forall ((Uu tptp.product_prod_int_int) (Uua tptp.product_prod_int_int)) (let ((_let_1 (tptp.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int Uua))) (let ((_let_2 (tptp.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int Uu))) (= (tptp.aa_Pro6970504127699319548nt_int (tptp.aa_Pro4124234152028750080nt_int tptp.aTP_Lamm_aoi Uu) Uua) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_Pro6799258434465214121nt_int tptp.product_fst_int_int Uu)) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_Pro6799258434465214121nt_int tptp.product_fst_int_int Uua)) _let_2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_2) _let_1)))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aTP_Lamm_pe Uu) Uua) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) Uua)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger Uua))) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_pc Uu) Uua) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) Uua)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uua))) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int tptp.aTP_Lamm_pd Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) Uua)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Uua))) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_abw Uu) Uua) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) Uua))) Uua)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)))) (forall ((Uu tptp.product_prod_int_int) (Uua tptp.product_prod_int_int)) (= (tptp.aa_Pro6970504127699319548nt_int (tptp.aa_Pro4124234152028750080nt_int tptp.aTP_Lamm_aom Uu) Uua) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_Pro6799258434465214121nt_int tptp.product_fst_int_int Uu)) (tptp.aa_Pro6799258434465214121nt_int tptp.product_fst_int_int Uua))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int Uu)) (tptp.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int Uua))))) (forall ((Uu tptp.rat) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aTP_Lamm_anp Uu) Uua)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat Uua)) Uu)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Uu) (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Uua) tptp.one_one_int))))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aTP_Lamm_pb Uu) Uua) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) Uua)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_oz Uu) Uua) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) Uua)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int tptp.aTP_Lamm_pa Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) Uua)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))))) (forall ((Uu tptp.rat) (Uua tptp.product_prod_int_int)) (let ((_let_1 (tptp.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int Uua))) (let ((_let_2 (tptp.aa_Pro6799258434465214121nt_int tptp.product_fst_int_int Uua))) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aTP_Lamm_aoo Uu) Uua)) (and (= Uu (tptp.aa_int_rat (tptp.aa_int_fun_int_rat tptp.fract _let_2) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.algebr932160517623751201me_int _let_2) _let_1))))))) (forall ((Uu tptp.rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_oj Uu) Uua) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Uu) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uua))) Uua))) (forall ((Uu tptp.rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_ack Uu) Uua) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.gbinomial_rat Uu) Uua)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat Uu) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uua))))) (forall ((Uu tptp.rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_os Uu) Uua) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.gbinomial_rat Uu) Uua)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_adw Uu) Uua)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat Uu) Uua)) (not (= Uu Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_ra Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((Uu tptp.set_int) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aTP_Lamm_aor Uu) Uua)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uua) Uu)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_set_int_bool (tptp.member_int X4) Uu)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X4) Uua))))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.set_Code_integer)) (= (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.aa_set8732061614394825996r_bool tptp.aTP_Lamm_ahm Uu) Uua)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le1307284697595431911nteger Uu) Uua)) (tptp.pp (tptp.aa_set1374477347934578310r_bool tptp.finite6017078050557962740nteger Uua))))) (forall ((Uu tptp.set_Pr1261947904930325089at_nat) (Uua tptp.set_Pr1261947904930325089at_nat)) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.aTP_Lamm_ahn Uu) Uua)) (and (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le7866589430770878221at_nat Uu) Uua)) (tptp.pp (tptp.aa_set3135850010578026034t_bool tptp.finite6177210948735845034at_nat Uua))))) (forall ((Uu tptp.set_nat) (Uua tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.aTP_Lamm_ahk Uu) Uua)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat Uu) Uua)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat Uua))))) (forall ((Uu tptp.set_int) (Uua tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.aTP_Lamm_ahl Uu) Uua)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int Uu) Uua)) (tptp.pp (tptp.aa_set_int_bool tptp.finite_finite_int Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_anf Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Uu) Uua)) Uua))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_yg Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) Uua)) Uu))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_yf Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) Uua)) Uua))) (forall ((Uu tptp.rat) (Uua tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.aTP_Lamm_abf Uu) Uua)) (and (tptp.member_rat Uua tptp.ring_1_Ints_rat) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat Uua)) Uu))))) (forall ((Uu tptp.fun_nat_Code_integer) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (= (tptp.aa_nat_Code_integer (tptp.aTP_Lamm_ya Uu) Uua) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer Uu _let_1)) (tptp.aa_nat_Code_integer Uu (tptp.aa_nat_nat tptp.suc _let_1)))))) (forall ((Uu tptp.fun_nat_assn) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (= (tptp.aa_nat_assn (tptp.aTP_Lamm_yb Uu) Uua) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.aa_nat_assn Uu _let_1)) (tptp.aa_nat_assn Uu (tptp.aa_nat_nat tptp.suc _let_1)))))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_yc Uu) Uua) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat Uu _let_1)) (tptp.aa_nat_rat Uu (tptp.aa_nat_nat tptp.suc _let_1)))))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (= (tptp.aa_nat_nat (tptp.aTP_Lamm_yd Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat Uu _let_1)) (tptp.aa_nat_nat Uu (tptp.aa_nat_nat tptp.suc _let_1)))))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (= (tptp.aa_nat_int (tptp.aTP_Lamm_ye Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int Uu _let_1)) (tptp.aa_nat_int Uu (tptp.aa_nat_nat tptp.suc _let_1)))))) (forall ((Uu tptp.fun_na2338080690716861136at_nat) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (= (tptp.aa_nat2240542744625857721at_nat (tptp.aTP_Lamm_xw Uu) Uua) (tptp.aa_mul5754855110707352700at_nat (tptp.plus_p7104986032573967614at_nat (tptp.aa_nat2240542744625857721at_nat Uu _let_1)) (tptp.aa_nat2240542744625857721at_nat Uu (tptp.aa_nat_nat tptp.suc _let_1)))))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_xx Uu) Uua) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat Uu _let_1)) (tptp.aa_nat_rat Uu (tptp.aa_nat_nat tptp.suc _let_1)))))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (= (tptp.aa_nat_nat (tptp.aTP_Lamm_xz Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat Uu _let_1)) (tptp.aa_nat_nat Uu (tptp.aa_nat_nat tptp.suc _let_1)))))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (= (tptp.aa_nat_int (tptp.aTP_Lamm_xy Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int Uu _let_1)) (tptp.aa_nat_int Uu (tptp.aa_nat_nat tptp.suc _let_1)))))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_kd Uu) Uua) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_nat_rat Uu (tptp.aa_nat_nat tptp.suc Uua))) (tptp.aa_nat_rat Uu Uua)))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aTP_Lamm_ke Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int Uu (tptp.aa_nat_nat tptp.suc Uua))) (tptp.aa_nat_int Uu Uua)))) (forall ((Uu tptp.fun_nat_fun_nat_nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aTP_Lamm_abs Uu) Uua) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat Uu Uua)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) Uua)))) (forall ((Uu tptp.fun_nat_fun_nat_int) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aTP_Lamm_abu Uu) Uua) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_nat_fun_nat_int Uu Uua)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) Uua)))) (forall ((Uu tptp.fun_nat_fun_nat_nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aTP_Lamm_abp Uu) Uua) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat Uu Uua)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) Uua)))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_qv Uu) Uua) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat Uu Uua)) (tptp.aa_nat_rat (tptp.power_power_rat tptp.zero_zero_rat) Uua)))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_kq Uu) Uua) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_nat_rat Uu Uua)) (tptp.aa_nat_rat Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) tptp.one_one_nat))))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aTP_Lamm_kr Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int Uu Uua)) (tptp.aa_nat_int Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) tptp.one_one_nat))))) (forall ((Uu tptp.fun_nat_Code_integer) (Uua tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aTP_Lamm_kn Uu) Uua) (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_nat_Code_integer Uu Uua)) (tptp.aa_nat_Code_integer Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) tptp.one_one_nat))))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_ko Uu) Uua) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_nat_rat Uu Uua)) (tptp.aa_nat_rat Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) tptp.one_one_nat))))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aTP_Lamm_kp Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int Uu Uua)) (tptp.aa_nat_int Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) tptp.one_one_nat))))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_oc Uu) Uua) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_nat_rat Uu Uua)) (tptp.aa_nat_rat Uu (tptp.aa_nat_nat tptp.suc Uua))))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aTP_Lamm_od Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int Uu Uua)) (tptp.aa_nat_int Uu (tptp.aa_nat_nat tptp.suc Uua))))) (forall ((Uu tptp.fun_nat_fun_nat_nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aTP_Lamm_aij Uu) Uua) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat Uu Uua)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat Uua)))) (forall ((Uu tptp.fun_nat_fun_nat_int) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aTP_Lamm_aik Uu) Uua) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_nat_fun_nat_int Uu Uua)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat Uua)))) (forall ((Uu tptp.fun_nat_fun_nat_nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aTP_Lamm_aii Uu) Uua) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat Uu Uua)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat Uua)))) (forall ((Uu tptp.fun_Co8499238673658658103nteger) (Uua tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aTP_Lamm_zl Uu) Uua)) (= (tptp.aa_Cod1783974652533396728nteger Uu Uua) tptp.zero_z3403309356797280102nteger))) (forall ((Uu tptp.fun_Code_integer_rat) (Uua tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aTP_Lamm_zn Uu) Uua)) (= (tptp.aa_Code_integer_rat Uu Uua) tptp.zero_zero_rat))) (forall ((Uu tptp.fun_Code_integer_nat) (Uua tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aTP_Lamm_zp Uu) Uua)) (= (tptp.aa_Code_integer_nat Uu Uua) tptp.zero_zero_nat))) (forall ((Uu tptp.fun_Code_integer_int) (Uua tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aTP_Lamm_zq Uu) Uua)) (= (tptp.aa_Code_integer_int Uu Uua) tptp.zero_zero_int))) (forall ((Uu tptp.fun_nat_Code_integer) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aTP_Lamm_zr Uu) Uua)) (= (tptp.aa_nat_Code_integer Uu Uua) tptp.zero_z3403309356797280102nteger))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aTP_Lamm_zs Uu) Uua)) (= (tptp.aa_nat_rat Uu Uua) tptp.zero_zero_rat))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aTP_Lamm_zt Uu) Uua)) (= (tptp.aa_nat_int Uu Uua) tptp.zero_zero_int))) (forall ((Uu tptp.fun_int_Code_integer) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aTP_Lamm_zk Uu) Uua)) (= (tptp.aa_int_Code_integer Uu Uua) tptp.zero_z3403309356797280102nteger))) (forall ((Uu tptp.fun_int_rat) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aTP_Lamm_zm Uu) Uua)) (= (tptp.aa_int_rat Uu Uua) tptp.zero_zero_rat))) (forall ((Uu tptp.fun_int_nat) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aTP_Lamm_zo Uu) Uua)) (= (tptp.aa_int_nat Uu Uua) tptp.zero_zero_nat))) (forall ((Uu tptp.fun_Co8499238673658658103nteger) (Uua tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aTP_Lamm_aaw Uu) Uua)) (= (tptp.aa_Cod1783974652533396728nteger Uu Uua) tptp.one_one_Code_integer))) (forall ((Uu tptp.fun_Co4490034186337852034r_assn) (Uua tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aTP_Lamm_aay Uu) Uua)) (= (tptp.aa_Code_integer_assn Uu Uua) tptp.one_one_assn))) (forall ((Uu tptp.fun_Code_integer_rat) (Uua tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aTP_Lamm_aba Uu) Uua)) (= (tptp.aa_Code_integer_rat Uu Uua) tptp.one_one_rat))) (forall ((Uu tptp.fun_Code_integer_nat) (Uua tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aTP_Lamm_abc Uu) Uua)) (= (tptp.aa_Code_integer_nat Uu Uua) tptp.one_one_nat))) (forall ((Uu tptp.fun_Code_integer_int) (Uua tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aTP_Lamm_abd Uu) Uua)) (= (tptp.aa_Code_integer_int Uu Uua) tptp.one_one_int))) (forall ((Uu tptp.fun_nat_Code_integer) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aTP_Lamm_abe Uu) Uua)) (= (tptp.aa_nat_Code_integer Uu Uua) tptp.one_one_Code_integer))) (forall ((Uu tptp.fun_int_Code_integer) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aTP_Lamm_aav Uu) Uua)) (= (tptp.aa_int_Code_integer Uu Uua) tptp.one_one_Code_integer))) (forall ((Uu tptp.fun_int_assn) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aTP_Lamm_aax Uu) Uua)) (= (tptp.aa_int_assn Uu Uua) tptp.one_one_assn))) (forall ((Uu tptp.fun_int_rat) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aTP_Lamm_aaz Uu) Uua)) (= (tptp.aa_int_rat Uu Uua) tptp.one_one_rat))) (forall ((Uu tptp.fun_int_nat) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aTP_Lamm_abb Uu) Uua)) (= (tptp.aa_int_nat Uu Uua) tptp.one_one_nat))) (forall ((Uu tptp.num) (Uua tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat Uu))) (= (tptp.aa_num_int (tptp.aTP_Lamm_agr Uu) Uua) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1)) (tptp.aa_num_int tptp.numeral_numeral_int Uua)))))) (forall ((Uu tptp.assn) (Uua tptp.produc3658429121746597890et_nat)) (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.aTP_Lamm_gz Uu) Uua)) (and (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.in_range Uua)) (not (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn Uu) Uua)))))) (forall ((Uu tptp.num) (Uua tptp.num)) (= (tptp.aa_num_int (tptp.aa_num_fun_num_int tptp.aTP_Lamm_aop Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_num_int tptp.numeral_numeral_int Uu)) (tptp.aa_num_int tptp.numeral_numeral_int Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_ks Uu) Uua) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uua)) Uu))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer)) (= (tptp.aa_Cod6977894654539884864nteger (tptp.aa_Cod8380929501330563836nteger tptp.aTP_Lamm_ahy Uu) Uua) (tptp.produc1086072967326762835nteger Uu (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)) tptp.one_one_Code_integer)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.aTP_Lamm_ahx Uu) Uua) (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)) tptp.one_one_nat)))) (forall ((Uu tptp.int) (Uua tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.aTP_Lamm_ahw Uu) Uua) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Uu) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)) tptp.one_one_int)))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer)) (= (tptp.aa_Cod6977894654539884864nteger (tptp.aa_Cod8380929501330563836nteger tptp.aTP_Lamm_agu Uu) Uua) (tptp.produc1086072967326762835nteger Uu (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.aTP_Lamm_agt Uu) Uua) (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)))) (forall ((Uu tptp.int) (Uua tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.aTP_Lamm_ags Uu) Uua) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Uu) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)))) (forall ((Uu tptp.rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_pf Uu) Uua) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Uu) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uua)) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_tt Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua)))) (forall ((Uu tptp.int) (Uua tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.aTP_Lamm_agw Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Uu) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int Uua) tptp.zero_zero_int)))))) (forall ((Uu tptp.code_natural) (Uua tptp.nat)) (= (tptp.aa_nat_Code_natural (tptp.aTP_Lamm_me Uu) Uua) (tptp.minus_7197305767214868737atural Uu (tptp.aa_nat_Code_natural tptp.semiri3763490453095760265atural Uua)))) (forall ((Uu tptp.code_integer) (Uua tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aTP_Lamm_mf Uu) Uua) (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger Uu) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger Uua)))) (forall ((Uu tptp.rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_md Uu) Uua) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat Uu) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_mg Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat Uua)))) (forall ((Uu tptp.int) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.aTP_Lamm_mh Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Uu) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Uua)))) (forall ((Uu tptp.code_integer) (Uua tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aTP_Lamm_ol Uu) Uua) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger Uu) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger Uua)))) (forall ((Uu tptp.rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_ok Uu) Uua) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Uu) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_om Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat Uua)))) (forall ((Uu tptp.int) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.aTP_Lamm_on Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Uu) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_anb Uu) Uua)) (= Uua (tptp.aa_nat_nat tptp.suc Uu)))) (forall ((Uu tptp.assn) (Uua tptp.assn)) (= (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.aTP_Lamm_db Uu) Uua)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_eq_assn Uua) Uu)))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.set_Code_integer)) (= (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.aTP_Lamm_acz Uu) Uua)) (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger Uua) Uu)))) (forall ((Uu tptp.set_Pr8693737435421807431at_nat) (Uua tptp.set_Pr8693737435421807431at_nat)) (= (tptp.pp (tptp.aa_set1680211184867041100t_bool (tptp.aa_set2354966250726584670t_bool tptp.aTP_Lamm_cp Uu) Uua)) (tptp.ord_le3000389064537975527at_nat Uua Uu))) (forall ((Uu tptp.set_Pr8551490117392284871at_nat) (Uua tptp.set_Pr8551490117392284871at_nat)) (= (tptp.pp (tptp.aa_set4800428189156605132t_bool (tptp.aa_set4590457447208766046t_bool tptp.aTP_Lamm_cr Uu) Uua)) (tptp.ord_le8081472938463900775at_nat Uua Uu))) (forall ((Uu tptp.set_Pr4329608150637261639at_nat) (Uua tptp.set_Pr4329608150637261639at_nat)) (= (tptp.pp (tptp.aa_set4148026973699692364t_bool (tptp.aa_set6699703996738328926t_bool tptp.aTP_Lamm_ct Uu) Uua)) (tptp.ord_le1268244103169919719at_nat Uua Uu))) (forall ((Uu tptp.set_Pr1261947904930325089at_nat) (Uua tptp.set_Pr1261947904930325089at_nat)) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.aTP_Lamm_cv Uu) Uua)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat Uua) Uu)))) (forall ((Uu tptp.set_bool) (Uua tptp.set_bool)) (= (tptp.pp (tptp.aa_set_bool_bool (tptp.aa_set36795378406917470l_bool tptp.aTP_Lamm_cx Uu) Uua)) (tptp.ord_less_eq_set_bool Uua Uu))) (forall ((Uu tptp.set_nat) (Uua tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.aTP_Lamm_cz Uu) Uua)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat Uua) Uu)))) (forall ((Uu tptp.set_int) (Uua tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.aTP_Lamm_dd Uu) Uua)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int Uua) Uu)))) (forall ((Uu tptp.rat) (Uua tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.aTP_Lamm_dh Uu) Uua)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Uua) Uu)))) (forall ((Uu tptp.num) (Uua tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.aTP_Lamm_nm Uu) Uua)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Uua) Uu)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_df Uu) Uua)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Uua) Uu)))) (forall ((Uu tptp.int) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_dj Uu) Uua)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Uua) Uu)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_amn Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat Uua) Uu))) (forall ((Uu tptp.rat) (Uua tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.aTP_Lamm_ik Uu) Uua) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat Uua) Uu))) (forall ((Uu tptp.assn) (Uua tptp.assn)) (= (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.aTP_Lamm_dc Uu) Uua)) (tptp.pp (tptp.aa_assn_bool (tptp.aa_ass5323576183532441186n_bool tptp.ord_less_assn Uua) Uu)))) (forall ((Uu tptp.set_Pr8693737435421807431at_nat) (Uua tptp.set_Pr8693737435421807431at_nat)) (= (tptp.pp (tptp.aa_set1680211184867041100t_bool (tptp.aa_set2354966250726584670t_bool tptp.aTP_Lamm_cq Uu) Uua)) (tptp.ord_le6428140832669894131at_nat Uua Uu))) (forall ((Uu tptp.set_Pr8551490117392284871at_nat) (Uua tptp.set_Pr8551490117392284871at_nat)) (= (tptp.pp (tptp.aa_set4800428189156605132t_bool (tptp.aa_set4590457447208766046t_bool tptp.aTP_Lamm_cs Uu) Uua)) (tptp.ord_le7642048601412989811at_nat Uua Uu))) (forall ((Uu tptp.set_Pr4329608150637261639at_nat) (Uua tptp.set_Pr4329608150637261639at_nat)) (= (tptp.pp (tptp.aa_set4148026973699692364t_bool (tptp.aa_set6699703996738328926t_bool tptp.aTP_Lamm_cu Uu) Uua)) (tptp.ord_le2604355607129572851at_nat Uua Uu))) (forall ((Uu tptp.set_Pr1261947904930325089at_nat) (Uua tptp.set_Pr1261947904930325089at_nat)) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.aTP_Lamm_cw Uu) Uua)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le7866589430770878221at_nat Uua) Uu)))) (forall ((Uu tptp.set_bool) (Uua tptp.set_bool)) (= (tptp.pp (tptp.aa_set_bool_bool (tptp.aa_set36795378406917470l_bool tptp.aTP_Lamm_cy Uu) Uua)) (tptp.ord_less_set_bool Uua Uu))) (forall ((Uu tptp.set_nat) (Uua tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.aTP_Lamm_da Uu) Uua)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_set_nat Uua) Uu)))) (forall ((Uu tptp.set_int) (Uua tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.aTP_Lamm_de Uu) Uua)) (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_set_int Uua) Uu)))) (forall ((Uu tptp.rat) (Uua tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.aTP_Lamm_di Uu) Uua)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Uua) Uu)))) (forall ((Uu tptp.num) (Uua tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.aTP_Lamm_fb Uu) Uua)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Uua) Uu)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_dg Uu) Uua)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uua) Uu)))) (forall ((Uu tptp.int) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_dk Uu) Uua)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Uua) Uu)))) (forall ((Uu tptp.rat) (Uua tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.aTP_Lamm_hr Uu) Uua) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Uua) Uu))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aTP_Lamm_hy Uu) Uua) (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger Uua) Uu))) (forall ((Uu tptp.rat) (Uua tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.aTP_Lamm_hw Uu) Uua) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat Uua) Uu))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_amp Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) Uu))) (forall ((Uu tptp.int) (Uua tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.aTP_Lamm_hx Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Uua) Uu))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aTP_Lamm_hv Uu) Uua) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger Uua) Uu))) (forall ((Uu tptp.rat) (Uua tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.aTP_Lamm_hs Uu) Uua) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Uua) Uu))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_hu Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) Uu))) (forall ((Uu tptp.int) (Uua tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.aTP_Lamm_ht Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Uua) Uu))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.aTP_Lamm_adu Uu) Uua)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer Uua) Uu)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_adt Uu) Uua)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat Uua) Uu)))) (forall ((Uu tptp.int) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_adv Uu) Uua)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int Uua) Uu)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.aTP_Lamm_ams Uu) Uua) (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat Uua) Uu))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_tu Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uua) Uu))) (forall ((Uu tptp.set_Pr8693737435421807431at_nat) (Uua tptp.produc859450856879609959at_nat)) (= (tptp.pp (tptp.aa_Pro6098352494050694700t_bool (tptp.aTP_Lamm_ai Uu) Uua)) (tptp.member8206827879206165904at_nat Uua Uu))) (forall ((Uu tptp.set_Pr8551490117392284871at_nat) (Uua tptp.produc4166570645942440679at_nat)) (= (tptp.pp (tptp.aa_Pro5063669228512387756t_bool (tptp.aTP_Lamm_aj Uu) Uua)) (tptp.member6689249552917799696at_nat Uua Uu))) (forall ((Uu tptp.set_Pr4329608150637261639at_nat) (Uua tptp.produc3843707927480180839at_nat)) (= (tptp.pp (tptp.aa_Pro1809015098595223084t_bool (tptp.aTP_Lamm_ak Uu) Uua)) (tptp.member8757157785044589968at_nat Uua Uu))) (forall ((Uu tptp.set_Pr1261947904930325089at_nat) (Uua tptp.product_prod_nat_nat)) (= (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aTP_Lamm_a Uu) Uua)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat Uua) Uu)))) (forall ((Uu tptp.set_Pr958786334691620121nt_int) (Uua tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aTP_Lamm_ab Uu) Uua)) (tptp.member5262025264175285858nt_int Uua Uu))) (forall ((Uu tptp.set_list_nat) (Uua tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool (tptp.aTP_Lamm_ac Uu) Uua)) (tptp.member_list_nat Uua Uu))) (forall ((Uu tptp.set_bool) (Uua tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aTP_Lamm_aa Uu) Uua)) (tptp.pp (tptp.member_bool Uua Uu)))) (forall ((Uu tptp.set_set_nat) (Uua tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aTP_Lamm_ad Uu) Uua)) (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat Uua) Uu)))) (forall ((Uu tptp.set_nat) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aTP_Lamm_ae Uu) Uua)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uua) Uu)))) (forall ((Uu tptp.set_int) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aTP_Lamm_af Uu) Uua)) (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uua) Uu)))) (forall ((Uu tptp.produc8664842809031399944it_nat) (Uua tptp.produc8664842809031399944it_nat)) (= (tptp.pp (tptp.aa_Pro8715207439678120785t_bool (tptp.aTP_Lamm_fh Uu) Uua)) (= Uua Uu))) (forall ((Uu tptp.produc3260487557148687353it_nat) (Uua tptp.produc3260487557148687353it_nat)) (= (tptp.pp (tptp.aa_Pro8278066377857552544t_bool (tptp.aTP_Lamm_ff Uu) Uua)) (= Uua Uu))) (forall ((Uu tptp.num) (Uua tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.aTP_Lamm_fg Uu) Uua)) (= Uua Uu))) (forall ((Uu tptp.fun_Code_integer_nat) (Uua tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aTP_Lamm_we Uu) Uua)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_Code_integer_nat Uu Uua))))) (forall ((Uu tptp.fun_Pr2602117396471556196at_nat) (Uua tptp.product_prod_nat_nat)) (= (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aTP_Lamm_wg Uu) Uua)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_Pro4243173770044397973at_nat Uu Uua))))) (forall ((Uu tptp.fun_Pr5160692531401422620nt_nat) (Uua tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aTP_Lamm_vu Uu) Uua)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_Pro6801748904974264397nt_nat Uu Uua))))) (forall ((Uu tptp.fun_list_nat_nat) (Uua tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool (tptp.aTP_Lamm_vw Uu) Uua)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_list_nat_nat Uu Uua))))) (forall ((Uu tptp.fun_set_nat_nat) (Uua tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aTP_Lamm_vy Uu) Uua)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_set_nat_nat Uu Uua))))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aTP_Lamm_wa Uu) Uua)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat Uu Uua))))) (forall ((Uu tptp.fun_int_nat) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aTP_Lamm_wc Uu) Uua)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_int_nat Uu Uua))))) (forall ((Uu tptp.fun_nat_Code_integer) (Uua tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aTP_Lamm_nk Uu) Uua) (tptp.aa_nat_Code_integer Uu (tptp.aa_nat_nat tptp.suc Uua)))) (forall ((Uu tptp.fun_na2338080690716861136at_nat) (Uua tptp.nat)) (= (tptp.aa_nat2240542744625857721at_nat (tptp.aTP_Lamm_ka Uu) Uua) (tptp.aa_nat2240542744625857721at_nat Uu (tptp.aa_nat_nat tptp.suc Uua)))) (forall ((Uu tptp.fun_nat_assn) (Uua tptp.nat)) (= (tptp.aa_nat_assn (tptp.aTP_Lamm_nl Uu) Uua) (tptp.aa_nat_assn Uu (tptp.aa_nat_nat tptp.suc Uua)))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aTP_Lamm_aov Uu) Uua)) (tptp.pp (tptp.aa_nat_bool Uu (tptp.aa_nat_nat tptp.suc Uua))))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_kb Uu) Uua) (tptp.aa_nat_rat Uu (tptp.aa_nat_nat tptp.suc Uua)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aTP_Lamm_jx Uu) Uua) (tptp.aa_nat_nat Uu (tptp.aa_nat_nat tptp.suc Uua)))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aTP_Lamm_kc Uu) Uua) (tptp.aa_nat_int Uu (tptp.aa_nat_nat tptp.suc Uua)))) (forall ((Uu tptp.nat) (Uua tptp.num)) (= (tptp.aa_num_option_num (tptp.aTP_Lamm_ajf Uu) Uua) (tptp.aa_num_option_num tptp.some_num (tptp.aa_option_num_num (tptp.case_option_num_num tptp.one tptp.bit1) (tptp.aa_num_option_num (tptp.bit_take_bit_num Uu) Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool tptp.aTP_Lamm_aot Uu) Uua) (tptp.produc8955392012077580105t_bool (tptp.aa_nat8637530788439456283t_bool (tptp.aTP_Lamm_aos Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat7997280740862404369at_nat (tptp.aa_nat5682243440470347102at_nat tptp.aTP_Lamm_ana Uu) Uua) (tptp.produc2626176000494625587at_nat (tptp.aa_nat4158579785191972357at_nat (tptp.aTP_Lamm_amz Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat7997280740862404369at_nat (tptp.aa_nat5682243440470347102at_nat tptp.aTP_Lamm_amy Uu) Uua) (tptp.produc2626176000494625587at_nat (tptp.aa_nat4158579785191972357at_nat (tptp.aTP_Lamm_amx Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool tptp.aTP_Lamm_amw Uu) Uua) (tptp.produc8955392012077580105t_bool (tptp.aa_nat8637530788439456283t_bool (tptp.aTP_Lamm_amv Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool tptp.aTP_Lamm_amu Uu) Uua) (tptp.produc8955392012077580105t_bool (tptp.aa_nat8637530788439456283t_bool (tptp.aTP_Lamm_amt Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat7997280740862404369at_nat (tptp.aa_nat5682243440470347102at_nat tptp.aTP_Lamm_amr Uu) Uua) (tptp.produc2626176000494625587at_nat (tptp.aa_nat4158579785191972357at_nat (tptp.aTP_Lamm_amq Uu) Uua)))) (forall ((Uu tptp.fun_a_2990225006182978344t_unit) (Uua tptp.a)) (= (tptp.aa_a_f2724909083865345251it_nat (tptp.aTP_Lamm_ahi Uu) Uua) (tptp.produc7488178964372371019it_nat (tptp.aa_a_f112692477493148739it_nat (tptp.aTP_Lamm_ahh Uu) Uua)))) (forall ((Uu tptp.fun_a_6093291656547882009Heap_a) (Uua tptp.a)) (= (tptp.aa_a_f2042851359257671380it_nat (tptp.aTP_Lamm_ahe Uu) Uua) (tptp.produc5645566021302314940it_nat (tptp.aa_a_f1761598956578211508it_nat (tptp.aTP_Lamm_ahd Uu) Uua)))) (forall ((Uu tptp.fun_he5123621388056232515t_unit) (Uua tptp.heap_e7401611519738050253t_unit)) (= (tptp.aa_hea684056619475940329it_nat (tptp.aTP_Lamm_gb Uu) Uua) (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat (tptp.produc7133225469290080770it_nat (tptp.aa_hea4146273921685161788t_unit Uu Uua) (tptp.produc584006145561248582it_nat Uua tptp.one_one_nat))))) (forall ((Uu tptp.fun_he6342020308413958580unit_a) (Uua tptp.heap_e7401611519738050253t_unit)) (= (tptp.aa_hea4724376117875161946it_nat (tptp.aTP_Lamm_ga Uu) Uua) (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat (tptp.aa_hea5100639427662539565unit_a Uu Uua)) (tptp.produc584006145561248582it_nat Uua tptp.one_one_nat))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_afb Uu) Uua)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) Uua)))))))) (forall ((Uu tptp.code_natural) (Uua tptp.code_natural)) (= (tptp.aa_Cod6352003912080677724atural (tptp.aTP_Lamm_apa Uu) Uua) (tptp.produc6639722614265839536atural (tptp.plus_p4538020629002901425atural Uua (tptp.times_2397367101498566445atural Uu (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 tptp.one)))))))))))))))))))))))))))))))))))) (forall ((Uu tptp.rat) (Uua tptp.nat)) (= (tptp.aa_nat_fun_rat_rat (tptp.aTP_Lamm_hm Uu) Uua) (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat Uu) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uua))))) (forall ((Uu tptp.code_integer) (Uua tptp.nat)) (= (tptp.aa_nat6383147911832638789nteger (tptp.aTP_Lamm_gi Uu) Uua) (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger Uu) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger Uua))))) (forall ((Uu tptp.rat) (Uua tptp.nat)) (= (tptp.aa_nat_fun_rat_rat (tptp.aTP_Lamm_gg Uu) Uua) (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Uu) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_gj Uu) Uua) (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat Uua))))) (forall ((Uu tptp.int) (Uua tptp.nat)) (= (tptp.aa_nat_fun_int_int (tptp.aTP_Lamm_gh Uu) Uua) (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Uu) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Uua))))) (forall ((Uu tptp.set_Pr8693737435421807431at_nat) (Uua tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set6661686244540357314at_nat (tptp.aTP_Lamm_dl Uu) Uua) (tptp.some_s579751585967276588at_nat (tptp.aa_set5535132180132642428at_nat (tptp.aa_set3125807151510273166at_nat tptp.sup_su718114333110466843at_nat Uu) Uua)))) (forall ((Uu tptp.set_Pr8551490117392284871at_nat) (Uua tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set1897275755269116354at_nat (tptp.aTP_Lamm_dn Uu) Uua) (tptp.some_s287724117700012716at_nat (tptp.aa_set6734554978791863420at_nat (tptp.aa_set4622835569371386638at_nat tptp.sup_su3035147773818789531at_nat Uu) Uua)))) (forall ((Uu tptp.set_Pr4329608150637261639at_nat) (Uua tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set7071694670514008770at_nat (tptp.aTP_Lamm_dp Uu) Uua) (tptp.some_s5890477192898017836at_nat (tptp.aa_set4883462369968598652at_nat (tptp.aa_set7704514097189807246at_nat tptp.sup_su5525570899277871387at_nat Uu) Uua)))) (forall ((Uu tptp.set_nat) (Uua tptp.set_nat)) (= (tptp.aa_set6119337032432945050et_nat (tptp.aTP_Lamm_dr Uu) Uua) (tptp.some_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.sup_sup_set_nat Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_option_nat (tptp.aTP_Lamm_dt Uu) Uua) (tptp.aa_nat_option_nat tptp.some_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.sup_sup_nat Uu) Uua)))) (forall ((Uu tptp.product_unit) (Uua tptp.product_unit)) (= (tptp.aa_Pro7616171890175246658t_unit (tptp.aTP_Lamm_ek Uu) Uua) (tptp.some_Product_unit (tptp.aa_Pro8294289767544744956t_unit (tptp.aa_Pro1375803928533059540t_unit tptp.inf_inf_Product_unit Uu) Uua)))) (forall ((Uu tptp.assn) (Uua tptp.assn)) (= (tptp.aa_assn_option_assn (tptp.aTP_Lamm_eg Uu) Uua) (tptp.some_assn (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.inf_inf_assn Uu) Uua)))) (forall ((Uu tptp.set_Pr1261947904930325089at_nat) (Uua tptp.set_Pr1261947904930325089at_nat)) (= (tptp.aa_set2934564513904597954at_nat (tptp.aTP_Lamm_em Uu) Uua) (tptp.some_s147305329494351046at_nat (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.inf_in2572325071724192079at_nat Uu) Uua)))) (forall ((Uu tptp.set_nat) (Uua tptp.set_nat)) (= (tptp.aa_set6119337032432945050et_nat (tptp.aTP_Lamm_ee Uu) Uua) (tptp.some_set_nat (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.inf_inf_set_nat Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_option_nat (tptp.aTP_Lamm_ei Uu) Uua) (tptp.aa_nat_option_nat tptp.some_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.inf_inf_nat Uu) Uua)))) (forall ((Uu tptp.code_natural) (Uua tptp.code_natural)) (= (tptp.aa_Cod6352003912080677724atural (tptp.aTP_Lamm_apc Uu) Uua) (tptp.produc6639722614265839536atural (tptp.modulo8411746178871703098atural Uua Uu)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_anm Uu) Uua) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_anl Uu) Uua) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_min_nat Uua) Uu)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_ann Uu) Uua) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_ano Uu) Uua) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat Uua) Uu)))) (forall ((Uu tptp.set_Pr1261947904930325089at_nat) (Uua tptp.product_prod_nat_nat)) (= (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aTP_Lamm_hf Uu) Uua)) (not (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat Uua) Uu))))) (forall ((Uu tptp.set_Pr958786334691620121nt_int) (Uua tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aTP_Lamm_hh Uu) Uua)) (not (tptp.member5262025264175285858nt_int Uua Uu)))) (forall ((Uu tptp.set_list_nat) (Uua tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool (tptp.aTP_Lamm_hi Uu) Uua)) (not (tptp.member_list_nat Uua Uu)))) (forall ((Uu tptp.set_bool) (Uua tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aTP_Lamm_hg Uu) Uua)) (not (tptp.pp (tptp.member_bool Uua Uu))))) (forall ((Uu tptp.set_set_nat) (Uua tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aTP_Lamm_hj Uu) Uua)) (not (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat Uua) Uu))))) (forall ((Uu tptp.set_nat) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aTP_Lamm_hk Uu) Uua)) (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uua) Uu))))) (forall ((Uu tptp.set_int) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aTP_Lamm_hl Uu) Uua)) (not (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uua) Uu))))) (forall ((Uu tptp.nat) (Uua tptp.heap_e7401611519738050253t_unit)) (= (tptp.aa_hea684056619475940329it_nat (tptp.aTP_Lamm_aox Uu) Uua) (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat (tptp.produc7133225469290080770it_nat tptp.product_Unity (tptp.produc584006145561248582it_nat Uua Uu))))) (forall ((Uu tptp.fun_Co8822979462182099027r_bool) (Uua tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aTP_Lamm_ake Uu) Uua) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_Code_integer_bool Uu Uua)))) (forall ((Uu tptp.fun_Co8822979462182099027r_bool) (Uua tptp.code_integer)) (= (tptp.aa_Code_integer_nat (tptp.aTP_Lamm_akh Uu) Uua) (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat (tptp.aa_Code_integer_bool Uu Uua)))) (forall ((Uu tptp.fun_Co8822979462182099027r_bool) (Uua tptp.code_integer)) (= (tptp.aa_Code_integer_int (tptp.aTP_Lamm_aki Uu) Uua) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_Code_integer_bool Uu Uua)))) (forall ((Uu tptp.fun_set_nat_bool) (Uua tptp.set_nat)) (= (tptp.aa_set871585252387937313nteger (tptp.aTP_Lamm_akm Uu) Uua) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_set_nat_bool Uu Uua)))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aTP_Lamm_akf Uu) Uua) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_nat_bool Uu Uua)))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aTP_Lamm_akk Uu) Uua) (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat (tptp.aa_nat_bool Uu Uua)))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aTP_Lamm_akj Uu) Uua) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_nat_bool Uu Uua)))) (forall ((Uu tptp.fun_int_bool) (Uua tptp.int)) (= (tptp.aa_int_Code_integer (tptp.aTP_Lamm_akd Uu) Uua) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_int_bool Uu Uua)))) (forall ((Uu tptp.fun_int_bool) (Uua tptp.int)) (= (tptp.aa_int_nat (tptp.aTP_Lamm_akg Uu) Uua) (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat (tptp.aa_int_bool Uu Uua)))) (forall ((Uu tptp.fun_int_bool) (Uua tptp.int)) (= (tptp.aa_int_int (tptp.aTP_Lamm_akl Uu) Uua) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_int_bool Uu Uua)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aTP_Lamm_jr Uu) Uua) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat Uu Uua)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aTP_Lamm_js Uu) Uua) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat Uu Uua)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aTP_Lamm_jq Uu) Uua) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat Uu Uua)))) (forall ((Uu tptp.fun_int_nat) (Uua tptp.int)) (= (tptp.aa_int_int (tptp.aTP_Lamm_jp Uu) Uua) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_int_nat Uu Uua)))) (forall ((Uu tptp.fun_int_int) (Uua tptp.int)) (= (tptp.aa_int_int (tptp.aTP_Lamm_ma Uu) Uua) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int Uu Uua)))) (forall ((Uu tptp.fun_nat_Code_integer) (Uua tptp.nat)) (= (tptp.aa_nat6383147911832638789nteger (tptp.aTP_Lamm_oe Uu) Uua) (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer Uu Uua)))) (forall ((Uu tptp.fun_nat_assn) (Uua tptp.nat)) (= (tptp.aa_nat_fun_assn_assn (tptp.aTP_Lamm_of Uu) Uua) (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.aa_nat_assn Uu Uua)))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.nat)) (= (tptp.aa_nat_fun_rat_rat (tptp.aTP_Lamm_og Uu) Uua) (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat Uu Uua)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat)) (= (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_oh Uu) Uua) (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat Uu Uua)))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat)) (= (tptp.aa_nat_fun_int_int (tptp.aTP_Lamm_oi Uu) Uua) (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int Uu Uua)))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_mm Uu) Uua) (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_nat_int Uu Uua)))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aTP_Lamm_mn Uu) Uua) (tptp.aa_int_int tptp.ring_1_of_int_int (tptp.aa_nat_int Uu Uua)))) (forall ((Uu tptp.fun_int_int) (Uua tptp.int)) (= (tptp.aa_int_rat (tptp.aTP_Lamm_jt Uu) Uua) (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_int_int Uu Uua)))) (forall ((Uu tptp.fun_int_int) (Uua tptp.int)) (= (tptp.aa_int_int (tptp.aTP_Lamm_ju Uu) Uua) (tptp.aa_int_int tptp.ring_1_of_int_int (tptp.aa_int_int Uu Uua)))) (forall ((Uu tptp.fun_nat_Code_integer) (Uua tptp.nat)) (= (tptp.aa_nat6383147911832638789nteger (tptp.aTP_Lamm_ki Uu) Uua) (tptp.plus_p5714425477246183910nteger (tptp.aa_nat_Code_integer Uu Uua)))) (forall ((Uu tptp.fun_na2338080690716861136at_nat) (Uua tptp.nat)) (= (tptp.aa_nat1862996181841379217at_nat (tptp.aTP_Lamm_kj Uu) Uua) (tptp.plus_p7104986032573967614at_nat (tptp.aa_nat2240542744625857721at_nat Uu Uua)))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.nat)) (= (tptp.aa_nat_fun_rat_rat (tptp.aTP_Lamm_kk Uu) Uua) (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat Uu Uua)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat)) (= (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_km Uu) Uua) (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat Uu Uua)))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat)) (= (tptp.aa_nat_fun_int_int (tptp.aTP_Lamm_kl Uu) Uua) (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int Uu Uua)))) (forall ((Uu tptp.fun_int_int) (Uua tptp.int)) (= (tptp.aa_int_int (tptp.aTP_Lamm_kt Uu) Uua) (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int Uu Uua)))) (forall ((Uu tptp.fun_list_nat_nat) (Uua tptp.list_nat)) (= (tptp.aa_list_nat_nat (tptp.aTP_Lamm_amb Uu) Uua) (tptp.aa_nat_nat tptp.suc (tptp.aa_list_nat_nat Uu Uua)))) (forall ((Uu tptp.fun_set_nat_nat) (Uua tptp.set_nat)) (= (tptp.aa_set_nat_nat (tptp.aTP_Lamm_ama Uu) Uua) (tptp.aa_nat_nat tptp.suc (tptp.aa_set_nat_nat Uu Uua)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aTP_Lamm_amc Uu) Uua) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat Uu Uua)))) (forall ((Uu tptp.fun_Pr7757163693017731481t_bool) (Uua tptp.product_prod_nat_nat)) (= (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_fun830836278467416944t_bool tptp.aTP_Lamm_ii Uu) Uua)) (not (tptp.pp (tptp.aa_Pro2232559814647311250t_bool Uu Uua))))) (forall ((Uu tptp.fun_Pr803113274115125473t_bool) (Uua tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aTP_Lamm_ha Uu) Uua)) (not (tptp.pp (tptp.aa_Pro4501881432599481050t_bool Uu Uua))))) (forall ((Uu tptp.fun_list_nat_bool) (Uua tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool (tptp.aTP_Lamm_hb Uu) Uua)) (not (tptp.pp (tptp.aa_list_nat_bool Uu Uua))))) (forall ((Uu tptp.fun_set_nat_bool) (Uua tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aTP_Lamm_hc Uu) Uua)) (not (tptp.pp (tptp.aa_set_nat_bool Uu Uua))))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aTP_Lamm_hd Uu) Uua)) (not (tptp.pp (tptp.aa_nat_bool Uu Uua))))) (forall ((Uu tptp.fun_int_bool) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aTP_Lamm_he Uu) Uua)) (not (tptp.pp (tptp.aa_int_bool Uu Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.aTP_Lamm_apd Uu) Uua) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_dg Uu)))) (forall ((Uu tptp.num) (Uua tptp.code_integer) (Uub tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (let ((_let_2 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger Uu))) (= (tptp.aa_Cod6977894654539884864nteger (tptp.aa_Cod8380929501330563836nteger (tptp.aTP_Lamm_afe Uu) Uua) Uub) (tptp.if_Pro6119634080678213985nteger (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger _let_2) Uub) (tptp.produc1086072967326762835nteger (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger Uub) _let_2)) (tptp.produc1086072967326762835nteger _let_1 Uub)))))) (forall ((Uu tptp.num) (Uua tptp.nat) (Uub tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat Uu))) (= (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat (tptp.aTP_Lamm_afc Uu) Uua) Uub) (tptp.aa_Pro262675715343573244at_nat (tptp.aa_Pro8023792847356852296at_nat (tptp.if_Pro6206227464963214023at_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_2) Uub)) (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) _let_2))) (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat _let_1) Uub)))))) (forall ((Uu tptp.num) (Uua tptp.int) (Uub tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int Uu))) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int (tptp.aTP_Lamm_afd Uu) Uua) Uub) (tptp.aa_Pro6970504127699319548nt_int (tptp.if_Pro3027730157355071871nt_int (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_2) Uub) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Uub) _let_2))) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int _let_1) Uub)))))) (forall ((Uu tptp.fun_Co8499238673658658103nteger) (Uua tptp.set_Code_integer) (Uub tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_set4294055438810586376nteger (tptp.aTP_Lamm_yq Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Uub) Uua) (tptp.aa_Cod1783974652533396728nteger Uu Uub)) tptp.zero_z3403309356797280102nteger))) (forall ((Uu tptp.fun_Code_integer_rat) (Uua tptp.set_Code_integer) (Uub tptp.code_integer)) (= (tptp.aa_Code_integer_rat (tptp.aa_set7344733238996822275er_rat (tptp.aTP_Lamm_yt Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Uub) Uua)) (tptp.aa_Code_integer_rat Uu Uub)) tptp.zero_zero_rat))) (forall ((Uu tptp.fun_Code_integer_nat) (Uua tptp.set_Code_integer) (Uub tptp.code_integer)) (= (tptp.aa_Code_integer_nat (tptp.aa_set1629589760535443195er_nat (tptp.aTP_Lamm_yw Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Uub) Uua)) (tptp.aa_Code_integer_nat Uu Uub)) tptp.zero_zero_nat))) (forall ((Uu tptp.fun_bo7282069421189217543nteger) (Uua tptp.set_bool) (Uub tptp.bool)) (= (tptp.aa_bool_Code_integer (tptp.aa_set2829807854720747148nteger (tptp.aTP_Lamm_yo Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.member_bool Uub Uua) (tptp.aa_bool_Code_integer Uu Uub)) tptp.zero_z3403309356797280102nteger))) (forall ((Uu tptp.fun_bool_rat) (Uua tptp.set_bool) (Uub tptp.bool)) (= (tptp.aa_bool_rat (tptp.aa_set1787953457065026183ol_rat (tptp.aTP_Lamm_yr Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.member_bool Uub Uua)) (tptp.aa_bool_rat Uu Uub)) tptp.zero_zero_rat))) (forall ((Uu tptp.fun_bool_nat) (Uua tptp.set_bool) (Uub tptp.bool)) (= (tptp.aa_bool_nat (tptp.aa_set5296182015458422911ol_nat (tptp.aTP_Lamm_yu Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.member_bool Uub Uua)) (tptp.aa_bool_nat Uu Uub)) tptp.zero_zero_nat))) (forall ((Uu tptp.fun_bool_int) (Uua tptp.set_bool) (Uub tptp.bool)) (= (tptp.aa_bool_int (tptp.aa_set1118330995949226203ol_int (tptp.aTP_Lamm_yx Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.if_int (tptp.member_bool Uub Uua)) (tptp.aa_bool_int Uu Uub)) tptp.zero_zero_int))) (forall ((Uu tptp.fun_int_Code_integer) (Uua tptp.set_int) (Uub tptp.int)) (= (tptp.aa_int_Code_integer (tptp.aa_set5517701783735052070nteger (tptp.aTP_Lamm_yp Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_set_int_bool (tptp.member_int Uub) Uua) (tptp.aa_int_Code_integer Uu Uub)) tptp.zero_z3403309356797280102nteger))) (forall ((Uu tptp.fun_int_rat) (Uua tptp.set_int) (Uub tptp.int)) (= (tptp.aa_int_rat (tptp.aa_set7979663334043413281nt_rat (tptp.aTP_Lamm_ys Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.aa_set_int_bool (tptp.member_int Uub) Uua)) (tptp.aa_int_rat Uu Uub)) tptp.zero_zero_rat))) (forall ((Uu tptp.fun_int_nat) (Uua tptp.set_int) (Uub tptp.int)) (= (tptp.aa_int_nat (tptp.aa_set2264519855582034201nt_nat (tptp.aTP_Lamm_yv Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_set_int_bool (tptp.member_int Uub) Uua)) (tptp.aa_int_nat Uu Uub)) tptp.zero_zero_nat))) (forall ((Uu tptp.fun_Co8499238673658658103nteger) (Uua tptp.set_Code_integer) (Uub tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_set4294055438810586376nteger (tptp.aTP_Lamm_aan Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Uub) Uua) (tptp.aa_Cod1783974652533396728nteger Uu Uub)) tptp.one_one_Code_integer))) (forall ((Uu tptp.fun_Co4490034186337852034r_assn) (Uua tptp.set_Code_integer) (Uub tptp.code_integer)) (= (tptp.aa_Code_integer_assn (tptp.aa_set2437433236263590995r_assn (tptp.aTP_Lamm_aaq Uu) Uua) Uub) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn (tptp.if_assn (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Uub) Uua)) (tptp.aa_Code_integer_assn Uu Uub)) tptp.one_one_assn))) (forall ((Uu tptp.fun_Code_integer_rat) (Uua tptp.set_Code_integer) (Uub tptp.code_integer)) (= (tptp.aa_Code_integer_rat (tptp.aa_set7344733238996822275er_rat (tptp.aTP_Lamm_aat Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Uub) Uua)) (tptp.aa_Code_integer_rat Uu Uub)) tptp.one_one_rat))) (forall ((Uu tptp.fun_bo7282069421189217543nteger) (Uua tptp.set_bool) (Uub tptp.bool)) (= (tptp.aa_bool_Code_integer (tptp.aa_set2829807854720747148nteger (tptp.aTP_Lamm_aal Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.member_bool Uub Uua) (tptp.aa_bool_Code_integer Uu Uub)) tptp.one_one_Code_integer))) (forall ((Uu tptp.fun_bool_assn) (Uua tptp.set_bool) (Uub tptp.bool)) (= (tptp.aa_bool_assn (tptp.aa_set3043482617886199255l_assn (tptp.aTP_Lamm_aao Uu) Uua) Uub) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn (tptp.if_assn (tptp.member_bool Uub Uua)) (tptp.aa_bool_assn Uu Uub)) tptp.one_one_assn))) (forall ((Uu tptp.fun_bool_rat) (Uua tptp.set_bool) (Uub tptp.bool)) (= (tptp.aa_bool_rat (tptp.aa_set1787953457065026183ol_rat (tptp.aTP_Lamm_aar Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.member_bool Uub Uua)) (tptp.aa_bool_rat Uu Uub)) tptp.one_one_rat))) (forall ((Uu tptp.fun_bool_nat) (Uua tptp.set_bool) (Uub tptp.bool)) (= (tptp.aa_bool_nat (tptp.aa_set5296182015458422911ol_nat (tptp.aTP_Lamm_aau Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.member_bool Uub Uua)) (tptp.aa_bool_nat Uu Uub)) tptp.one_one_nat))) (forall ((Uu tptp.fun_int_Code_integer) (Uua tptp.set_int) (Uub tptp.int)) (= (tptp.aa_int_Code_integer (tptp.aa_set5517701783735052070nteger (tptp.aTP_Lamm_aam Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_set_int_bool (tptp.member_int Uub) Uua) (tptp.aa_int_Code_integer Uu Uub)) tptp.one_one_Code_integer))) (forall ((Uu tptp.fun_int_assn) (Uua tptp.set_int) (Uub tptp.int)) (= (tptp.aa_int_assn (tptp.aa_set5310648174735401585t_assn (tptp.aTP_Lamm_aap Uu) Uua) Uub) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn (tptp.if_assn (tptp.aa_set_int_bool (tptp.member_int Uub) Uua)) (tptp.aa_int_assn Uu Uub)) tptp.one_one_assn))) (forall ((Uu tptp.fun_int_rat) (Uua tptp.set_int) (Uub tptp.int)) (= (tptp.aa_int_rat (tptp.aa_set7979663334043413281nt_rat (tptp.aTP_Lamm_aas Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.aa_set_int_bool (tptp.member_int Uub) Uua)) (tptp.aa_int_rat Uu Uub)) tptp.one_one_rat))) (forall ((Uu tptp.code_integer) (Uua tptp.fun_Co8499238673658658103nteger) (Uub tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_fun4435975922079263404nteger (tptp.aTP_Lamm_pk Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer Uu) Uub) (tptp.aa_Cod1783974652533396728nteger Uua Uub)) tptp.zero_z3403309356797280102nteger))) (forall ((Uu tptp.code_integer) (Uua tptp.fun_Code_integer_rat) (Uub tptp.code_integer)) (= (tptp.aa_Code_integer_rat (tptp.aa_fun8169474305930283170er_rat (tptp.aTP_Lamm_po Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer Uu) Uub)) (tptp.aa_Code_integer_rat Uua Uub)) tptp.zero_zero_rat))) (forall ((Uu tptp.bool) (Uua tptp.fun_bo7282069421189217543nteger) (Uub tptp.bool)) (= (tptp.aa_bool_Code_integer (tptp.aa_fun1377107737837666940nteger (tptp.aTP_Lamm_ph Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fequal_bool Uu) Uub) (tptp.aa_bool_Code_integer Uua Uub)) tptp.zero_z3403309356797280102nteger))) (forall ((Uu tptp.bool) (Uua tptp.fun_bool_rat) (Uub tptp.bool)) (= (tptp.aa_bool_rat (tptp.aa_fun224000846028461884ol_rat (tptp.aTP_Lamm_pl Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fequal_bool Uu) Uub)) (tptp.aa_bool_rat Uua Uub)) tptp.zero_zero_rat))) (forall ((Uu tptp.bool) (Uua tptp.fun_bool_nat) (Uub tptp.bool)) (= (tptp.aa_bool_nat (tptp.aa_fun9101744387563128124ol_nat (tptp.aTP_Lamm_pp Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fequal_bool Uu) Uub)) (tptp.aa_bool_nat Uua Uub)) tptp.zero_zero_nat))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_Code_integer) (Uub tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aa_fun589076786913273746nteger (tptp.aTP_Lamm_pi Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uu) Uub) (tptp.aa_nat_Code_integer Uua Uub)) tptp.zero_z3403309356797280102nteger))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_rat) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_pm Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uu) Uub)) (tptp.aa_nat_rat Uua Uub)) tptp.zero_zero_rat))) (forall ((Uu tptp.int) (Uua tptp.fun_int_Code_integer) (Uub tptp.int)) (= (tptp.aa_int_Code_integer (tptp.aa_fun5304498221708291146nteger (tptp.aTP_Lamm_pj Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int Uu) Uub) (tptp.aa_int_Code_integer Uua Uub)) tptp.zero_z3403309356797280102nteger))) (forall ((Uu tptp.int) (Uua tptp.fun_int_rat) (Uub tptp.int)) (= (tptp.aa_int_rat (tptp.aa_fun1481061427733998144nt_rat (tptp.aTP_Lamm_pn Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int Uu) Uub)) (tptp.aa_int_rat Uua Uub)) tptp.zero_zero_rat))) (forall ((Uu tptp.int) (Uua tptp.fun_int_nat) (Uub tptp.int)) (= (tptp.aa_int_nat (tptp.aa_fun6506752150744536624nt_nat (tptp.aTP_Lamm_pq Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int Uu) Uub)) (tptp.aa_int_nat Uua Uub)) tptp.zero_zero_nat))) (forall ((Uu tptp.code_integer) (Uua tptp.fun_Co8499238673658658103nteger) (Uub tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_fun4435975922079263404nteger (tptp.aTP_Lamm_qe Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer Uu) Uub) (tptp.aa_Cod1783974652533396728nteger Uua Uub)) tptp.one_one_Code_integer))) (forall ((Uu tptp.code_integer) (Uua tptp.fun_Co4490034186337852034r_assn) (Uub tptp.code_integer)) (= (tptp.aa_Code_integer_assn (tptp.aa_fun4119713415300323650r_assn (tptp.aTP_Lamm_qi Uu) Uua) Uub) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn (tptp.if_assn (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer Uu) Uub)) (tptp.aa_Code_integer_assn Uua Uub)) tptp.one_one_assn))) (forall ((Uu tptp.bool) (Uua tptp.fun_bo7282069421189217543nteger) (Uub tptp.bool)) (= (tptp.aa_bool_Code_integer (tptp.aa_fun1377107737837666940nteger (tptp.aTP_Lamm_qb Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fequal_bool Uu) Uub) (tptp.aa_bool_Code_integer Uua Uub)) tptp.one_one_Code_integer))) (forall ((Uu tptp.bool) (Uua tptp.fun_bool_assn) (Uub tptp.bool)) (= (tptp.aa_bool_assn (tptp.aa_fun923664478788943164l_assn (tptp.aTP_Lamm_qf Uu) Uua) Uub) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn (tptp.if_assn (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fequal_bool Uu) Uub)) (tptp.aa_bool_assn Uua Uub)) tptp.one_one_assn))) (forall ((Uu tptp.bool) (Uua tptp.fun_bool_rat) (Uub tptp.bool)) (= (tptp.aa_bool_rat (tptp.aa_fun224000846028461884ol_rat (tptp.aTP_Lamm_qj Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fequal_bool Uu) Uub)) (tptp.aa_bool_rat Uua Uub)) tptp.one_one_rat))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_Code_integer) (Uub tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aa_fun589076786913273746nteger (tptp.aTP_Lamm_qc Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uu) Uub) (tptp.aa_nat_Code_integer Uua Uub)) tptp.one_one_Code_integer))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_assn) (Uub tptp.nat)) (= (tptp.aa_nat_assn (tptp.aa_fun785744391571715112t_assn (tptp.aTP_Lamm_qg Uu) Uua) Uub) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn (tptp.if_assn (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uu) Uub)) (tptp.aa_nat_assn Uua Uub)) tptp.one_one_assn))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_rat) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_qk Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uu) Uub)) (tptp.aa_nat_rat Uua Uub)) tptp.one_one_rat))) (forall ((Uu tptp.int) (Uua tptp.fun_int_Code_integer) (Uub tptp.int)) (= (tptp.aa_int_Code_integer (tptp.aa_fun5304498221708291146nteger (tptp.aTP_Lamm_qd Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int Uu) Uub) (tptp.aa_int_Code_integer Uua Uub)) tptp.one_one_Code_integer))) (forall ((Uu tptp.int) (Uua tptp.fun_int_assn) (Uub tptp.int)) (= (tptp.aa_int_assn (tptp.aa_fun919007281442365664t_assn (tptp.aTP_Lamm_qh Uu) Uua) Uub) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn (tptp.if_assn (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int Uu) Uub)) (tptp.aa_int_assn Uua Uub)) tptp.one_one_assn))) (forall ((Uu tptp.code_integer) (Uua tptp.fun_Co8499238673658658103nteger) (Uub tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_fun4435975922079263404nteger (tptp.aTP_Lamm_pu Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer Uub) Uu) (tptp.aa_Cod1783974652533396728nteger Uua Uub)) tptp.zero_z3403309356797280102nteger))) (forall ((Uu tptp.code_integer) (Uua tptp.fun_Code_integer_rat) (Uub tptp.code_integer)) (= (tptp.aa_Code_integer_rat (tptp.aa_fun8169474305930283170er_rat (tptp.aTP_Lamm_py Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer Uub) Uu)) (tptp.aa_Code_integer_rat Uua Uub)) tptp.zero_zero_rat))) (forall ((Uu tptp.bool) (Uua tptp.fun_bo7282069421189217543nteger) (Uub tptp.bool)) (= (tptp.aa_bool_Code_integer (tptp.aa_fun1377107737837666940nteger (tptp.aTP_Lamm_pr Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fequal_bool Uub) Uu) (tptp.aa_bool_Code_integer Uua Uub)) tptp.zero_z3403309356797280102nteger))) (forall ((Uu tptp.bool) (Uua tptp.fun_bool_rat) (Uub tptp.bool)) (= (tptp.aa_bool_rat (tptp.aa_fun224000846028461884ol_rat (tptp.aTP_Lamm_pv Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fequal_bool Uub) Uu)) (tptp.aa_bool_rat Uua Uub)) tptp.zero_zero_rat))) (forall ((Uu tptp.bool) (Uua tptp.fun_bool_nat) (Uub tptp.bool)) (= (tptp.aa_bool_nat (tptp.aa_fun9101744387563128124ol_nat (tptp.aTP_Lamm_pz Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fequal_bool Uub) Uu)) (tptp.aa_bool_nat Uua Uub)) tptp.zero_zero_nat))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_Code_integer) (Uub tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aa_fun589076786913273746nteger (tptp.aTP_Lamm_ps Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uub) Uu) (tptp.aa_nat_Code_integer Uua Uub)) tptp.zero_z3403309356797280102nteger))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_rat) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_pw Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uub) Uu)) (tptp.aa_nat_rat Uua Uub)) tptp.zero_zero_rat))) (forall ((Uu tptp.int) (Uua tptp.fun_int_Code_integer) (Uub tptp.int)) (= (tptp.aa_int_Code_integer (tptp.aa_fun5304498221708291146nteger (tptp.aTP_Lamm_pt Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int Uub) Uu) (tptp.aa_int_Code_integer Uua Uub)) tptp.zero_z3403309356797280102nteger))) (forall ((Uu tptp.int) (Uua tptp.fun_int_rat) (Uub tptp.int)) (= (tptp.aa_int_rat (tptp.aa_fun1481061427733998144nt_rat (tptp.aTP_Lamm_px Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int Uub) Uu)) (tptp.aa_int_rat Uua Uub)) tptp.zero_zero_rat))) (forall ((Uu tptp.int) (Uua tptp.fun_int_nat) (Uub tptp.int)) (= (tptp.aa_int_nat (tptp.aa_fun6506752150744536624nt_nat (tptp.aTP_Lamm_qa Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int Uub) Uu)) (tptp.aa_int_nat Uua Uub)) tptp.zero_zero_nat))) (forall ((Uu tptp.code_integer) (Uua tptp.fun_Co8499238673658658103nteger) (Uub tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_fun4435975922079263404nteger (tptp.aTP_Lamm_qo Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer Uub) Uu) (tptp.aa_Cod1783974652533396728nteger Uua Uub)) tptp.one_one_Code_integer))) (forall ((Uu tptp.code_integer) (Uua tptp.fun_Co4490034186337852034r_assn) (Uub tptp.code_integer)) (= (tptp.aa_Code_integer_assn (tptp.aa_fun4119713415300323650r_assn (tptp.aTP_Lamm_qs Uu) Uua) Uub) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn (tptp.if_assn (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer Uub) Uu)) (tptp.aa_Code_integer_assn Uua Uub)) tptp.one_one_assn))) (forall ((Uu tptp.bool) (Uua tptp.fun_bo7282069421189217543nteger) (Uub tptp.bool)) (= (tptp.aa_bool_Code_integer (tptp.aa_fun1377107737837666940nteger (tptp.aTP_Lamm_ql Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fequal_bool Uub) Uu) (tptp.aa_bool_Code_integer Uua Uub)) tptp.one_one_Code_integer))) (forall ((Uu tptp.bool) (Uua tptp.fun_bool_assn) (Uub tptp.bool)) (= (tptp.aa_bool_assn (tptp.aa_fun923664478788943164l_assn (tptp.aTP_Lamm_qp Uu) Uua) Uub) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn (tptp.if_assn (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fequal_bool Uub) Uu)) (tptp.aa_bool_assn Uua Uub)) tptp.one_one_assn))) (forall ((Uu tptp.bool) (Uua tptp.fun_bool_rat) (Uub tptp.bool)) (= (tptp.aa_bool_rat (tptp.aa_fun224000846028461884ol_rat (tptp.aTP_Lamm_qt Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fequal_bool Uub) Uu)) (tptp.aa_bool_rat Uua Uub)) tptp.one_one_rat))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_Code_integer) (Uub tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aa_fun589076786913273746nteger (tptp.aTP_Lamm_qm Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uub) Uu) (tptp.aa_nat_Code_integer Uua Uub)) tptp.one_one_Code_integer))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_assn) (Uub tptp.nat)) (= (tptp.aa_nat_assn (tptp.aa_fun785744391571715112t_assn (tptp.aTP_Lamm_qq Uu) Uua) Uub) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn (tptp.if_assn (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uub) Uu)) (tptp.aa_nat_assn Uua Uub)) tptp.one_one_assn))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_rat) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_qu Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uub) Uu)) (tptp.aa_nat_rat Uua Uub)) tptp.one_one_rat))) (forall ((Uu tptp.int) (Uua tptp.fun_int_Code_integer) (Uub tptp.int)) (= (tptp.aa_int_Code_integer (tptp.aa_fun5304498221708291146nteger (tptp.aTP_Lamm_qn Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int Uub) Uu) (tptp.aa_int_Code_integer Uua Uub)) tptp.one_one_Code_integer))) (forall ((Uu tptp.int) (Uua tptp.fun_int_assn) (Uub tptp.int)) (= (tptp.aa_int_assn (tptp.aa_fun919007281442365664t_assn (tptp.aTP_Lamm_qr Uu) Uua) Uub) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn (tptp.if_assn (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int Uub) Uu)) (tptp.aa_int_assn Uua Uub)) tptp.one_one_assn))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer) (Uub tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger Uua))) (= (tptp.aa_Cod6977894654539884864nteger (tptp.aa_Cod8380929501330563836nteger (tptp.aTP_Lamm_aml Uu) Uua) Uub) (tptp.if_Pro6119634080678213985nteger (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer Uub) tptp.zero_z3403309356797280102nteger) (tptp.produc1086072967326762835nteger _let_1 tptp.zero_z3403309356797280102nteger) (tptp.produc1086072967326762835nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger Uu)) Uub)))))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer) (Uub tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger Uua))) (= (tptp.aa_Cod6977894654539884864nteger (tptp.aa_Cod8380929501330563836nteger (tptp.aTP_Lamm_amm Uu) Uua) Uub) (tptp.if_Pro6119634080678213985nteger (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer Uub) tptp.zero_z3403309356797280102nteger) (tptp.produc1086072967326762835nteger _let_1 tptp.zero_z3403309356797280102nteger) (tptp.produc1086072967326762835nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.abs_abs_Code_integer Uu)) Uub)))))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer) (Uub tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger Uua))) (= (tptp.aa_Cod6977894654539884864nteger (tptp.aa_Cod8380929501330563836nteger (tptp.aTP_Lamm_amk Uu) Uua) Uub) (tptp.if_Pro6119634080678213985nteger (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer Uub) tptp.zero_z3403309356797280102nteger) (tptp.produc1086072967326762835nteger _let_1 tptp.zero_z3403309356797280102nteger) (tptp.produc1086072967326762835nteger (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger Uu) Uub)))))) (forall ((Uu tptp.fun_Co8499238673658658103nteger) (Uua tptp.fun_Co8822979462182099027r_bool) (Uub tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_fun526110101794841038nteger (tptp.aTP_Lamm_vn Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_Code_integer_bool Uua Uub) (tptp.aa_Cod1783974652533396728nteger Uu Uub)) tptp.zero_z3403309356797280102nteger))) (forall ((Uu tptp.fun_Code_integer_rat) (Uua tptp.fun_Co8822979462182099027r_bool) (Uub tptp.code_integer)) (= (tptp.aa_Code_integer_rat (tptp.aa_fun4600455420518417865er_rat (tptp.aTP_Lamm_vr Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.aa_Code_integer_bool Uua Uub)) (tptp.aa_Code_integer_rat Uu Uub)) tptp.zero_zero_rat))) (forall ((Uu tptp.fun_bo7282069421189217543nteger) (Uua tptp.fun_bool_bool) (Uub tptp.bool)) (= (tptp.aa_bool_Code_integer (tptp.aa_fun6792447306164353798nteger (tptp.aTP_Lamm_vj Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_bool_bool Uua Uub) (tptp.aa_bool_Code_integer Uu Uub)) tptp.zero_z3403309356797280102nteger))) (forall ((Uu tptp.fun_bool_rat) (Uua tptp.fun_bool_bool) (Uub tptp.bool)) (= (tptp.aa_bool_rat (tptp.aa_fun4278745445771542273ol_rat (tptp.aTP_Lamm_vo Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.aa_bool_bool Uua Uub)) (tptp.aa_bool_rat Uu Uub)) tptp.zero_zero_rat))) (forall ((Uu tptp.fun_bool_nat) (Uua tptp.fun_bool_bool) (Uub tptp.bool)) (= (tptp.aa_bool_nat (tptp.aa_fun7786974004164939001ol_nat (tptp.aTP_Lamm_vs Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_bool_bool Uua Uub)) (tptp.aa_bool_nat Uu Uub)) tptp.zero_zero_nat))) (forall ((Uu tptp.fun_nat_Code_integer) (Uua tptp.fun_nat_bool) (Uub tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aa_fun42370497693836430nteger (tptp.aTP_Lamm_vk Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_nat_bool Uua Uub) (tptp.aa_nat_Code_integer Uu Uub)) tptp.zero_z3403309356797280102nteger))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.fun_nat_bool) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_fun5656162108953708681at_rat (tptp.aTP_Lamm_vp Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.aa_nat_bool Uua Uub)) (tptp.aa_nat_rat Uu Uub)) tptp.zero_zero_rat))) (forall ((Uu tptp.fun_int_Code_integer) (Uua tptp.fun_int_bool) (Uub tptp.int)) (= (tptp.aa_int_Code_integer (tptp.aa_fun5397227419668681614nteger (tptp.aTP_Lamm_vl Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_int_bool Uua Uub) (tptp.aa_int_Code_integer Uu Uub)) tptp.zero_z3403309356797280102nteger))) (forall ((Uu tptp.fun_int_rat) (Uua tptp.fun_int_bool) (Uub tptp.int)) (= (tptp.aa_int_rat (tptp.aa_fun4400602662665189257nt_rat (tptp.aTP_Lamm_vq Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.aa_int_bool Uua Uub)) (tptp.aa_int_rat Uu Uub)) tptp.zero_zero_rat))) (forall ((Uu tptp.fun_int_nat) (Uua tptp.fun_int_bool) (Uub tptp.int)) (= (tptp.aa_int_nat (tptp.aa_fun7908831221058585985nt_nat (tptp.aTP_Lamm_vt Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_int_bool Uua Uub)) (tptp.aa_int_nat Uu Uub)) tptp.zero_zero_nat))) (forall ((Uu tptp.fun_Co8499238673658658103nteger) (Uua tptp.fun_Co8822979462182099027r_bool) (Uub tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_fun526110101794841038nteger (tptp.aTP_Lamm_xd Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_Code_integer_bool Uua Uub) (tptp.aa_Cod1783974652533396728nteger Uu Uub)) tptp.one_one_Code_integer))) (forall ((Uu tptp.fun_Co4490034186337852034r_assn) (Uua tptp.fun_Co8822979462182099027r_bool) (Uub tptp.code_integer)) (= (tptp.aa_Code_integer_assn (tptp.aa_fun8033543692415806745r_assn (tptp.aTP_Lamm_xh Uu) Uua) Uub) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn (tptp.if_assn (tptp.aa_Code_integer_bool Uua Uub)) (tptp.aa_Code_integer_assn Uu Uub)) tptp.one_one_assn))) (forall ((Uu tptp.fun_bo7282069421189217543nteger) (Uua tptp.fun_bool_bool) (Uub tptp.bool)) (= (tptp.aa_bool_Code_integer (tptp.aa_fun6792447306164353798nteger (tptp.aTP_Lamm_xa Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_bool_bool Uua Uub) (tptp.aa_bool_Code_integer Uu Uub)) tptp.one_one_Code_integer))) (forall ((Uu tptp.fun_bool_assn) (Uua tptp.fun_bool_bool) (Uub tptp.bool)) (= (tptp.aa_bool_assn (tptp.aa_fun5239432835080189521l_assn (tptp.aTP_Lamm_xe Uu) Uua) Uub) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn (tptp.if_assn (tptp.aa_bool_bool Uua Uub)) (tptp.aa_bool_assn Uu Uub)) tptp.one_one_assn))) (forall ((Uu tptp.fun_bool_rat) (Uua tptp.fun_bool_bool) (Uub tptp.bool)) (= (tptp.aa_bool_rat (tptp.aa_fun4278745445771542273ol_rat (tptp.aTP_Lamm_xi Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.aa_bool_bool Uua Uub)) (tptp.aa_bool_rat Uu Uub)) tptp.one_one_rat))) (forall ((Uu tptp.fun_nat_Code_integer) (Uua tptp.fun_nat_bool) (Uub tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aa_fun42370497693836430nteger (tptp.aTP_Lamm_xb Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_nat_bool Uua Uub) (tptp.aa_nat_Code_integer Uu Uub)) tptp.one_one_Code_integer))) (forall ((Uu tptp.fun_nat_assn) (Uua tptp.fun_nat_bool) (Uub tptp.nat)) (= (tptp.aa_nat_assn (tptp.aa_fun1954384836919635929t_assn (tptp.aTP_Lamm_xf Uu) Uua) Uub) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn (tptp.if_assn (tptp.aa_nat_bool Uua Uub)) (tptp.aa_nat_assn Uu Uub)) tptp.one_one_assn))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.fun_nat_bool) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_fun5656162108953708681at_rat (tptp.aTP_Lamm_xj Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.aa_nat_bool Uua Uub)) (tptp.aa_nat_rat Uu Uub)) tptp.one_one_rat))) (forall ((Uu tptp.fun_int_Code_integer) (Uua tptp.fun_int_bool) (Uub tptp.int)) (= (tptp.aa_int_Code_integer (tptp.aa_fun5397227419668681614nteger (tptp.aTP_Lamm_xc Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_int_bool Uua Uub) (tptp.aa_int_Code_integer Uu Uub)) tptp.one_one_Code_integer))) (forall ((Uu tptp.fun_int_assn) (Uua tptp.fun_int_bool) (Uub tptp.int)) (= (tptp.aa_int_assn (tptp.aa_fun6196142345855524569t_assn (tptp.aTP_Lamm_xg Uu) Uua) Uub) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn (tptp.if_assn (tptp.aa_int_bool Uua Uub)) (tptp.aa_int_assn Uu Uub)) tptp.one_one_assn))) (forall ((Uu tptp.fun_he6201055237484778573t_bool) (Uua tptp.fun_he4944555133437423336it_nat) (Uub tptp.heap_e7401611519738050253t_unit)) (= (tptp.aa_hea684056619475940329it_nat (tptp.aa_fun2986507860694160780it_nat (tptp.aTP_Lamm_fj Uu) Uua) Uub) (tptp.if_opt1729522071442692626it_nat (tptp.aa_hea1793595068369496646t_bool Uu Uub) (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat (tptp.aa_hea256619718444519449it_nat Uua Uub)) tptp.none_P9117596204409417319it_nat))) (forall ((Uu tptp.fun_he6201055237484778573t_bool) (Uua tptp.fun_he8889679731534893401it_nat) (Uub tptp.heap_e7401611519738050253t_unit)) (= (tptp.aa_hea4724376117875161946it_nat (tptp.aa_fun3370411987892275404it_nat (tptp.aTP_Lamm_fi Uu) Uua) Uub) (tptp.if_opt6883606601682554499it_nat (tptp.aa_hea1793595068369496646t_bool Uu Uub) (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat (tptp.aa_hea5645563107516622602it_nat Uua Uub)) tptp.none_P2651198173097904984it_nat))) (forall ((Uu tptp.fun_num_fun_num_num) (Uua tptp.option_num) (Uub tptp.num)) (= (tptp.aa_num_option_num (tptp.aa_opt8899475237019873193on_num (tptp.aTP_Lamm_fq Uu) Uua) Uub) (tptp.aa_opt5369159329878751634on_num (tptp.case_o6005452278849405969um_num (tptp.aa_num_option_num tptp.some_num Uub) (tptp.aa_num6390622462783740633on_num (tptp.aTP_Lamm_fp Uu) Uub)) Uua))) (forall ((Uu tptp.fun_Pr1003294667014919570it_nat) (Uua tptp.option8956607266484857688it_nat) (Uub tptp.produc8664842809031399944it_nat)) (= (tptp.aa_Pro8996696869555642526it_nat (tptp.aa_opt7728438819757478003it_nat (tptp.aTP_Lamm_fo Uu) Uua) Uub) (tptp.case_o2963978774867076333it_nat (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat Uub) (tptp.aa_Pro5635350972512700067it_nat (tptp.aTP_Lamm_fn Uu) Uub) Uua))) (forall ((Uu tptp.fun_Pr7750636411365408485it_nat) (Uua tptp.option3562590408128118217it_nat) (Uub tptp.produc3260487557148687353it_nat)) (= (tptp.aa_Pro5302094286594872192it_nat (tptp.aa_opt996909609682481350it_nat (tptp.aTP_Lamm_fm Uu) Uua) Uub) (tptp.case_o6061097939050036047it_nat (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat Uub) (tptp.aa_Pro7038079567744603766it_nat (tptp.aTP_Lamm_fl Uu) Uub) Uua))) (forall ((Uu tptp.option_nat) (Uua tptp.option_nat) (Uub tptp.nat)) (= (tptp.aa_nat_option_nat (tptp.aa_opt1558076126722380235on_nat (tptp.aTP_Lamm_du Uu) Uua) Uub) (tptp.case_o7429725398727453821at_nat Uu (tptp.aTP_Lamm_dt Uub) Uua))) (forall ((Uu tptp.option_set_nat) (Uua tptp.option_set_nat) (Uub tptp.set_nat)) (= (tptp.aa_set6119337032432945050et_nat (tptp.aa_opt5648106117674462701et_nat (tptp.aTP_Lamm_ds Uu) Uua) Uub) (tptp.case_o4054078431260844265et_nat Uu (tptp.aTP_Lamm_dr Uub) Uua))) (forall ((Uu tptp.option1583680563626158861at_nat) (Uua tptp.option1583680563626158861at_nat) (Uub tptp.set_Pr4329608150637261639at_nat)) (= (tptp.aa_set7071694670514008770at_nat (tptp.aa_opt1027706798495913626at_nat (tptp.aTP_Lamm_dq Uu) Uua) Uub) (tptp.case_o9080059180780454917at_nat Uu (tptp.aTP_Lamm_dp Uub) Uua))) (forall ((Uu tptp.option2498585697089621389at_nat) (Uua tptp.option2498585697089621389at_nat) (Uub tptp.set_Pr8551490117392284871at_nat)) (= (tptp.aa_set1897275755269116354at_nat (tptp.aa_opt1741456117285354266at_nat (tptp.aTP_Lamm_do Uu) Uua) Uub) (tptp.case_o8757249484648823045at_nat Uu (tptp.aTP_Lamm_dn Uub) Uua))) (forall ((Uu tptp.option2158460348403737357at_nat) (Uua tptp.option2158460348403737357at_nat) (Uub tptp.set_Pr8693737435421807431at_nat)) (= (tptp.aa_set6661686244540357314at_nat (tptp.aa_opt2198001859980869274at_nat (tptp.aTP_Lamm_dm Uu) Uua) Uub) (tptp.case_o7467001542679133189at_nat Uu (tptp.aTP_Lamm_dl Uub) Uua))) (forall ((Uu tptp.heap_Time_Heap_a) (Uua tptp.fun_a_2990225006182978344t_unit) (Uub tptp.heap_e7401611519738050253t_unit)) (= (tptp.aa_hea684056619475940329it_nat (tptp.aa_fun372765568861188684it_nat (tptp.aTP_Lamm_ahj Uu) Uua) Uub) (tptp.case_o7727800614283616222it_nat tptp.none_P9117596204409417319it_nat (tptp.produc5648861294512138360it_nat (tptp.aTP_Lamm_ahi Uua)) (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a Uu) Uub)))) (forall ((Uu tptp.heap_Time_Heap_a) (Uua tptp.fun_a_6093291656547882009Heap_a) (Uub tptp.heap_e7401611519738050253t_unit)) (= (tptp.aa_hea4724376117875161946it_nat (tptp.aa_fun6119220767042692876it_nat (tptp.aTP_Lamm_ahg Uu) Uua) Uub) (tptp.case_o6061097939050036047it_nat tptp.none_P2651198173097904984it_nat (tptp.produc7850007024774191849it_nat (tptp.aTP_Lamm_ahe Uua)) (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a Uu) Uub)))) (forall ((Uu tptp.fun_nat_fun_nat_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_agy Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat Uu Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) Uub)))) (forall ((Uu tptp.fun_nat_fun_nat_int) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_ahb Uu) Uua) Uub) (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int Uu Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) Uub)))) (forall ((Uu tptp.fun_Co3312552843764780407at_nat) (Uua tptp.nat) (Uub tptp.code_integer)) (= (tptp.aa_Code_integer_nat (tptp.aa_nat5852537043073606456er_nat (tptp.aTP_Lamm_rp Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_Cod8670293052248272184at_nat Uu Uub) Uua))) (forall ((Uu tptp.fun_Co822469698833053651at_int) (Uua tptp.nat) (Uub tptp.code_integer)) (= (tptp.aa_Code_integer_int (tptp.aa_nat1674686023564409748er_int (tptp.aTP_Lamm_th Uu) Uua) Uub) (tptp.aa_nat_int (tptp.aa_Cod4492442032739075476at_int Uu Uub) Uua))) (forall ((Uu tptp.fun_Co3009391273526075439nt_int) (Uua tptp.int) (Uub tptp.code_integer)) (= (tptp.aa_Code_integer_int (tptp.aa_int1390634949194299888er_int (tptp.aTP_Lamm_sd Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_Cod5491795744640130032nt_int Uu Uub) Uua))) (forall ((Uu tptp.fun_bool_fun_nat_nat) (Uua tptp.nat) (Uub tptp.bool)) (= (tptp.aa_bool_nat (tptp.aa_nat_fun_bool_nat (tptp.aTP_Lamm_rf Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_bool_fun_nat_nat Uu Uub) Uua))) (forall ((Uu tptp.fun_bool_fun_nat_int) (Uua tptp.nat) (Uub tptp.bool)) (= (tptp.aa_bool_int (tptp.aa_nat_fun_bool_int (tptp.aTP_Lamm_te Uu) Uua) Uub) (tptp.aa_nat_int (tptp.aa_bool_fun_nat_int Uu Uub) Uua))) (forall ((Uu tptp.fun_bool_fun_int_int) (Uua tptp.int) (Uub tptp.bool)) (= (tptp.aa_bool_int (tptp.aa_int_fun_bool_int (tptp.aTP_Lamm_ru Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_bool_fun_int_int Uu Uub) Uua))) (forall ((Uu tptp.fun_na5492297256294505719er_nat) (Uua tptp.code_integer) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_Cod8670293052248272184at_nat (tptp.aTP_Lamm_sq Uu) Uua) Uub) (tptp.aa_Code_integer_nat (tptp.aa_nat5852537043073606456er_nat Uu Uub) Uua))) (forall ((Uu tptp.fun_nat_fun_bool_nat) (Uua tptp.bool) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_bool_fun_nat_nat (tptp.aTP_Lamm_si Uu) Uua) Uub) (tptp.aa_bool_nat (tptp.aa_nat_fun_bool_nat Uu Uub) Uua))) (forall ((Uu tptp.fun_nat_fun_nat_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_lk Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat Uu Uub) Uua))) (forall ((Uu tptp.fun_nat_fun_nat_int) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_mr Uu) Uua) Uub) (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int Uu Uub) Uua))) (forall ((Uu tptp.fun_nat_fun_int_nat) (Uua tptp.int) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_int_fun_nat_nat (tptp.aTP_Lamm_sm Uu) Uua) Uub) (tptp.aa_int_nat (tptp.aa_nat_fun_int_nat Uu Uub) Uua))) (forall ((Uu tptp.fun_nat_fun_int_int) (Uua tptp.int) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_mu Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_nat_fun_int_int Uu Uub) Uua))) (forall ((Uu tptp.fun_int_fun_nat_nat) (Uua tptp.nat) (Uub tptp.int)) (= (tptp.aa_int_nat (tptp.aa_nat_fun_int_nat (tptp.aTP_Lamm_rk Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_int_fun_nat_nat Uu Uub) Uua))) (forall ((Uu tptp.fun_int_fun_nat_int) (Uua tptp.nat) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int (tptp.aTP_Lamm_mx Uu) Uua) Uub) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int Uu Uub) Uua))) (forall ((Uu tptp.fun_int_fun_int_int) (Uua tptp.int) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.aTP_Lamm_ln Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int Uu Uub) Uua))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer) (Uub tptp.code_integer)) (= (tptp.aa_Cod2825494507867081354r_bool (tptp.aa_Cod4981436349852597092r_bool (tptp.aTP_Lamm_ami Uu) Uua) Uub) (tptp.produc5135875973608410785r_bool (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) Uu) Uua) (tptp.aa_Cod1783974652533396728nteger (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger Uua)) Uub)) (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer Uub) tptp.one_one_Code_integer)))) (forall ((Uu tptp.fun_nat_fun_nat_int) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_abv Uu) Uua) Uub) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_mr Uu) Uub)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc Uub)) Uua)))) (forall ((Uu tptp.fun_nat_fun_nat_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_abt Uu) Uua) Uub) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_lk Uu) Uub)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc Uub)) Uua)))) (forall ((Uu tptp.fun_nat_fun_nat_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_abq Uu) Uua) Uub) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_lk Uu) Uub)) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc Uub)) Uua)))) (forall ((Uu tptp.produc7822875418678951345atural) (Uua tptp.code_natural) (Uub tptp.code_natural)) (= (tptp.aa_Cod6808739660676082561atural (tptp.aa_Cod4292056611156568242atural (tptp.aTP_Lamm_aoz Uu) Uua) Uub) (tptp.produc8282080750456430313atural (tptp.aa_Cod8811915439870959971atural (tptp.aTP_Lamm_aoy Uua) Uub) (tptp.produc6591912806276919810atural (tptp.aa_Pro7165575656943818355atural tptp.next Uu))))) (forall ((Uu tptp.rat) (Uua tptp.int) (Uub tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int (tptp.aTP_Lamm_aoe Uu) Uua) Uub) (tptp.aa_Pro6970504127699319548nt_int (tptp.aa_fun8026974734089330650nt_int tptp.produc4245557441103728435nt_int (tptp.aa_int1966403025003302569nt_int (tptp.aTP_Lamm_aod Uua) Uub)) (tptp.quotient_of Uu)))) (forall ((Uu tptp.rat) (Uua tptp.int) (Uub tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int (tptp.aTP_Lamm_aoc Uu) Uua) Uub) (tptp.aa_Pro6970504127699319548nt_int (tptp.aa_fun8026974734089330650nt_int tptp.produc4245557441103728435nt_int (tptp.aa_int1966403025003302569nt_int (tptp.aTP_Lamm_aob Uua) Uub)) (tptp.quotient_of Uu)))) (forall ((Uu tptp.rat) (Uua tptp.int) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_anz Uu) Uua) Uub)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool (tptp.aa_int2327297053056786951t_bool (tptp.aTP_Lamm_any Uua) Uub)) (tptp.quotient_of Uu))))) (forall ((Uu tptp.rat) (Uua tptp.int) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_anx Uu) Uua) Uub)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun2111382812409994774t_bool tptp.produc8560705615207772305t_bool (tptp.aa_int2327297053056786951t_bool (tptp.aTP_Lamm_anw Uua) Uub)) (tptp.quotient_of Uu))))) (forall ((Uu tptp.rat) (Uua tptp.int) (Uub tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int (tptp.aTP_Lamm_anv Uu) Uua) Uub) (tptp.aa_Pro6970504127699319548nt_int (tptp.aa_fun8026974734089330650nt_int tptp.produc4245557441103728435nt_int (tptp.aa_int1966403025003302569nt_int (tptp.aTP_Lamm_anu Uua) Uub)) (tptp.quotient_of Uu)))) (forall ((Uu tptp.rat) (Uua tptp.int) (Uub tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int (tptp.aTP_Lamm_ant Uu) Uua) Uub) (tptp.aa_Pro6970504127699319548nt_int (tptp.aa_fun8026974734089330650nt_int tptp.produc4245557441103728435nt_int (tptp.aa_int1966403025003302569nt_int (tptp.aTP_Lamm_ans Uua) Uub)) (tptp.quotient_of Uu)))) (forall ((Uu tptp.fun_int_fun_nat_int) (Uua tptp.set_int) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_set6310687161026558745at_int (tptp.aTP_Lamm_my Uu) Uua) Uub) (tptp.groups1705073143266064639nt_int (tptp.aa_nat_fun_int_int (tptp.aTP_Lamm_mx Uu) Uub) Uua))) (forall ((Uu tptp.fun_nat_fun_int_int) (Uua tptp.set_nat) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_set3358596244511904025nt_int (tptp.aTP_Lamm_mv Uu) Uua) Uub) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_mu Uu) Uub)) Uua))) (forall ((Uu tptp.fun_nat_fun_nat_int) (Uua tptp.set_nat) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_set2359242532610849469at_int (tptp.aTP_Lamm_ms Uu) Uua) Uub) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_mr Uu) Uub)) Uua))) (forall ((Uu tptp.fun_int_fun_int_int) (Uua tptp.set_int) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_set7310040872927613301nt_int (tptp.aTP_Lamm_na Uu) Uua) Uub) (tptp.groups1705073143266064639nt_int (tptp.aa_int_fun_int_int (tptp.aTP_Lamm_ln Uu) Uub) Uua))) (forall ((Uu tptp.fun_nat_fun_nat_nat) (Uua tptp.set_nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_set6537093552120046177at_nat (tptp.aTP_Lamm_mp Uu) Uua) Uub) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_lk Uu) Uub)) Uua))) (forall ((Uu tptp.fun_int_fun_int_int) (Uua tptp.set_int) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_set7310040872927613301nt_int (tptp.aTP_Lamm_lo Uu) Uua) Uub) (tptp.groups4538972089207619220nt_int (tptp.aa_int_fun_int_int (tptp.aTP_Lamm_ln Uu) Uub) Uua))) (forall ((Uu tptp.fun_nat_fun_nat_nat) (Uua tptp.set_nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_set6537093552120046177at_nat (tptp.aTP_Lamm_ll Uu) Uua) Uub) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_lk Uu) Uub)) Uua))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.fun_nat_rat) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_pg Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat Uu Uub)) (tptp.aa_nat_rat (tptp.power_power_rat tptp.zero_zero_rat) Uub))) (tptp.aa_nat_rat Uua Uub)))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool (tptp.aa_nat2079453845469346690t_bool (tptp.aTP_Lamm_ani Uu) Uua) Uub)) (and (= (tptp.aa_list_nat_nat tptp.size_size_list_nat Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) tptp.one_one_nat)) (= (tptp.aa_list_nat_nat tptp.groups4561878855575611511st_nat Uub) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool (tptp.aa_nat2079453845469346690t_bool (tptp.aTP_Lamm_anj Uu) Uua) Uub)) (and (= (tptp.aa_list_nat_nat tptp.size_size_list_nat Uub) Uu) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_list_nat_nat tptp.groups4561878855575611511st_nat Uub)) tptp.one_one_nat) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool (tptp.aa_nat2079453845469346690t_bool (tptp.aTP_Lamm_anh Uu) Uua) Uub)) (and (= (tptp.aa_list_nat_nat tptp.size_size_list_nat Uub) Uu) (= (tptp.aa_list_nat_nat tptp.groups4561878855575611511st_nat Uub) Uua)))) (forall ((Uu tptp.heap_e7401611519738050253t_unit) (Uua tptp.heap_e7401611519738050253t_unit) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_hea5076648075882977743t_bool (tptp.aTP_Lamm_cn Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.lim_Product_unit Uu)) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uub) (tptp.lim_Product_unit Uua)))))) (forall ((Uu tptp.set_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_aly Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat (tptp.aa_nat_nat tptp.suc Uub)) Uu)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uub) Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_nat8857836526276733660t_bool (tptp.aTP_Lamm_ang Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat Uub) (tptp.pow_nat (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) Uu)))) (= (tptp.aa_set_nat_nat tptp.finite_card_nat Uub) Uua)))) (forall ((Uu tptp.rat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_nat_fun_nat_rat (tptp.aTP_Lamm_acr Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat Uu) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uub))) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) Uub))))) (forall ((Uu tptp.heap_e7401611519738050253t_unit) (Uua tptp.set_nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_set3744802623701456604t_bool (tptp.aTP_Lamm_co Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uub) (tptp.lim_Product_unit Uu))) (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uub) Uua)))))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_aou Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uua) Uu)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uub) Uu)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Uua) Uub))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.nat) (Uub tptp.set_Code_integer)) (= (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.aa_nat1024103762897335311r_bool (tptp.aTP_Lamm_aky Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.ord_le7084787975880047091nteger Uub) Uu)) (= (tptp.finite4902975817058060853nteger Uub) Uua)))) (forall ((Uu tptp.set_Pr1261947904930325089at_nat) (Uua tptp.nat) (Uub tptp.set_Pr1261947904930325089at_nat)) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_nat1303072629729950279t_bool (tptp.aTP_Lamm_akz Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool tptp.ord_le3146513528884898305at_nat Uub) Uu)) (= (tptp.finite711546835091564841at_nat Uub) Uua)))) (forall ((Uu tptp.set_list_nat) (Uua tptp.nat) (Uub tptp.set_list_nat)) (= (tptp.pp (tptp.aa_set_list_nat_bool (tptp.aa_nat87836351786748620t_bool (tptp.aTP_Lamm_akw Uu) Uua) Uub)) (and (tptp.ord_le6045566169113846134st_nat Uub Uu) (= (tptp.finite_card_list_nat Uub) Uua)))) (forall ((Uu tptp.set_set_nat) (Uua tptp.nat) (Uub tptp.set_set_nat)) (= (tptp.pp (tptp.aa_set_set_nat_bool (tptp.aa_nat7515184090834925478t_bool (tptp.aTP_Lamm_akv Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_set_nat_bool (tptp.ord_le6893508408891458716et_nat Uub) Uu)) (= (tptp.finite_card_set_nat Uub) Uua)))) (forall ((Uu tptp.set_nat) (Uua tptp.nat) (Uub tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_nat8857836526276733660t_bool (tptp.aTP_Lamm_akx Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.ord_less_eq_set_nat Uub) Uu)) (= (tptp.aa_set_nat_nat tptp.finite_card_nat Uub) Uua)))) (forall ((Uu tptp.set_int) (Uua tptp.nat) (Uub tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_nat8397553574630087040t_bool (tptp.aTP_Lamm_ala Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool tptp.ord_less_eq_set_int Uub) Uu)) (= (tptp.finite_card_int Uub) Uua)))) (forall ((Uu tptp.set_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_alz Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uub) Uu)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uub) (tptp.aa_nat_nat tptp.suc Uua)))))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_abm Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) Uub)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uub)))) (forall ((Uu tptp.assn) (Uua tptp.assn) (Uub tptp.produc3658429121746597890et_nat)) (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.aa_ass8975924923219239432t_bool (tptp.aTP_Lamm_ep Uu) Uua) Uub)) (or (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn Uu) Uub)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn Uua) Uub))))) (forall ((Uu tptp.set_Pr8693737435421807431at_nat) (Uua tptp.set_Pr8693737435421807431at_nat) (Uub tptp.produc859450856879609959at_nat)) (= (tptp.pp (tptp.aa_Pro6098352494050694700t_bool (tptp.aa_set6997699984206591038t_bool (tptp.aTP_Lamm_cb Uu) Uua) Uub)) (or (tptp.member8206827879206165904at_nat Uub Uu) (tptp.member8206827879206165904at_nat Uub Uua)))) (forall ((Uu tptp.set_Pr8551490117392284871at_nat) (Uua tptp.set_Pr8551490117392284871at_nat) (Uub tptp.produc4166570645942440679at_nat)) (= (tptp.pp (tptp.aa_Pro5063669228512387756t_bool (tptp.aa_set5968938463291210814t_bool (tptp.aTP_Lamm_cc Uu) Uua) Uub)) (or (tptp.member6689249552917799696at_nat Uub Uu) (tptp.member6689249552917799696at_nat Uub Uua)))) (forall ((Uu tptp.set_Pr4329608150637261639at_nat) (Uua tptp.set_Pr4329608150637261639at_nat) (Uub tptp.produc3843707927480180839at_nat)) (= (tptp.pp (tptp.aa_Pro1809015098595223084t_bool (tptp.aa_set377272637606474814t_bool (tptp.aTP_Lamm_cd Uu) Uua) Uub)) (or (tptp.member8757157785044589968at_nat Uub Uu) (tptp.member8757157785044589968at_nat Uub Uua)))) (forall ((Uu tptp.set_Pr1261947904930325089at_nat) (Uua tptp.set_Pr1261947904930325089at_nat) (Uub tptp.product_prod_nat_nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat Uub))) (= (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_set5223363028666124222t_bool (tptp.aTP_Lamm_bv Uu) Uua) Uub)) (or (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 Uu)) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 Uua)))))) (forall ((Uu tptp.set_Pr958786334691620121nt_int) (Uua tptp.set_Pr958786334691620121nt_int) (Uub tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_set1381271197253378494t_bool (tptp.aTP_Lamm_bx Uu) Uua) Uub)) (or (tptp.member5262025264175285858nt_int Uub Uu) (tptp.member5262025264175285858nt_int Uub Uua)))) (forall ((Uu tptp.set_list_nat) (Uua tptp.set_list_nat) (Uub tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool (tptp.aa_set257547205302447420t_bool (tptp.aTP_Lamm_by Uu) Uua) Uub)) (or (tptp.member_list_nat Uub Uu) (tptp.member_list_nat Uub Uua)))) (forall ((Uu tptp.set_bool) (Uua tptp.set_bool) (Uub tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_set6670506438128111678l_bool (tptp.aTP_Lamm_bw Uu) Uua) Uub)) (or (tptp.pp (tptp.member_bool Uub Uu)) (tptp.pp (tptp.member_bool Uub Uua))))) (forall ((Uu tptp.set_set_nat) (Uua tptp.set_set_nat) (Uub tptp.set_nat)) (let ((_let_1 (tptp.member_set_nat Uub))) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set9121396911425987952t_bool (tptp.aTP_Lamm_bz Uu) Uua) Uub)) (or (tptp.pp (tptp.aa_set_set_nat_bool _let_1 Uu)) (tptp.pp (tptp.aa_set_set_nat_bool _let_1 Uua)))))) (forall ((Uu tptp.set_nat) (Uua tptp.set_nat) (Uub tptp.nat)) (let ((_let_1 (tptp.member_nat Uub))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_set3744802623701456604t_bool (tptp.aTP_Lamm_ce Uu) Uua) Uub)) (or (tptp.pp (tptp.aa_set_nat_bool _let_1 Uu)) (tptp.pp (tptp.aa_set_nat_bool _let_1 Uua)))))) (forall ((Uu tptp.set_int) (Uua tptp.set_int) (Uub tptp.int)) (let ((_let_1 (tptp.member_int Uub))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_set7012339369581096484t_bool (tptp.aTP_Lamm_ca Uu) Uua) Uub)) (or (tptp.pp (tptp.aa_set_int_bool _let_1 Uu)) (tptp.pp (tptp.aa_set_int_bool _let_1 Uua)))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_aia Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Uu) Uua)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Uua) Uub))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_acv Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Uu) Uub)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Uub) Uua))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_ahz Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Uu) Uub)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Uua) Uub))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_acy Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Uu) Uub)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Uub) Uua))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_acx Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Uu) Uub)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Uub) Uua))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_acw Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Uu) Uub)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Uub) Uua))))) (forall ((Uu tptp.assn) (Uua tptp.assn) (Uub tptp.produc3658429121746597890et_nat)) (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.aa_ass8975924923219239432t_bool (tptp.aTP_Lamm_eq Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn Uu) Uub)) (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.rep_assn Uua) Uub))))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat Uub))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_aog Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_nat_bool _let_1 Uua)) (tptp.pp (tptp.aa_nat_bool _let_1 Uu)))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int Uub))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_anq Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_int_bool _let_1 Uua)) (tptp.pp (tptp.aa_int_bool _let_1 Uu)))))) (forall ((Uu tptp.set_Pr1261947904930325089at_nat) (Uua tptp.set_Pr1261947904930325089at_nat) (Uub tptp.product_prod_nat_nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat Uub))) (= (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_set5223363028666124222t_bool (tptp.aTP_Lamm_bo Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 Uu)) (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 Uua)))))) (forall ((Uu tptp.set_Pr958786334691620121nt_int) (Uua tptp.set_Pr958786334691620121nt_int) (Uub tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_set1381271197253378494t_bool (tptp.aTP_Lamm_bj Uu) Uua) Uub)) (and (tptp.member5262025264175285858nt_int Uub Uu) (tptp.member5262025264175285858nt_int Uub Uua)))) (forall ((Uu tptp.set_list_nat) (Uua tptp.set_list_nat) (Uub tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool (tptp.aa_set257547205302447420t_bool (tptp.aTP_Lamm_bk Uu) Uua) Uub)) (and (tptp.member_list_nat Uub Uu) (tptp.member_list_nat Uub Uua)))) (forall ((Uu tptp.set_bool) (Uua tptp.set_bool) (Uub tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_set6670506438128111678l_bool (tptp.aTP_Lamm_bi Uu) Uua) Uub)) (and (tptp.pp (tptp.member_bool Uub Uu)) (tptp.pp (tptp.member_bool Uub Uua))))) (forall ((Uu tptp.set_set_nat) (Uua tptp.set_set_nat) (Uub tptp.set_nat)) (let ((_let_1 (tptp.member_set_nat Uub))) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set9121396911425987952t_bool (tptp.aTP_Lamm_bl Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_set_nat_bool _let_1 Uu)) (tptp.pp (tptp.aa_set_set_nat_bool _let_1 Uua)))))) (forall ((Uu tptp.set_nat) (Uua tptp.set_nat) (Uub tptp.nat)) (let ((_let_1 (tptp.member_nat Uub))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_set3744802623701456604t_bool (tptp.aTP_Lamm_bn Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool _let_1 Uu)) (tptp.pp (tptp.aa_set_nat_bool _let_1 Uua)))))) (forall ((Uu tptp.set_int) (Uua tptp.set_int) (Uub tptp.int)) (let ((_let_1 (tptp.member_int Uub))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_set7012339369581096484t_bool (tptp.aTP_Lamm_bm Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_int_bool _let_1 Uu)) (tptp.pp (tptp.aa_set_int_bool _let_1 Uua)))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.set_Code_integer) (Uub tptp.set_Code_integer)) (= (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.aa_set8732061614394825996r_bool (tptp.aTP_Lamm_qx Uu) Uua) Uub)) (= (tptp.minus_2355218937544613996nteger Uub Uu) (tptp.minus_2355218937544613996nteger Uua Uu)))) (forall ((Uu tptp.set_Pr1261947904930325089at_nat) (Uua tptp.set_Pr1261947904930325089at_nat) (Uub tptp.set_Pr1261947904930325089at_nat)) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool (tptp.aTP_Lamm_qy Uu) Uua) Uub)) (= (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat Uub) Uu) (tptp.aa_set8868280134176360700at_nat (tptp.aa_set3608868651603078568at_nat tptp.minus_1356011639430497352at_nat Uua) Uu)))) (forall ((Uu tptp.set_nat) (Uua tptp.set_nat) (Uub tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool (tptp.aTP_Lamm_qz Uu) Uua) Uub)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat Uub) Uu) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat tptp.minus_minus_set_nat Uua) Uu)))) (forall ((Uu tptp.set_int) (Uua tptp.set_int) (Uub tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aa_set7694327796961020398t_bool (tptp.aTP_Lamm_qw Uu) Uua) Uub)) (= (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int Uub) Uu) (tptp.aa_set_int_set_int (tptp.aa_set4234024024286713313et_int tptp.minus_minus_set_int Uua) Uu)))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_Co8822979462182099027r_bool) (Uub tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_fun8875953811088571772r_bool (tptp.aTP_Lamm_vm Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Uub) Uu)) (tptp.pp (tptp.aa_Code_integer_bool Uua Uub))))) (forall ((Uu tptp.set_Pr1261947904930325089at_nat) (Uua tptp.fun_Pr7757163693017731481t_bool) (Uub tptp.product_prod_nat_nat)) (= (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_fun830836278467416944t_bool (tptp.aTP_Lamm_al Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat Uub) Uu)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool Uua Uub))))) (forall ((Uu tptp.set_Pr958786334691620121nt_int) (Uua tptp.fun_Pr803113274115125473t_bool) (Uub tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun8917503761599146496t_bool (tptp.aTP_Lamm_an Uu) Uua) Uub)) (and (tptp.member5262025264175285858nt_int Uub Uu) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool Uua Uub))))) (forall ((Uu tptp.set_list_nat) (Uua tptp.fun_list_nat_bool) (Uub tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool (tptp.aa_fun6009467934925565500t_bool (tptp.aTP_Lamm_ao Uu) Uua) Uub)) (and (tptp.member_list_nat Uub Uu) (tptp.pp (tptp.aa_list_nat_bool Uua Uub))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bool_bool) (Uub tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_fun8098540714523660868l_bool (tptp.aTP_Lamm_am Uu) Uua) Uub)) (and (tptp.pp (tptp.member_bool Uub Uu)) (tptp.pp (tptp.aa_bool_bool Uua Uub))))) (forall ((Uu tptp.set_set_nat) (Uua tptp.fun_set_nat_bool) (Uub tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_fun3565389549526402364t_bool (tptp.aTP_Lamm_ap Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_set_nat_bool (tptp.member_set_nat Uub) Uu)) (tptp.pp (tptp.aa_set_nat_bool Uua Uub))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_bool) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_aq Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uub) Uu)) (tptp.pp (tptp.aa_nat_bool Uua Uub))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_bool) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun5146555767781538748t_bool (tptp.aTP_Lamm_ar Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uub) Uu)) (tptp.pp (tptp.aa_int_bool Uua Uub))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_Co8499238673658658103nteger) (Uub tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_fun6999757421500609566r_bool (tptp.aTP_Lamm_ub Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Uub) Uu)) (not (= (tptp.aa_Cod1783974652533396728nteger Uua Uub) tptp.zero_z3403309356797280102nteger))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_Code_integer_rat) (Uub tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_fun6870034422411604195r_bool (tptp.aTP_Lamm_uj Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Uub) Uu)) (not (= (tptp.aa_Code_integer_rat Uua Uub) tptp.zero_zero_rat))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bo7282069421189217543nteger) (Uub tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_fun7063430368917475406l_bool (tptp.aTP_Lamm_tv Uu) Uua) Uub)) (and (tptp.pp (tptp.member_bool Uub Uu)) (not (= (tptp.aa_bool_Code_integer Uua Uub) tptp.zero_z3403309356797280102nteger))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bool_rat) (Uub tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_fun4510340986217973961l_bool (tptp.aTP_Lamm_ud Uu) Uua) Uub)) (and (tptp.pp (tptp.member_bool Uub Uu)) (not (= (tptp.aa_bool_rat Uua Uub) tptp.zero_zero_rat))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bool_nat) (Uub tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_fun7969004623323359937l_bool (tptp.aTP_Lamm_ul Uu) Uua) Uub)) (and (tptp.pp (tptp.member_bool Uub Uu)) (not (= (tptp.aa_bool_nat Uua Uub) tptp.zero_zero_nat))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_Code_integer) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun1752071697927428280t_bool (tptp.aTP_Lamm_tx Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uub) Uu)) (not (= (tptp.aa_nat_Code_integer Uua Uub) tptp.zero_z3403309356797280102nteger))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_rat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun5637262893798792573t_bool (tptp.aTP_Lamm_uf Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uub) Uu)) (not (= (tptp.aa_nat_rat Uua Uub) tptp.zero_zero_rat))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun1783405840085286277t_bool (tptp.aTP_Lamm_un Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uub) Uu)) (not (= (tptp.aa_nat_nat Uua Uub) tptp.zero_zero_nat))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_Code_integer) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun3610984093196804608t_bool (tptp.aTP_Lamm_tz Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uub) Uu)) (not (= (tptp.aa_int_Code_integer Uua Uub) tptp.zero_z3403309356797280102nteger))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_rat) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun258058769140594373t_bool (tptp.aTP_Lamm_uh Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uub) Uu)) (not (= (tptp.aa_int_rat Uua Uub) tptp.zero_zero_rat))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_Co8499238673658658103nteger) (Uub tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_fun6999757421500609566r_bool (tptp.aTP_Lamm_uv Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Uub) Uu)) (not (= (tptp.aa_Cod1783974652533396728nteger Uua Uub) tptp.one_one_Code_integer))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_Co4490034186337852034r_assn) (Uub tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_fun8795547071341169043r_bool (tptp.aTP_Lamm_vd Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Uub) Uu)) (not (= (tptp.aa_Code_integer_assn Uua Uub) tptp.one_one_assn))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bo7282069421189217543nteger) (Uub tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_fun7063430368917475406l_bool (tptp.aTP_Lamm_up Uu) Uua) Uub)) (and (tptp.pp (tptp.member_bool Uub Uu)) (not (= (tptp.aa_bool_Code_integer Uua Uub) tptp.one_one_Code_integer))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bool_assn) (Uub tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_fun4109262947370446873l_bool (tptp.aTP_Lamm_ux Uu) Uua) Uub)) (and (tptp.pp (tptp.member_bool Uub Uu)) (not (= (tptp.aa_bool_assn Uua Uub) tptp.one_one_assn))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bool_rat) (Uub tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_fun4510340986217973961l_bool (tptp.aTP_Lamm_vf Uu) Uua) Uub)) (and (tptp.pp (tptp.member_bool Uub Uu)) (not (= (tptp.aa_bool_rat Uua Uub) tptp.one_one_rat))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_Code_integer) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun1752071697927428280t_bool (tptp.aTP_Lamm_ur Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uub) Uu)) (not (= (tptp.aa_nat_Code_integer Uua Uub) tptp.one_one_Code_integer))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_assn) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun1272683333798124589t_bool (tptp.aTP_Lamm_uz Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uub) Uu)) (not (= (tptp.aa_nat_assn Uua Uub) tptp.one_one_assn))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_rat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun5637262893798792573t_bool (tptp.aTP_Lamm_vh Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uub) Uu)) (not (= (tptp.aa_nat_rat Uua Uub) tptp.one_one_rat))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_Code_integer) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun3610984093196804608t_bool (tptp.aTP_Lamm_ut Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uub) Uu)) (not (= (tptp.aa_int_Code_integer Uua Uub) tptp.one_one_Code_integer))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_assn) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun1414614411059211637t_bool (tptp.aTP_Lamm_vb Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uub) Uu)) (not (= (tptp.aa_int_assn Uua Uub) tptp.one_one_assn))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_Co8499238673658658103nteger) (Uub tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_fun6999757421500609566r_bool (tptp.aTP_Lamm_ajr Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Uub) Uu)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_Cod1783974652533396728nteger Uua Uub))))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_Code_integer_nat) (Uub tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_fun3540204951715082475r_bool (tptp.aTP_Lamm_ajk Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Uub) Uu)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_Code_integer_nat Uua Uub))))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_Code_integer_int) (Uub tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_fun6578047036179216271r_bool (tptp.aTP_Lamm_ajn Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Uub) Uu)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_Code_integer_int Uua Uub))))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bo7282069421189217543nteger) (Uub tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_fun7063430368917475406l_bool (tptp.aTP_Lamm_ajo Uu) Uua) Uub)) (and (tptp.pp (tptp.member_bool Uub Uu)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_bool_Code_integer Uua Uub))))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bool_nat) (Uub tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_fun7969004623323359937l_bool (tptp.aTP_Lamm_aji Uu) Uua) Uub)) (and (tptp.pp (tptp.member_bool Uub Uu)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_bool_nat Uua Uub))))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bool_int) (Uub tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_fun1758939502137048349l_bool (tptp.aTP_Lamm_ajl Uu) Uua) Uub)) (and (tptp.pp (tptp.member_bool Uub Uu)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_bool_int Uua Uub))))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_Code_integer) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun1752071697927428280t_bool (tptp.aTP_Lamm_ajp Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uub) Uu)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_Code_integer Uua Uub))))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_int) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun8175233552433550377t_bool (tptp.aTP_Lamm_ajm Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uub) Uu)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_int Uua Uub))))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_Code_integer) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun3610984093196804608t_bool (tptp.aTP_Lamm_ajq Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uub) Uu)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_int_Code_integer Uua Uub))))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_nat) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun5627573752281863885t_bool (tptp.aTP_Lamm_ajj Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uub) Uu)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_int_nat Uua Uub))))))) (forall ((Uu tptp.set_Pr1261947904930325089at_nat) (Uua tptp.set_Pr1261947904930325089at_nat) (Uub tptp.product_prod_nat_nat)) (let ((_let_1 (tptp.member8440522571783428010at_nat Uub))) (= (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_set5223363028666124222t_bool (tptp.aTP_Lamm_gk Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 Uu)) (not (tptp.pp (tptp.aa_set3135850010578026034t_bool _let_1 Uua))))))) (forall ((Uu tptp.set_Pr958786334691620121nt_int) (Uua tptp.set_Pr958786334691620121nt_int) (Uub tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_set1381271197253378494t_bool (tptp.aTP_Lamm_gm Uu) Uua) Uub)) (and (tptp.member5262025264175285858nt_int Uub Uu) (not (tptp.member5262025264175285858nt_int Uub Uua))))) (forall ((Uu tptp.set_list_nat) (Uua tptp.set_list_nat) (Uub tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool (tptp.aa_set257547205302447420t_bool (tptp.aTP_Lamm_gn Uu) Uua) Uub)) (and (tptp.member_list_nat Uub Uu) (not (tptp.member_list_nat Uub Uua))))) (forall ((Uu tptp.set_bool) (Uua tptp.set_bool) (Uub tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_set6670506438128111678l_bool (tptp.aTP_Lamm_gl Uu) Uua) Uub)) (and (tptp.pp (tptp.member_bool Uub Uu)) (not (tptp.pp (tptp.member_bool Uub Uua)))))) (forall ((Uu tptp.set_set_nat) (Uua tptp.set_set_nat) (Uub tptp.set_nat)) (let ((_let_1 (tptp.member_set_nat Uub))) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set9121396911425987952t_bool (tptp.aTP_Lamm_go Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_set_nat_bool _let_1 Uu)) (not (tptp.pp (tptp.aa_set_set_nat_bool _let_1 Uua))))))) (forall ((Uu tptp.set_nat) (Uua tptp.set_nat) (Uub tptp.nat)) (let ((_let_1 (tptp.member_nat Uub))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_set3744802623701456604t_bool (tptp.aTP_Lamm_gq Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool _let_1 Uu)) (not (tptp.pp (tptp.aa_set_nat_bool _let_1 Uua))))))) (forall ((Uu tptp.set_int) (Uua tptp.set_int) (Uub tptp.int)) (let ((_let_1 (tptp.member_int Uub))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_set7012339369581096484t_bool (tptp.aTP_Lamm_gp Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_int_bool _let_1 Uu)) (not (tptp.pp (tptp.aa_set_int_bool _let_1 Uua))))))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_ane Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Uub) Uu)) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_agx Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) Uub)) Uu)))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_aic Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) Uub)) Uu)))) (forall ((Uu tptp.rat) (Uua tptp.rat) (Uub tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.aTP_Lamm_hn Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat Uub) Uu)) Uua))) (forall ((Uu tptp.rat) (Uua tptp.rat) (Uub tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.aTP_Lamm_hp Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Uu) Uub)) Uua))) (forall ((Uu tptp.rat) (Uua tptp.rat) (Uub tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.aTP_Lamm_ho Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat Uub) Uu)) Uua))) (forall ((Uu tptp.rat) (Uua tptp.rat) (Uub tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.aTP_Lamm_hq Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat Uu) Uub)) Uua))) (forall ((Uu tptp.set_Pr8693737435421807431at_nat) (Uua tptp.product_prod_nat_nat) (Uub tptp.product_prod_nat_nat)) (= (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool (tptp.aTP_Lamm_ay Uu) Uua) Uub)) (tptp.member8206827879206165904at_nat (tptp.produc6161850002892822231at_nat Uua Uub) Uu))) (forall ((Uu tptp.set_Pr8551490117392284871at_nat) (Uua tptp.multis2468970476368604999at_nat) (Uub tptp.multis2468970476368604999at_nat)) (= (tptp.pp (tptp.aa_mul7406001252470835788t_bool (tptp.aa_mul6531253083629095518t_bool (tptp.aTP_Lamm_az Uu) Uua) Uub)) (tptp.member6689249552917799696at_nat (tptp.produc4348348721325984599at_nat Uua Uub) Uu))) (forall ((Uu tptp.set_Pr4329608150637261639at_nat) (Uua tptp.set_Pr1261947904930325089at_nat) (Uub tptp.set_Pr1261947904930325089at_nat)) (= (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.aa_set7594618562247239262t_bool (tptp.aTP_Lamm_ba Uu) Uua) Uub)) (tptp.member8757157785044589968at_nat (tptp.produc2922128104949294807at_nat Uua Uub) Uu))) (forall ((Uu tptp.set_Pr1261947904930325089at_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_as Uu) Uua) Uub)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat Uua) Uub)) Uu)))) (forall ((Uu tptp.set_Pr1106803562331729365et_nat) (Uua tptp.fun_Pr6001797050664311790t_bool) (Uub tptp.produc3658429121746597890et_nat)) (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.aa_fun6808777976510360636t_bool (tptp.aTP_Lamm_at Uu) Uua) Uub)) (tptp.member8615881266069945910et_nat (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat Uua) Uub) Uu))) (forall ((Uu tptp.set_Pr9222568342844664434et_nat) (Uua tptp.fun_Pr6001797050664311790t_bool) (Uub tptp.produc6108883039684432031et_nat)) (= (tptp.pp (tptp.aa_Pro7454463142485379962t_bool (tptp.aa_fun1003322038264691679t_bool (tptp.aTP_Lamm_au Uu) Uua) Uub)) (tptp.member2818932950976722259et_nat (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat Uua) Uub) Uu))) (forall ((Uu tptp.set_Pr233528076387193594nt_int) (Uua tptp.fun_Pr9164807099015279978e_term) (Uub tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun5300525129335604105t_bool (tptp.aTP_Lamm_av Uu) Uua) Uub)) (tptp.member690604328116145115nt_int (tptp.aa_Pro3513184699142849729nt_int (tptp.aa_fun1388719692539776744nt_int tptp.produc1560874099174258678nt_int Uua) Uub) Uu))) (forall ((Uu tptp.set_Pr5033440245338114598nt_int) (Uua tptp.fun_in6429348457993719614e_term) (Uub tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun4446166836006121821t_bool (tptp.aTP_Lamm_aw Uu) Uua) Uub)) (tptp.member500491123954006279nt_int (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int Uua) Uub) Uu))) (forall ((Uu tptp.set_Pr7098220151150636591it_nat) (Uua tptp.a) (Uub tptp.produc6653097349344004940it_nat)) (= (tptp.pp (tptp.aa_Pro3182513528956304653t_bool (tptp.aa_a_f736957945511644770t_bool (tptp.aTP_Lamm_ax Uu) Uua) Uub)) (tptp.member4554412811331277712it_nat (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat Uua) Uub) Uu))) (forall ((Uu tptp.rat) (Uua tptp.rat) (Uub tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool (tptp.aTP_Lamm_xu Uu) Uua) Uub)) (and (tptp.member_rat Uub tptp.ring_1_Ints_rat) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Uu) Uub)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Uub) Uua))))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_rb Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_nat_bool Uu Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uub) Uua))))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.fun_nat_nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_nd Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat Uu Uub)) (tptp.aa_nat_nat Uua Uub)))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.fun_nat_int) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun5565043122120104496at_int (tptp.aTP_Lamm_ne Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int Uu Uub)) (tptp.aa_nat_int Uua Uub)))) (forall ((Uu tptp.fun_int_int) (Uua tptp.fun_int_int) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_fun6280345759651049192nt_int (tptp.aTP_Lamm_nf Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int Uu Uub)) (tptp.aa_int_int Uua Uub)))) (forall ((Uu tptp.fun_bo7282069421189217543nteger) (Uua tptp.fun_bo7282069421189217543nteger) (Uub tptp.bool)) (= (tptp.aa_bool_Code_integer (tptp.aa_fun1377107737837666940nteger (tptp.aTP_Lamm_ku Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_bool_Code_integer Uua Uub)) (tptp.aa_bool_Code_integer Uu Uub)))) (forall ((Uu tptp.fun_bool_rat) (Uua tptp.fun_bool_rat) (Uub tptp.bool)) (= (tptp.aa_bool_rat (tptp.aa_fun224000846028461884ol_rat (tptp.aTP_Lamm_kx Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_bool_rat Uua Uub)) (tptp.aa_bool_rat Uu Uub)))) (forall ((Uu tptp.fun_bool_int) (Uua tptp.fun_bool_int) (Uub tptp.bool)) (= (tptp.aa_bool_int (tptp.aa_fun2092349043547419708ol_int (tptp.aTP_Lamm_la Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_bool_int Uua Uub)) (tptp.aa_bool_int Uu Uub)))) (forall ((Uu tptp.fun_se7586849273513198688nteger) (Uua tptp.fun_se7586849273513198688nteger) (Uub tptp.set_nat)) (= (tptp.aa_set871585252387937313nteger (tptp.aa_fun4587287018503165694nteger (tptp.aTP_Lamm_ld Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_set871585252387937313nteger Uua Uub)) (tptp.aa_set871585252387937313nteger Uu Uub)))) (forall ((Uu tptp.fun_nat_Code_integer) (Uua tptp.fun_nat_Code_integer) (Uub tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aa_fun589076786913273746nteger (tptp.aTP_Lamm_kv Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer Uua Uub)) (tptp.aa_nat_Code_integer Uu Uub)))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.fun_nat_rat) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_ky Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat Uua Uub)) (tptp.aa_nat_rat Uu Uub)))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.fun_nat_int) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun5565043122120104496at_int (tptp.aTP_Lamm_lb Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int Uua Uub)) (tptp.aa_nat_int Uu Uub)))) (forall ((Uu tptp.fun_int_Code_integer) (Uua tptp.fun_int_Code_integer) (Uub tptp.int)) (= (tptp.aa_int_Code_integer (tptp.aa_fun5304498221708291146nteger (tptp.aTP_Lamm_kw Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_int_Code_integer Uua Uub)) (tptp.aa_int_Code_integer Uu Uub)))) (forall ((Uu tptp.fun_int_rat) (Uua tptp.fun_int_rat) (Uub tptp.int)) (= (tptp.aa_int_rat (tptp.aa_fun1481061427733998144nt_rat (tptp.aTP_Lamm_kz Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_int_rat Uua Uub)) (tptp.aa_int_rat Uu Uub)))) (forall ((Uu tptp.fun_int_int) (Uua tptp.fun_int_int) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_fun6280345759651049192nt_int (tptp.aTP_Lamm_lc Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int Uua Uub)) (tptp.aa_int_int Uu Uub)))) (forall ((Uu tptp.fun_int_int) (Uua tptp.fun_int_int) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_fun6280345759651049192nt_int (tptp.aTP_Lamm_lz Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int Uu Uub)) (tptp.aa_int_int Uua Uub)))) (forall ((Uu tptp.fun_Pr2602117396471556196at_nat) (Uua tptp.fun_Pr2602117396471556196at_nat) (Uub tptp.product_prod_nat_nat)) (= (tptp.aa_Pro4243173770044397973at_nat (tptp.aa_fun2351638177499875132at_nat (tptp.aTP_Lamm_le Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_Pro4243173770044397973at_nat Uua Uub)) (tptp.aa_Pro4243173770044397973at_nat Uu Uub)))) (forall ((Uu tptp.fun_bool_nat) (Uua tptp.fun_bool_nat) (Uub tptp.bool)) (= (tptp.aa_bool_nat (tptp.aa_fun9101744387563128124ol_nat (tptp.aTP_Lamm_lf Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_bool_nat Uua Uub)) (tptp.aa_bool_nat Uu Uub)))) (forall ((Uu tptp.fun_set_nat_nat) (Uua tptp.fun_set_nat_nat) (Uub tptp.set_nat)) (= (tptp.aa_set_nat_nat (tptp.aa_fun3386010016858254564at_nat (tptp.aTP_Lamm_lg Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_set_nat_nat Uua Uub)) (tptp.aa_set_nat_nat Uu Uub)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.fun_nat_nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_li Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat Uua Uub)) (tptp.aa_nat_nat Uu Uub)))) (forall ((Uu tptp.fun_int_nat) (Uua tptp.fun_int_nat) (Uub tptp.int)) (= (tptp.aa_int_nat (tptp.aa_fun6506752150744536624nt_nat (tptp.aTP_Lamm_lh Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_int_nat Uua Uub)) (tptp.aa_int_nat Uu Uub)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.fun_nat_nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_lp Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat Uu Uub)) (tptp.aa_nat_nat Uua Uub)))) (forall ((Uu tptp.fun_int_int) (Uua tptp.fun_int_int) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_fun6280345759651049192nt_int (tptp.aTP_Lamm_lq Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int Uu Uub)) (tptp.aa_int_int Uua Uub)))) (forall ((Uu tptp.fun_Pr446604468264085555t_bool) (Uua tptp.fun_Pr446604468264085555t_bool) (Uub tptp.produc859450856879609959at_nat)) (= (tptp.pp (tptp.aa_Pro6098352494050694700t_bool (tptp.aa_fun3665199231186260388t_bool (tptp.aTP_Lamm_gv Uu) Uua) Uub)) (=> (tptp.pp (tptp.aa_Pro6098352494050694700t_bool Uu Uub)) (tptp.pp (tptp.aa_Pro6098352494050694700t_bool Uua Uub))))) (forall ((Uu tptp.fun_Pr3976602594631769267t_bool) (Uua tptp.fun_Pr3976602594631769267t_bool) (Uub tptp.produc4166570645942440679at_nat)) (= (tptp.pp (tptp.aa_Pro5063669228512387756t_bool (tptp.aa_fun3556822901603992740t_bool (tptp.aTP_Lamm_gw Uu) Uua) Uub)) (=> (tptp.pp (tptp.aa_Pro5063669228512387756t_bool Uu Uub)) (tptp.pp (tptp.aa_Pro5063669228512387756t_bool Uua Uub))))) (forall ((Uu tptp.fun_Pr1607443439640623155t_bool) (Uua tptp.fun_Pr1607443439640623155t_bool) (Uub tptp.produc3843707927480180839at_nat)) (= (tptp.pp (tptp.aa_Pro1809015098595223084t_bool (tptp.aa_fun5022828243006652836t_bool (tptp.aTP_Lamm_gx Uu) Uua) Uub)) (=> (tptp.pp (tptp.aa_Pro1809015098595223084t_bool Uu Uub)) (tptp.pp (tptp.aa_Pro1809015098595223084t_bool Uua Uub))))) (forall ((Uu tptp.fun_Pr803113274115125473t_bool) (Uua tptp.fun_Pr803113274115125473t_bool) (Uub tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun8917503761599146496t_bool (tptp.aTP_Lamm_gr Uu) Uua) Uub)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool Uu Uub)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool Uua Uub))))) (forall ((Uu tptp.fun_list_nat_bool) (Uua tptp.fun_list_nat_bool) (Uub tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool (tptp.aa_fun6009467934925565500t_bool (tptp.aTP_Lamm_gs Uu) Uua) Uub)) (=> (tptp.pp (tptp.aa_list_nat_bool Uu Uub)) (tptp.pp (tptp.aa_list_nat_bool Uua Uub))))) (forall ((Uu tptp.fun_set_nat_bool) (Uua tptp.fun_set_nat_bool) (Uub tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_fun3565389549526402364t_bool (tptp.aTP_Lamm_gt Uu) Uua) Uub)) (=> (tptp.pp (tptp.aa_set_nat_bool Uu Uub)) (tptp.pp (tptp.aa_set_nat_bool Uua Uub))))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.fun_nat_bool) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_gy Uu) Uua) Uub)) (=> (tptp.pp (tptp.aa_nat_bool Uu Uub)) (tptp.pp (tptp.aa_nat_bool Uua Uub))))) (forall ((Uu tptp.fun_int_bool) (Uua tptp.fun_int_bool) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun5146555767781538748t_bool (tptp.aTP_Lamm_gu Uu) Uua) Uub)) (=> (tptp.pp (tptp.aa_int_bool Uu Uub)) (tptp.pp (tptp.aa_int_bool Uua Uub))))) (forall ((Uu tptp.fun_Co8822979462182099027r_bool) (Uua tptp.fun_Co8822979462182099027r_bool) (Uub tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_fun8875953811088571772r_bool (tptp.aTP_Lamm_act Uu) Uua) Uub)) (or (tptp.pp (tptp.aa_Code_integer_bool Uu Uub)) (tptp.pp (tptp.aa_Code_integer_bool Uua Uub))))) (forall ((Uu tptp.fun_Pr446604468264085555t_bool) (Uua tptp.fun_Pr446604468264085555t_bool) (Uub tptp.produc859450856879609959at_nat)) (= (tptp.pp (tptp.aa_Pro6098352494050694700t_bool (tptp.aa_fun3665199231186260388t_bool (tptp.aTP_Lamm_cj Uu) Uua) Uub)) (or (tptp.pp (tptp.aa_Pro6098352494050694700t_bool Uu Uub)) (tptp.pp (tptp.aa_Pro6098352494050694700t_bool Uua Uub))))) (forall ((Uu tptp.fun_Pr3976602594631769267t_bool) (Uua tptp.fun_Pr3976602594631769267t_bool) (Uub tptp.produc4166570645942440679at_nat)) (= (tptp.pp (tptp.aa_Pro5063669228512387756t_bool (tptp.aa_fun3556822901603992740t_bool (tptp.aTP_Lamm_ck Uu) Uua) Uub)) (or (tptp.pp (tptp.aa_Pro5063669228512387756t_bool Uu Uub)) (tptp.pp (tptp.aa_Pro5063669228512387756t_bool Uua Uub))))) (forall ((Uu tptp.fun_Pr1607443439640623155t_bool) (Uua tptp.fun_Pr1607443439640623155t_bool) (Uub tptp.produc3843707927480180839at_nat)) (= (tptp.pp (tptp.aa_Pro1809015098595223084t_bool (tptp.aa_fun5022828243006652836t_bool (tptp.aTP_Lamm_cl Uu) Uua) Uub)) (or (tptp.pp (tptp.aa_Pro1809015098595223084t_bool Uu Uub)) (tptp.pp (tptp.aa_Pro1809015098595223084t_bool Uua Uub))))) (forall ((Uu tptp.fun_Pr7757163693017731481t_bool) (Uua tptp.fun_Pr7757163693017731481t_bool) (Uub tptp.product_prod_nat_nat)) (= (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_fun830836278467416944t_bool (tptp.aTP_Lamm_acu Uu) Uua) Uub)) (or (tptp.pp (tptp.aa_Pro2232559814647311250t_bool Uu Uub)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool Uua Uub))))) (forall ((Uu tptp.fun_Pr803113274115125473t_bool) (Uua tptp.fun_Pr803113274115125473t_bool) (Uub tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun8917503761599146496t_bool (tptp.aTP_Lamm_cf Uu) Uua) Uub)) (or (tptp.pp (tptp.aa_Pro4501881432599481050t_bool Uu Uub)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool Uua Uub))))) (forall ((Uu tptp.fun_list_nat_bool) (Uua tptp.fun_list_nat_bool) (Uub tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool (tptp.aa_fun6009467934925565500t_bool (tptp.aTP_Lamm_cg Uu) Uua) Uub)) (or (tptp.pp (tptp.aa_list_nat_bool Uu Uub)) (tptp.pp (tptp.aa_list_nat_bool Uua Uub))))) (forall ((Uu tptp.fun_set_nat_bool) (Uua tptp.fun_set_nat_bool) (Uub tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_fun3565389549526402364t_bool (tptp.aTP_Lamm_ch Uu) Uua) Uub)) (or (tptp.pp (tptp.aa_set_nat_bool Uu Uub)) (tptp.pp (tptp.aa_set_nat_bool Uua Uub))))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.fun_nat_bool) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_cm Uu) Uua) Uub)) (or (tptp.pp (tptp.aa_nat_bool Uu Uub)) (tptp.pp (tptp.aa_nat_bool Uua Uub))))) (forall ((Uu tptp.fun_int_bool) (Uua tptp.fun_int_bool) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun5146555767781538748t_bool (tptp.aTP_Lamm_ci Uu) Uua) Uub)) (or (tptp.pp (tptp.aa_int_bool Uu Uub)) (tptp.pp (tptp.aa_int_bool Uua Uub))))) (forall ((Uu tptp.fun_Co8822979462182099027r_bool) (Uua tptp.fun_Co8822979462182099027r_bool) (Uub tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_fun8875953811088571772r_bool (tptp.aTP_Lamm_acs Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_Code_integer_bool Uu Uub)) (tptp.pp (tptp.aa_Code_integer_bool Uua Uub))))) (forall ((Uu tptp.fun_Pr7757163693017731481t_bool) (Uua tptp.fun_Pr7757163693017731481t_bool) (Uub tptp.product_prod_nat_nat)) (= (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_fun830836278467416944t_bool (tptp.aTP_Lamm_bu Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_Pro2232559814647311250t_bool Uu Uub)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool Uua Uub))))) (forall ((Uu tptp.fun_Pr803113274115125473t_bool) (Uua tptp.fun_Pr803113274115125473t_bool) (Uub tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun8917503761599146496t_bool (tptp.aTP_Lamm_bp Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_Pro4501881432599481050t_bool Uu Uub)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool Uua Uub))))) (forall ((Uu tptp.fun_list_nat_bool) (Uua tptp.fun_list_nat_bool) (Uub tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool (tptp.aa_fun6009467934925565500t_bool (tptp.aTP_Lamm_bq Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_list_nat_bool Uu Uub)) (tptp.pp (tptp.aa_list_nat_bool Uua Uub))))) (forall ((Uu tptp.fun_set_nat_bool) (Uua tptp.fun_set_nat_bool) (Uub tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_fun3565389549526402364t_bool (tptp.aTP_Lamm_br Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool Uu Uub)) (tptp.pp (tptp.aa_set_nat_bool Uua Uub))))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.fun_nat_bool) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_bt Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_nat_bool Uu Uub)) (tptp.pp (tptp.aa_nat_bool Uua Uub))))) (forall ((Uu tptp.fun_int_bool) (Uua tptp.fun_int_bool) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun5146555767781538748t_bool (tptp.aTP_Lamm_bs Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_int_bool Uu Uub)) (tptp.pp (tptp.aa_int_bool Uua Uub))))) (forall ((Uu tptp.fun_Co8499238673658658103nteger) (Uua tptp.fun_Co8822979462182099027r_bool) (Uub tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_fun526110101794841038nteger (tptp.aTP_Lamm_afg Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger Uu Uub)) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_Code_integer_bool Uua Uub))))) (forall ((Uu tptp.fun_Code_integer_rat) (Uua tptp.fun_Co8822979462182099027r_bool) (Uub tptp.code_integer)) (= (tptp.aa_Code_integer_rat (tptp.aa_fun4600455420518417865er_rat (tptp.aTP_Lamm_afj Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_Code_integer_rat Uu Uub)) (tptp.aa_bool_rat tptp.zero_n2052037380579107095ol_rat (tptp.aa_Code_integer_bool Uua Uub))))) (forall ((Uu tptp.fun_Code_integer_nat) (Uua tptp.fun_Co8822979462182099027r_bool) (Uub tptp.code_integer)) (= (tptp.aa_Code_integer_nat (tptp.aa_fun8108683978911814593er_nat (tptp.aTP_Lamm_afm Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_Code_integer_nat Uu Uub)) (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat (tptp.aa_Code_integer_bool Uua Uub))))) (forall ((Uu tptp.fun_Code_integer_int) (Uua tptp.fun_Co8822979462182099027r_bool) (Uub tptp.code_integer)) (= (tptp.aa_Code_integer_int (tptp.aa_fun3930832959402617885er_int (tptp.aTP_Lamm_afn Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_Code_integer_int Uu Uub)) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_Code_integer_bool Uua Uub))))) (forall ((Uu tptp.fun_nat_Code_integer) (Uua tptp.fun_nat_bool) (Uub tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aa_fun42370497693836430nteger (tptp.aTP_Lamm_afh Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer Uu Uub)) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_nat_bool Uua Uub))))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.fun_nat_bool) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_fun5656162108953708681at_rat (tptp.aTP_Lamm_afk Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat Uu Uub)) (tptp.aa_bool_rat tptp.zero_n2052037380579107095ol_rat (tptp.aa_nat_bool Uua Uub))))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.fun_nat_bool) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun4986539647837908701at_int (tptp.aTP_Lamm_afo Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int Uu Uub)) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_nat_bool Uua Uub))))) (forall ((Uu tptp.fun_int_Code_integer) (Uua tptp.fun_int_bool) (Uub tptp.int)) (= (tptp.aa_int_Code_integer (tptp.aa_fun5397227419668681614nteger (tptp.aTP_Lamm_aff Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_int_Code_integer Uu Uub)) (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_int_bool Uua Uub))))) (forall ((Uu tptp.fun_int_rat) (Uua tptp.fun_int_bool) (Uub tptp.int)) (= (tptp.aa_int_rat (tptp.aa_fun4400602662665189257nt_rat (tptp.aTP_Lamm_afi Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_int_rat Uu Uub)) (tptp.aa_bool_rat tptp.zero_n2052037380579107095ol_rat (tptp.aa_int_bool Uua Uub))))) (forall ((Uu tptp.fun_int_nat) (Uua tptp.fun_int_bool) (Uub tptp.int)) (= (tptp.aa_int_nat (tptp.aa_fun7908831221058585985nt_nat (tptp.aTP_Lamm_afl Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_int_nat Uu Uub)) (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat (tptp.aa_int_bool Uua Uub))))) (forall ((Uu tptp.fun_int_option_int) (Uua tptp.int) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_ahf Uu) Uua) Uub)) (= (tptp.aa_int_option_int Uu Uua) (tptp.aa_int_option_int tptp.some_int Uub)))) (forall ((Uu tptp.fun_nat_fun_nat_nat) (Uua tptp.set_nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_set6537093552120046177at_nat (tptp.aTP_Lamm_mo Uu) Uua) Uub) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_nat_fun_nat_nat Uu Uub)) Uua))) (forall ((Uu tptp.fun_nat_fun_nat_int) (Uua tptp.set_nat) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_set2359242532610849469at_int (tptp.aTP_Lamm_mq Uu) Uua) Uub) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_nat_fun_nat_int Uu Uub)) Uua))) (forall ((Uu tptp.fun_nat_fun_int_int) (Uua tptp.set_int) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_set6310687161026558745at_int (tptp.aTP_Lamm_mt Uu) Uua) Uub) (tptp.groups1705073143266064639nt_int (tptp.aa_nat_fun_int_int Uu Uub) Uua))) (forall ((Uu tptp.fun_int_fun_nat_int) (Uua tptp.set_nat) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_set3358596244511904025nt_int (tptp.aTP_Lamm_mw Uu) Uua) Uub) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_int_fun_nat_int Uu Uub)) Uua))) (forall ((Uu tptp.fun_int_fun_int_int) (Uua tptp.set_int) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_set7310040872927613301nt_int (tptp.aTP_Lamm_mz Uu) Uua) Uub) (tptp.groups1705073143266064639nt_int (tptp.aa_int_fun_int_int Uu Uub) Uua))) (forall ((Uu tptp.fun_nat_fun_nat_nat) (Uua tptp.set_nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_set6537093552120046177at_nat (tptp.aTP_Lamm_lj Uu) Uua) Uub) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat Uu Uub)) Uua))) (forall ((Uu tptp.fun_int_fun_int_int) (Uua tptp.set_int) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_set7310040872927613301nt_int (tptp.aTP_Lamm_lm Uu) Uua) Uub) (tptp.groups4538972089207619220nt_int (tptp.aa_int_fun_int_int Uu Uub) Uua))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_rc Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat Uu Uub)) Uua)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_jv Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat Uu Uub)) Uua))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.int) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_nj Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_nat_int Uu Uub)) Uua))) (forall ((Uu tptp.fun_int_int) (Uua tptp.int) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.aTP_Lamm_jw Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int Uu Uub)) Uua))) (forall ((Uu tptp.fun_Co3734316457315071362atural) (Uua tptp.code_natural) (Uub tptp.code_integer)) (= (tptp.aa_Cod607569804290114243atural (tptp.aa_Cod1476545362447692776atural (tptp.aTP_Lamm_aev Uu) Uua) Uub) (tptp.divide5121882707175180666atural (tptp.aa_Cod607569804290114243atural Uu Uub) Uua))) (forall ((Uu tptp.fun_Co8499238673658658103nteger) (Uua tptp.code_integer) (Uub tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger (tptp.aTP_Lamm_aem Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger Uu Uub)) Uua))) (forall ((Uu tptp.fun_Code_integer_nat) (Uua tptp.nat) (Uub tptp.code_integer)) (= (tptp.aa_Code_integer_nat (tptp.aa_nat5852537043073606456er_nat (tptp.aTP_Lamm_aea Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_Code_integer_nat Uu Uub)) Uua))) (forall ((Uu tptp.fun_Code_integer_int) (Uua tptp.int) (Uub tptp.code_integer)) (= (tptp.aa_Code_integer_int (tptp.aa_int1390634949194299888er_int (tptp.aTP_Lamm_aed Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_Code_integer_int Uu Uub)) Uua))) (forall ((Uu tptp.fun_nat_Code_natural) (Uua tptp.code_natural) (Uub tptp.nat)) (= (tptp.aa_nat_Code_natural (tptp.aa_Cod5320533616963873627atural (tptp.aTP_Lamm_aey Uu) Uua) Uub) (tptp.divide5121882707175180666atural (tptp.aa_nat_Code_natural Uu Uub) Uua))) (forall ((Uu tptp.fun_nat_Code_integer) (Uua tptp.code_integer) (Uub tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aa_Cod1578151519121547077nteger (tptp.aTP_Lamm_aep Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_nat_Code_integer Uu Uub)) Uua))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.int) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_aeg Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_nat_int Uu Uub)) Uua))) (forall ((Uu tptp.fun_int_Code_natural) (Uua tptp.code_natural) (Uub tptp.int)) (= (tptp.aa_int_Code_natural (tptp.aa_Cod5692187177200718263atural (tptp.aTP_Lamm_aes Uu) Uua) Uub) (tptp.divide5121882707175180666atural (tptp.aa_int_Code_natural Uu Uub) Uua))) (forall ((Uu tptp.fun_int_Code_integer) (Uua tptp.code_integer) (Uub tptp.int)) (= (tptp.aa_int_Code_integer (tptp.aa_Cod1949805079358391713nteger (tptp.aTP_Lamm_aej Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.divide6298287555418463151nteger (tptp.aa_int_Code_integer Uu Uub)) Uua))) (forall ((Uu tptp.fun_int_nat) (Uua tptp.nat) (Uub tptp.int)) (= (tptp.aa_int_nat (tptp.aa_nat_fun_int_nat (tptp.aTP_Lamm_adx Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_int_nat Uu Uub)) Uua))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_lv Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat Uu Uub)) Uua))) (forall ((Uu tptp.fun_int_int) (Uua tptp.int) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.aTP_Lamm_lw Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int Uu Uub)) Uua))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_ng Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat Uu Uub)) Uua))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_nh Uu) Uua) Uub) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_nat_int Uu Uub)) Uua))) (forall ((Uu tptp.fun_int_int) (Uua tptp.nat) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int (tptp.aTP_Lamm_ni Uu) Uua) Uub) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int Uu Uub)) Uua))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_nat_fun_nat_rat (tptp.aTP_Lamm_xv Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.divide_divide_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) Uub))) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uub))))) (forall ((Uu tptp.fun_Co8822979462182099027r_bool) (Uua tptp.fun_Co8499238673658658103nteger) (Uub tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_fun4435975922079263404nteger (tptp.aTP_Lamm_afq Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_Code_integer_bool Uu Uub))) (tptp.aa_Cod1783974652533396728nteger Uua Uub)))) (forall ((Uu tptp.fun_Co8822979462182099027r_bool) (Uua tptp.fun_Code_integer_rat) (Uub tptp.code_integer)) (= (tptp.aa_Code_integer_rat (tptp.aa_fun8169474305930283170er_rat (tptp.aTP_Lamm_aft Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_bool_rat tptp.zero_n2052037380579107095ol_rat (tptp.aa_Code_integer_bool Uu Uub))) (tptp.aa_Code_integer_rat Uua Uub)))) (forall ((Uu tptp.fun_Co8822979462182099027r_bool) (Uua tptp.fun_Code_integer_nat) (Uub tptp.code_integer)) (= (tptp.aa_Code_integer_nat (tptp.aa_fun3076867170244285586er_nat (tptp.aTP_Lamm_afw Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat (tptp.aa_Code_integer_bool Uu Uub))) (tptp.aa_Code_integer_nat Uua Uub)))) (forall ((Uu tptp.fun_Co8822979462182099027r_bool) (Uua tptp.fun_Code_integer_int) (Uub tptp.code_integer)) (= (tptp.aa_Code_integer_int (tptp.aa_fun3291479149765983562er_int (tptp.aTP_Lamm_afx Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_Code_integer_bool Uu Uub))) (tptp.aa_Code_integer_int Uua Uub)))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.fun_nat_Code_integer) (Uub tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aa_fun589076786913273746nteger (tptp.aTP_Lamm_afr Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_nat_bool Uu Uub))) (tptp.aa_nat_Code_integer Uua Uub)))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.fun_nat_rat) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_afu Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_bool_rat tptp.zero_n2052037380579107095ol_rat (tptp.aa_nat_bool Uu Uub))) (tptp.aa_nat_rat Uua Uub)))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.fun_nat_int) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun5565043122120104496at_int (tptp.aTP_Lamm_afy Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_nat_bool Uu Uub))) (tptp.aa_nat_int Uua Uub)))) (forall ((Uu tptp.fun_int_bool) (Uua tptp.fun_int_Code_integer) (Uub tptp.int)) (= (tptp.aa_int_Code_integer (tptp.aa_fun5304498221708291146nteger (tptp.aTP_Lamm_afp Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_bool_Code_integer tptp.zero_n356916108424825756nteger (tptp.aa_int_bool Uu Uub))) (tptp.aa_int_Code_integer Uua Uub)))) (forall ((Uu tptp.fun_int_bool) (Uua tptp.fun_int_rat) (Uub tptp.int)) (= (tptp.aa_int_rat (tptp.aa_fun1481061427733998144nt_rat (tptp.aTP_Lamm_afs Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_bool_rat tptp.zero_n2052037380579107095ol_rat (tptp.aa_int_bool Uu Uub))) (tptp.aa_int_rat Uua Uub)))) (forall ((Uu tptp.fun_int_bool) (Uua tptp.fun_int_nat) (Uub tptp.int)) (= (tptp.aa_int_nat (tptp.aa_fun6506752150744536624nt_nat (tptp.aTP_Lamm_afv Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat (tptp.aa_int_bool Uu Uub))) (tptp.aa_int_nat Uua Uub)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat) (Uub tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Uub) Uua))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_aig Uu) Uua) Uub) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat Uu) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) Uua)))))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat) (Uub tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Uub) Uua))) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_aih Uu) Uua) Uub) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int Uu) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) Uua)))))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat) (Uub tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Uub) Uua))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_aif Uu) Uua) Uub) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat Uu) (tptp.aa_nat_set_nat (tptp.aa_nat1818925681583257441et_nat tptp.set_or4665077453230672383an_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) Uua)))))) (forall ((Uu tptp.code_natural) (Uua tptp.code_natural) (Uub tptp.nat)) (= (tptp.aa_nat_Code_natural (tptp.aa_Cod5320533616963873627atural (tptp.aTP_Lamm_abi Uu) Uua) Uub) (tptp.plus_p4538020629002901425atural Uu (tptp.times_2397367101498566445atural (tptp.aa_nat_Code_natural tptp.semiri3763490453095760265atural Uub) Uua)))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer) (Uub tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aa_Cod1578151519121547077nteger (tptp.aTP_Lamm_abk Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger Uu) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger Uub)) Uua)))) (forall ((Uu tptp.rat) (Uua tptp.rat) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_rat_fun_nat_rat (tptp.aTP_Lamm_abh Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Uu) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uub)) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_abl Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat Uub)) Uua)))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_abj Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Uu) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Uub)) Uua)))) (forall ((Uu tptp.code_integer) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aa_nat2010205248571845816nteger (tptp.aTP_Lamm_air Uu) Uua) Uub) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) (tptp.aa_nat_nat tptp.suc Uub))))) (forall ((Uu tptp.rat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_nat_fun_nat_rat (tptp.aTP_Lamm_ais Uu) Uua) Uub) (tptp.aa_nat_rat (tptp.power_power_rat Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) (tptp.aa_nat_nat tptp.suc Uub))))) (forall ((Uu tptp.int) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_ait Uu) Uua) Uub) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) (tptp.aa_nat_nat tptp.suc Uub))))) (forall ((Uu tptp.code_integer) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aa_nat2010205248571845816nteger (tptp.aTP_Lamm_kf Uu) Uua) Uub) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) Uub)))) (forall ((Uu tptp.rat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_nat_fun_nat_rat (tptp.aTP_Lamm_kg Uu) Uua) Uub) (tptp.aa_nat_rat (tptp.power_power_rat Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) Uub)))) (forall ((Uu tptp.int) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_kh Uu) Uua) Uub) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) Uub)))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_abg Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Uub) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_lx Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Uu) (tptp.aa_nat_nat Uua Uub)))) (forall ((Uu tptp.int) (Uua tptp.fun_int_int) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_fun6280345759651049192nt_int (tptp.aTP_Lamm_ly Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uu) (tptp.aa_int_int Uua Uub)))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_nn Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Uu) (tptp.aa_nat_nat Uua Uub)))) (forall ((Uu tptp.int) (Uua tptp.fun_nat_nat) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun1613598493704395220at_int (tptp.aTP_Lamm_no Uu) Uua) Uub) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Uu) (tptp.aa_nat_nat Uua Uub)))) (forall ((Uu tptp.int) (Uua tptp.fun_int_nat) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_fun2328901131235339916nt_int (tptp.aTP_Lamm_np Uu) Uua) Uub) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Uu) (tptp.aa_int_nat Uua Uub)))) (forall ((Uu tptp.fun_Co3734316457315071362atural) (Uua tptp.code_natural) (Uub tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod8557728523445623661r_bool (tptp.aTP_Lamm_aew Uu) Uua) Uub)) (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural Uua) (tptp.aa_Cod607569804290114243atural Uu Uub))))) (forall ((Uu tptp.fun_Co8499238673658658103nteger) (Uua tptp.code_integer) (Uub tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool (tptp.aTP_Lamm_aen Uu) Uua) Uub)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer Uua) (tptp.aa_Cod1783974652533396728nteger Uu Uub))))) (forall ((Uu tptp.fun_Code_integer_nat) (Uua tptp.nat) (Uub tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_nat6120813132205607877r_bool (tptp.aTP_Lamm_aeb Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat Uua) (tptp.aa_Code_integer_nat Uu Uub))))) (forall ((Uu tptp.fun_Code_integer_int) (Uua tptp.int) (Uub tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_int3865899974016033897r_bool (tptp.aTP_Lamm_aee Uu) Uua) Uub)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int Uua) (tptp.aa_Code_integer_int Uu Uub))))) (forall ((Uu tptp.fun_nat_Code_natural) (Uua tptp.code_natural) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_Cod140358652193338554t_bool (tptp.aTP_Lamm_aez Uu) Uua) Uub)) (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural Uua) (tptp.aa_nat_Code_natural Uu Uub))))) (forall ((Uu tptp.fun_nat_Code_integer) (Uua tptp.code_integer) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_Cod2498268374540730821t_bool (tptp.aTP_Lamm_aeq Uu) Uua) Uub)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer Uua) (tptp.aa_nat_Code_integer Uu Uub))))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.int) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool (tptp.aTP_Lamm_aeh Uu) Uua) Uub)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int Uua) (tptp.aa_nat_int Uu Uub))))) (forall ((Uu tptp.fun_int_Code_natural) (Uua tptp.code_natural) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_Cod6239439722579490142t_bool (tptp.aTP_Lamm_aet Uu) Uua) Uub)) (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural Uua) (tptp.aa_int_Code_natural Uu Uub))))) (forall ((Uu tptp.fun_int_Code_integer) (Uua tptp.code_integer) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_Cod8597349444926882409t_bool (tptp.aTP_Lamm_aek Uu) Uua) Uub)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer Uua) (tptp.aa_int_Code_integer Uu Uub))))) (forall ((Uu tptp.fun_int_nat) (Uua tptp.nat) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_nat_fun_int_bool (tptp.aTP_Lamm_ady Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat Uua) (tptp.aa_int_nat Uu Uub))))) (forall ((Uu tptp.code_integer) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aa_nat2010205248571845816nteger (tptp.aTP_Lamm_op Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger Uu) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) Uub))))) (forall ((Uu tptp.rat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_nat_fun_nat_rat (tptp.aTP_Lamm_oo Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Uu) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) Uub))))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_oq Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) Uub))))) (forall ((Uu tptp.int) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_or Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Uu) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) Uub))))) (forall ((Uu tptp.fun_Code_integer_nat) (Uua tptp.code_integer) (Uub tptp.code_integer)) (let ((_let_1 (tptp.aa_Code_integer_nat Uu Uub))) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool (tptp.aTP_Lamm_ym Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer Uub) Uua)) (tptp.aa_nat_nat tptp.suc _let_1)) _let_1)))))) (forall ((Uu tptp.fun_Pr2602117396471556196at_nat) (Uua tptp.product_prod_nat_nat) (Uub tptp.product_prod_nat_nat)) (let ((_let_1 (tptp.aa_Pro4243173770044397973at_nat Uu Uub))) (= (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool (tptp.aTP_Lamm_yn Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool tptp.fequal9188845342289841878at_nat Uub) Uua)) (tptp.aa_nat_nat tptp.suc _let_1)) _let_1)))))) (forall ((Uu tptp.fun_Pr5160692531401422620nt_nat) (Uua tptp.product_prod_int_int) (Uub tptp.product_prod_int_int)) (let ((_let_1 (tptp.aa_Pro6801748904974264397nt_nat Uu Uub))) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool (tptp.aTP_Lamm_yh Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool tptp.fequal6010348034681699726nt_int Uub) Uua)) (tptp.aa_nat_nat tptp.suc _let_1)) _let_1)))))) (forall ((Uu tptp.fun_list_nat_nat) (Uua tptp.list_nat) (Uub tptp.list_nat)) (let ((_let_1 (tptp.aa_list_nat_nat Uu Uub))) (= (tptp.pp (tptp.aa_list_nat_bool (tptp.aa_lis4768068104879709938t_bool (tptp.aTP_Lamm_yi Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_list_nat_bool (tptp.fequal_list_nat Uub) Uua)) (tptp.aa_nat_nat tptp.suc _let_1)) _let_1)))))) (forall ((Uu tptp.fun_set_nat_nat) (Uua tptp.set_nat) (Uub tptp.set_nat)) (let ((_let_1 (tptp.aa_set_nat_nat Uu Uub))) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool (tptp.aTP_Lamm_yj Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.fequal_set_nat Uub) Uua)) (tptp.aa_nat_nat tptp.suc _let_1)) _let_1)))))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat) (Uub tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat Uu Uub))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_yk Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uub) Uua)) (tptp.aa_nat_nat tptp.suc _let_1)) _let_1)))))) (forall ((Uu tptp.fun_int_nat) (Uua tptp.int) (Uub tptp.int)) (let ((_let_1 (tptp.aa_int_nat Uu Uub))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_yl Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int Uub) Uua)) (tptp.aa_nat_nat tptp.suc _let_1)) _let_1)))))) (forall ((Uu tptp.fun_Code_integer_nat) (Uua tptp.fun_Co8822979462182099027r_bool) (Uub tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_fun8875953811088571772r_bool (tptp.aTP_Lamm_wf Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_Code_integer_bool Uua Uub)) (tptp.aa_Code_integer_nat Uu Uub)) tptp.zero_zero_nat))))) (forall ((Uu tptp.fun_Pr2602117396471556196at_nat) (Uua tptp.fun_Pr7757163693017731481t_bool) (Uub tptp.product_prod_nat_nat)) (= (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_fun830836278467416944t_bool (tptp.aTP_Lamm_wh Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_Pro2232559814647311250t_bool Uua Uub)) (tptp.aa_Pro4243173770044397973at_nat Uu Uub)) tptp.zero_zero_nat))))) (forall ((Uu tptp.fun_Pr5160692531401422620nt_nat) (Uua tptp.fun_Pr803113274115125473t_bool) (Uub tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun8917503761599146496t_bool (tptp.aTP_Lamm_vv Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_Pro4501881432599481050t_bool Uua Uub)) (tptp.aa_Pro6801748904974264397nt_nat Uu Uub)) tptp.zero_zero_nat))))) (forall ((Uu tptp.fun_list_nat_nat) (Uua tptp.fun_list_nat_bool) (Uub tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool (tptp.aa_fun6009467934925565500t_bool (tptp.aTP_Lamm_vx Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_list_nat_bool Uua Uub)) (tptp.aa_list_nat_nat Uu Uub)) tptp.zero_zero_nat))))) (forall ((Uu tptp.fun_set_nat_nat) (Uua tptp.fun_set_nat_bool) (Uub tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_fun3565389549526402364t_bool (tptp.aTP_Lamm_vz Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_set_nat_bool Uua Uub)) (tptp.aa_set_nat_nat Uu Uub)) tptp.zero_zero_nat))))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.fun_nat_bool) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_wb Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_nat_bool Uua Uub)) (tptp.aa_nat_nat Uu Uub)) tptp.zero_zero_nat))))) (forall ((Uu tptp.fun_int_nat) (Uua tptp.fun_int_bool) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun5146555767781538748t_bool (tptp.aTP_Lamm_wd Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_int_bool Uua Uub)) (tptp.aa_int_nat Uu Uub)) tptp.zero_zero_nat))))) (forall ((Uu tptp.fun_Code_integer_nat) (Uua tptp.fun_Code_integer_nat) (Uub tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_fun3540204951715082475r_bool (tptp.aTP_Lamm_zz Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_Code_integer_nat Uu Uub)) (tptp.aa_Code_integer_nat Uua Uub)))))) (forall ((Uu tptp.fun_Pr2602117396471556196at_nat) (Uua tptp.fun_Pr2602117396471556196at_nat) (Uub tptp.product_prod_nat_nat)) (= (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_fun3396476008067328193t_bool (tptp.aTP_Lamm_aaa Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_Pro4243173770044397973at_nat Uu Uub)) (tptp.aa_Pro4243173770044397973at_nat Uua Uub)))))) (forall ((Uu tptp.fun_Pr5160692531401422620nt_nat) (Uua tptp.fun_Pr5160692531401422620nt_nat) (Uub tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun5604724294258851521t_bool (tptp.aTP_Lamm_zu Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_Pro6801748904974264397nt_nat Uu Uub)) (tptp.aa_Pro6801748904974264397nt_nat Uua Uub)))))) (forall ((Uu tptp.fun_list_nat_nat) (Uua tptp.fun_list_nat_nat) (Uub tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool (tptp.aa_fun2581403542315806821t_bool (tptp.aTP_Lamm_zv Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_list_nat_nat Uu Uub)) (tptp.aa_list_nat_nat Uua Uub)))))) (forall ((Uu tptp.fun_set_nat_nat) (Uua tptp.fun_set_nat_nat) (Uub tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_fun806690937814068505t_bool (tptp.aTP_Lamm_zw Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_set_nat_nat Uu Uub)) (tptp.aa_set_nat_nat Uua Uub)))))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.fun_nat_nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun1783405840085286277t_bool (tptp.aTP_Lamm_zx Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat Uu Uub)) (tptp.aa_nat_nat Uua Uub)))))) (forall ((Uu tptp.fun_int_nat) (Uua tptp.fun_int_nat) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun5627573752281863885t_bool (tptp.aTP_Lamm_zy Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_int_nat Uu Uub)) (tptp.aa_int_nat Uua Uub)))))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_aid Uu) Uua) Uub) (tptp.aa_nat_nat Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) (tptp.aa_nat_nat tptp.suc Uub))))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_aie Uu) Uua) Uub) (tptp.aa_nat_int Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) (tptp.aa_nat_nat tptp.suc Uub))))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_aow Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uub) Uua))))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_jy Uu) Uua) Uub) (tptp.aa_nat_nat Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uub) Uua)))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_nq Uu) Uua) Uub) (tptp.aa_nat_int Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uub) Uua)))) (forall ((Uu tptp.fun_Pr2477239776880934807at_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat7997280740862404369at_nat (tptp.aa_nat5682243440470347102at_nat (tptp.aTP_Lamm_agl Uu) Uua) Uub) (tptp.aa_Pro8023792847356852296at_nat Uu (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat Uua) Uub)))) (forall ((Uu tptp.fun_Pr248683899324676269t_bool) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool (tptp.aTP_Lamm_agm Uu) Uua) Uub) (tptp.aa_Pro595088089689268830t_bool Uu (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat Uua) Uub)))) (forall ((Uu tptp.fun_Pr2478283820680522243nt_int) (Uua tptp.int) (Uub tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int (tptp.aTP_Lamm_agn Uu) Uua) Uub) (tptp.aa_Pro6970504127699319548nt_int Uu (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Uua) Uub)))) (forall ((Uu tptp.fun_Pr803113274115125473t_bool) (Uua tptp.int) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_ago Uu) Uua) Uub)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool Uu (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Uua) Uub))))) (forall ((Uu tptp.fun_Pr982841511892225912nt_int) (Uua tptp.int) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.aTP_Lamm_agp Uu) Uua) Uub) (tptp.aa_Pro6799258434465214121nt_int Uu (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Uua) Uub)))) (forall ((Uu tptp.fun_op8989173174992673105on_num) (Uua tptp.fun_num_option_num) (Uub tptp.num)) (= (tptp.aa_num_option_num (tptp.aa_fun3636977833914307392on_num (tptp.aTP_Lamm_dz Uu) Uua) Uub) (tptp.aa_opt5369159329878751634on_num Uu (tptp.aa_num_option_num Uua Uub)))) (forall ((Uu tptp.fun_op8989173174992673105on_num) (Uua tptp.fun_nat_option_num) (Uub tptp.nat)) (= (tptp.aa_nat_option_num (tptp.aa_fun7716400287237121964on_num (tptp.aTP_Lamm_akn Uu) Uua) Uub) (tptp.aa_opt5369159329878751634on_num Uu (tptp.aa_nat_option_num Uua Uub)))) (forall ((Uu tptp.fun_option_num_bool) (Uua tptp.fun_nat_option_num) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun5457149469851336939t_bool (tptp.aTP_Lamm_ako Uu) Uua) Uub)) (tptp.pp (tptp.aa_option_num_bool Uu (tptp.aa_nat_option_num Uua Uub))))) (forall ((Uu tptp.fun_option_num_num) (Uua tptp.fun_num_option_num) (Uub tptp.num)) (= (tptp.aa_num_num (tptp.aa_fun7142274290070961008um_num (tptp.aTP_Lamm_ea Uu) Uua) Uub) (tptp.aa_option_num_num Uu (tptp.aa_num_option_num Uua Uub)))) (forall ((Uu tptp.fun_option_num_nat) (Uua tptp.fun_nat_option_num) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun7387201323300553874at_nat (tptp.aTP_Lamm_akp Uu) Uua) Uub) (tptp.aa_option_num_nat Uu (tptp.aa_nat_option_num Uua Uub)))) (forall ((Uu tptp.fun_option_num_int) (Uua tptp.fun_num_option_num) (Uub tptp.num)) (= (tptp.aa_num_int (tptp.aa_fun2256179333612926594um_int (tptp.aTP_Lamm_dy Uu) Uua) Uub) (tptp.aa_option_num_int Uu (tptp.aa_num_option_num Uua Uub)))) (forall ((Uu tptp.fun_bool_option_num) (Uua tptp.fun_nat_bool) (Uub tptp.nat)) (= (tptp.aa_nat_option_num (tptp.aa_fun4234090970126001947on_num (tptp.aTP_Lamm_akq Uu) Uua) Uub) (tptp.aa_bool_option_num Uu (tptp.aa_nat_bool Uua Uub)))) (forall ((Uu tptp.fun_bool_bool) (Uua tptp.fun_nat_bool) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_akr Uu) Uua) Uub)) (tptp.pp (tptp.aa_bool_bool Uu (tptp.aa_nat_bool Uua Uub))))) (forall ((Uu tptp.fun_bool_nat) (Uua tptp.fun_nat_bool) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun9164390667347105409at_nat (tptp.aTP_Lamm_aks Uu) Uua) Uub) (tptp.aa_bool_nat Uu (tptp.aa_nat_bool Uua Uub)))) (forall ((Uu tptp.fun_set_nat_nat) (Uua tptp.fun_nat_set_nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun4820382421437094446at_nat (tptp.aTP_Lamm_it Uu) Uua) Uub) (tptp.aa_set_nat_nat Uu (tptp.aa_nat_set_nat Uua Uub)))) (forall ((Uu tptp.fun_set_nat_int) (Uua tptp.fun_nat_set_nat) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun642531401927897738at_int (tptp.aTP_Lamm_iu Uu) Uua) Uub) (tptp.aa_set_nat_int Uu (tptp.aa_nat_set_nat Uua Uub)))) (forall ((Uu tptp.fun_num_option_num) (Uua tptp.fun_num_num) (Uub tptp.num)) (= (tptp.aa_num_option_num (tptp.aa_fun612943910911948912on_num (tptp.aTP_Lamm_ec Uu) Uua) Uub) (tptp.aa_num_option_num Uu (tptp.aa_num_num Uua Uub)))) (forall ((Uu tptp.fun_num_num) (Uua tptp.fun_num_num) (Uub tptp.num)) (= (tptp.aa_num_num (tptp.aa_fun8048995283964520608um_num (tptp.aTP_Lamm_ed Uu) Uua) Uub) (tptp.aa_num_num Uu (tptp.aa_num_num Uua Uub)))) (forall ((Uu tptp.fun_num_int) (Uua tptp.fun_num_num) (Uub tptp.num)) (= (tptp.aa_num_int (tptp.aa_fun3162900327506486194um_int (tptp.aTP_Lamm_eb Uu) Uua) Uub) (tptp.aa_num_int Uu (tptp.aa_num_num Uua Uub)))) (forall ((Uu tptp.fun_nat_option_num) (Uua tptp.fun_nat_nat) (Uub tptp.nat)) (= (tptp.aa_nat_option_num (tptp.aa_fun6517009837249254290on_num (tptp.aTP_Lamm_akt Uu) Uua) Uub) (tptp.aa_nat_option_num Uu (tptp.aa_nat_nat Uua Uub)))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.fun_nat_nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun1783405840085286277t_bool (tptp.aTP_Lamm_aku Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool Uu (tptp.aa_nat_nat Uua Uub))))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.fun_nat_nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_il Uu) Uua) Uub) (tptp.aa_nat_nat Uu (tptp.aa_nat_nat Uua Uub)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.fun_int_nat) (Uub tptp.int)) (= (tptp.aa_int_nat (tptp.aa_fun6506752150744536624nt_nat (tptp.aTP_Lamm_im Uu) Uua) Uub) (tptp.aa_nat_nat Uu (tptp.aa_int_nat Uua Uub)))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.fun_nat_nat) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun1613598493704395220at_int (tptp.aTP_Lamm_in Uu) Uua) Uub) (tptp.aa_nat_int Uu (tptp.aa_nat_nat Uua Uub)))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.fun_int_nat) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_fun2328901131235339916nt_int (tptp.aTP_Lamm_io Uu) Uua) Uub) (tptp.aa_nat_int Uu (tptp.aa_int_nat Uua Uub)))) (forall ((Uu tptp.fun_int_option_num) (Uua tptp.fun_num_int) (Uub tptp.num)) (= (tptp.aa_num_option_num (tptp.aa_fun3858197967482829954on_num (tptp.aTP_Lamm_dw Uu) Uua) Uub) (tptp.aa_int_option_num Uu (tptp.aa_num_int Uua Uub)))) (forall ((Uu tptp.fun_int_num) (Uua tptp.fun_num_int) (Uub tptp.num)) (= (tptp.aa_num_num (tptp.aa_fun5215869348392759218um_num (tptp.aTP_Lamm_dx Uu) Uua) Uub) (tptp.aa_int_num Uu (tptp.aa_num_int Uua Uub)))) (forall ((Uu tptp.fun_int_nat) (Uua tptp.fun_nat_int) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun519522104774525396at_nat (tptp.aTP_Lamm_ip Uu) Uua) Uub) (tptp.aa_int_nat Uu (tptp.aa_nat_int Uua Uub)))) (forall ((Uu tptp.fun_int_nat) (Uua tptp.fun_int_int) (Uub tptp.int)) (= (tptp.aa_int_nat (tptp.aa_fun1234824742305470092nt_nat (tptp.aTP_Lamm_iq Uu) Uua) Uub) (tptp.aa_int_nat Uu (tptp.aa_int_int Uua Uub)))) (forall ((Uu tptp.fun_int_int) (Uua tptp.fun_num_int) (Uub tptp.num)) (= (tptp.aa_num_int (tptp.aa_fun329774391934724804um_int (tptp.aTP_Lamm_dv Uu) Uua) Uub) (tptp.aa_int_int Uu (tptp.aa_num_int Uua Uub)))) (forall ((Uu tptp.fun_int_int) (Uua tptp.fun_nat_int) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun5565043122120104496at_int (tptp.aTP_Lamm_ir Uu) Uua) Uub) (tptp.aa_int_int Uu (tptp.aa_nat_int Uua Uub)))) (forall ((Uu tptp.fun_int_int) (Uua tptp.fun_int_int) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_fun6280345759651049192nt_int (tptp.aTP_Lamm_is Uu) Uua) Uub) (tptp.aa_int_int Uu (tptp.aa_int_int Uua Uub)))) (forall ((Uu tptp.fun_Pr1003294667014919570it_nat) (Uua tptp.produc8664842809031399944it_nat) (Uub tptp.produc8664842809031399944it_nat)) (= (tptp.aa_Pro8996696869555642526it_nat (tptp.aa_Pro5635350972512700067it_nat (tptp.aTP_Lamm_fn Uu) Uua) Uub) (tptp.aa_Pro8996696869555642526it_nat tptp.some_P1914260805536162275it_nat (tptp.aa_Pro550487673543749710it_nat (tptp.aa_Pro4096753284154920275it_nat Uu Uua) Uub)))) (forall ((Uu tptp.fun_Pr7750636411365408485it_nat) (Uua tptp.produc3260487557148687353it_nat) (Uub tptp.produc3260487557148687353it_nat)) (= (tptp.aa_Pro5302094286594872192it_nat (tptp.aa_Pro7038079567744603766it_nat (tptp.aTP_Lamm_fl Uu) Uua) Uub) (tptp.aa_Pro5302094286594872192it_nat tptp.some_P7913643980934408916it_nat (tptp.aa_Pro4202338132779708464it_nat (tptp.aa_Pro2263720180353132454it_nat Uu Uua) Uub)))) (forall ((Uu tptp.fun_num_fun_num_num) (Uua tptp.num) (Uub tptp.num)) (= (tptp.aa_num_option_num (tptp.aa_num6390622462783740633on_num (tptp.aTP_Lamm_fp Uu) Uua) Uub) (tptp.aa_num_option_num tptp.some_num (tptp.aa_num_num (tptp.aa_num_fun_num_num Uu Uua) Uub)))) (forall ((Uu tptp.fun_Co3734316457315071362atural) (Uua tptp.code_natural) (Uub tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod8557728523445623661r_bool (tptp.aTP_Lamm_aex Uu) Uua) Uub)) (not (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural Uua) (tptp.aa_Cod607569804290114243atural Uu Uub)))))) (forall ((Uu tptp.fun_Co8499238673658658103nteger) (Uua tptp.code_integer) (Uub tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool (tptp.aTP_Lamm_aeo Uu) Uua) Uub)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer Uua) (tptp.aa_Cod1783974652533396728nteger Uu Uub)))))) (forall ((Uu tptp.fun_Code_integer_nat) (Uua tptp.nat) (Uub tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_nat6120813132205607877r_bool (tptp.aTP_Lamm_aec Uu) Uua) Uub)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat Uua) (tptp.aa_Code_integer_nat Uu Uub)))))) (forall ((Uu tptp.fun_Code_integer_int) (Uua tptp.int) (Uub tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_int3865899974016033897r_bool (tptp.aTP_Lamm_aef Uu) Uua) Uub)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int Uua) (tptp.aa_Code_integer_int Uu Uub)))))) (forall ((Uu tptp.fun_nat_Code_natural) (Uua tptp.code_natural) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_Cod140358652193338554t_bool (tptp.aTP_Lamm_afa Uu) Uua) Uub)) (not (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural Uua) (tptp.aa_nat_Code_natural Uu Uub)))))) (forall ((Uu tptp.fun_nat_Code_integer) (Uua tptp.code_integer) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_Cod2498268374540730821t_bool (tptp.aTP_Lamm_aer Uu) Uua) Uub)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer Uua) (tptp.aa_nat_Code_integer Uu Uub)))))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.int) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool (tptp.aTP_Lamm_aei Uu) Uua) Uub)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int Uua) (tptp.aa_nat_int Uu Uub)))))) (forall ((Uu tptp.fun_int_Code_natural) (Uua tptp.code_natural) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_Cod6239439722579490142t_bool (tptp.aTP_Lamm_aeu Uu) Uua) Uub)) (not (tptp.pp (tptp.aa_Code_natural_bool (tptp.dvd_dvd_Code_natural Uua) (tptp.aa_int_Code_natural Uu Uub)))))) (forall ((Uu tptp.fun_int_Code_integer) (Uua tptp.code_integer) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_Cod8597349444926882409t_bool (tptp.aTP_Lamm_ael Uu) Uua) Uub)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer Uua) (tptp.aa_int_Code_integer Uu Uub)))))) (forall ((Uu tptp.fun_int_nat) (Uua tptp.nat) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_nat_fun_int_bool (tptp.aTP_Lamm_adz Uu) Uua) Uub)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat Uua) (tptp.aa_int_nat Uu Uub)))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_Co8310303586393106575r_bool) (Uub tptp.code_integer)) (= (tptp.aa_Code_integer_nat (tptp.aa_fun4547260061994548733er_nat (tptp.aTP_Lamm_alu Uu) Uua) Uub) (tptp.finite4902975817058060853nteger (tptp.collect_Code_integer (tptp.aa_Cod7250484176784686200r_bool (tptp.aa_fun2374795795022016636r_bool (tptp.aTP_Lamm_alt Uu) Uua) Uub))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_Co3748208068438171869l_bool) (Uub tptp.code_integer)) (= (tptp.aa_Code_integer_nat (tptp.aa_fun4083829879951944645er_nat (tptp.aTP_Lamm_alq Uu) Uua) Uub) (tptp.finite_card_bool (tptp.collect_bool (tptp.aa_Cod8494480694608518558l_bool (tptp.aa_fun473675042869869048l_bool (tptp.aTP_Lamm_alp Uu) Uua) Uub))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_in5519481650651148416r_bool) (Uub tptp.int)) (= (tptp.aa_int_nat (tptp.aa_fun6776377250481993149nt_nat (tptp.aTP_Lamm_aln Uu) Uua) Uub) (tptp.finite4902975817058060853nteger (tptp.collect_Code_integer (tptp.aa_int3865899974016033897r_bool (tptp.aa_fun9015013955937593532r_bool (tptp.aTP_Lamm_alm Uu) Uua) Uub))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_fun_int_bool) (Uub tptp.int)) (= (tptp.aa_int_nat (tptp.aa_fun8170219554457397550nt_nat (tptp.aTP_Lamm_all Uu) Uua) Uub) (tptp.finite_card_int (tptp.collect_int (tptp.aa_int_fun_int_bool (tptp.aa_fun8168818243683596540t_bool (tptp.aTP_Lamm_alk Uu) Uua) Uub))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_in3865155034416861484l_bool) (Uub tptp.int)) (= (tptp.aa_int_nat (tptp.aa_fun6244226199881115619nt_nat (tptp.aTP_Lamm_alj Uu) Uua) Uub) (tptp.finite_card_bool (tptp.collect_bool (tptp.aa_int_fun_bool_bool (tptp.aa_fun3617675969253937942l_bool (tptp.aTP_Lamm_ali Uu) Uua) Uub))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_bo284609390884453567r_bool) (Uub tptp.bool)) (= (tptp.aa_bool_nat (tptp.aa_fun4256929549349463485ol_nat (tptp.aTP_Lamm_alg Uu) Uua) Uub) (tptp.finite4902975817058060853nteger (tptp.collect_Code_integer (tptp.aa_boo5858427943822696632r_bool (tptp.aa_fun5712573584333027516r_bool (tptp.aTP_Lamm_alf Uu) Uua) Uub))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bo1841576699660343469l_bool) (Uub tptp.bool)) (= (tptp.aa_bool_nat (tptp.aa_fun3941158123937086921ol_nat (tptp.aTP_Lamm_ald Uu) Uua) Uub) (tptp.finite_card_bool (tptp.collect_bool (tptp.aa_boo8970175072276269406l_bool (tptp.aa_fun1447330757145981436l_bool (tptp.aTP_Lamm_alc Uu) Uua) Uub))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_Co8197081679332685312t_bool) (Uub tptp.code_integer)) (= (tptp.aa_Code_integer_nat (tptp.aa_fun4709405206220679534er_nat (tptp.aTP_Lamm_alr Uu) Uua) Uub) (tptp.finite_card_int (tptp.collect_int (tptp.aa_Cod8597349444926882409t_bool (tptp.aa_fun6946700965406361788t_bool (tptp.aTP_Lamm_sb Uu) Uua) Uub))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_bo2827871560234191408t_bool) (Uub tptp.bool)) (= (tptp.aa_bool_nat (tptp.aa_fun7155190969624455820ol_nat (tptp.aTP_Lamm_ale Uu) Uua) Uub) (tptp.finite_card_int (tptp.collect_int (tptp.aa_bool_fun_int_bool (tptp.aa_fun4998116011708744478t_bool (tptp.aTP_Lamm_rs Uu) Uua) Uub))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_Co8657364630979331932t_bool) (Uub tptp.code_integer)) (= (tptp.aa_Code_integer_nat (tptp.aa_fun2949368542467568330er_nat (tptp.aTP_Lamm_ame Uu) Uua) Uub) (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.collect_nat (tptp.aa_Cod2498268374540730821t_bool (tptp.aa_fun498830667440607164t_bool (tptp.aTP_Lamm_rn Uu) Uua) Uub))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_int_fun_nat_bool) (Uub tptp.int)) (= (tptp.aa_int_nat (tptp.aa_fun5132377469993263754nt_nat (tptp.aTP_Lamm_amd Uu) Uua) Uub) (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.collect_nat (tptp.aa_int_fun_nat_bool (tptp.aa_fun3602880909931171836t_bool (tptp.aTP_Lamm_ri Uu) Uua) Uub))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_bo3288154511880838028t_bool) (Uub tptp.bool)) (= (tptp.aa_bool_nat (tptp.aa_fun7928520491197679664ol_nat (tptp.aTP_Lamm_alv Uu) Uua) Uub) (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.collect_nat (tptp.aa_bool_fun_nat_bool (tptp.aa_fun7537470554201192406t_bool (tptp.aTP_Lamm_rd Uu) Uua) Uub))))) (forall ((Uu tptp.fun_na1668100129766719005at_nat) (Uua tptp.product_prod_nat_nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat (tptp.aa_Pro6895555690143131534at_nat (tptp.aTP_Lamm_afz Uu) Uua) Uub) Uuc) (tptp.aa_Pro262675715343573244at_nat (tptp.aa_nat7997280740862404369at_nat (tptp.aa_nat5682243440470347102at_nat Uu Uub) Uuc) Uua))) (forall ((Uu tptp.fun_na4786964484885125043t_bool) (Uua tptp.product_prod_nat_nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aa_Pro3143461022101918244t_bool (tptp.aTP_Lamm_aga Uu) Uua) Uub) Uuc)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool Uu Uub) Uuc) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_Code_integer) (Uub tptp.fun_nat_Code_integer) (Uuc tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aa_fun589076786913273746nteger (tptp.aa_fun3918145391673965625nteger (tptp.aTP_Lamm_ot Uu) Uua) Uub) Uuc) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu) (tptp.aa_nat_Code_integer Uua Uuc)) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc) Uu) tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer Uub (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uuc) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))))) (forall ((Uu tptp.nat) (Uua tptp.fun_na2338080690716861136at_nat) (Uub tptp.fun_na2338080690716861136at_nat) (Uuc tptp.nat)) (= (tptp.aa_nat2240542744625857721at_nat (tptp.aa_fun4141531684813184444at_nat (tptp.aa_fun8230936523094545239at_nat (tptp.aTP_Lamm_ou Uu) Uua) Uub) Uuc) (tptp.if_mul8430962117462786573at_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu) (tptp.aa_nat2240542744625857721at_nat Uua Uuc) (tptp.if_mul8430962117462786573at_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc) Uu) tptp.zero_z1048942125864253310at_nat (tptp.aa_nat2240542744625857721at_nat Uub (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uuc) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_rat) (Uub tptp.fun_nat_rat) (Uuc tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_fun765758790203053448at_rat (tptp.aa_fun3638354034882855594at_rat (tptp.aTP_Lamm_ow Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu)) (tptp.aa_nat_rat Uua Uuc)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc) Uu)) tptp.zero_zero_rat) (tptp.aa_nat_rat Uub (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uuc) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_nat) (Uub tptp.fun_nat_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aa_fun6854695580826382482at_nat (tptp.aTP_Lamm_oy Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu)) (tptp.aa_nat_nat Uua Uuc)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc) Uu)) tptp.zero_zero_nat) (tptp.aa_nat_nat Uub (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uuc) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_int) (Uub tptp.fun_nat_int) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun5565043122120104496at_int (tptp.aa_fun5140708168904641446at_int (tptp.aTP_Lamm_ox Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.if_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu)) (tptp.aa_nat_int Uua Uuc)) (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.if_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc) Uu)) tptp.zero_zero_int) (tptp.aa_nat_int Uub (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uuc) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_Code_integer) (Uub tptp.fun_nat_Code_integer) (Uuc tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aa_fun589076786913273746nteger (tptp.aa_fun3918145391673965625nteger (tptp.aTP_Lamm_ns Uu) Uua) Uub) Uuc) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu) (tptp.aa_nat_Code_integer Uua Uuc)) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc) Uu) tptp.one_one_Code_integer) (tptp.aa_nat_Code_integer Uub (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uuc) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_assn) (Uub tptp.fun_nat_assn) (Uuc tptp.nat)) (= (tptp.aa_nat_assn (tptp.aa_fun785744391571715112t_assn (tptp.aa_fun6591345337174305434t_assn (tptp.aTP_Lamm_nu Uu) Uua) Uub) Uuc) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn (tptp.if_assn (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu)) (tptp.aa_nat_assn Uua Uuc)) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn (tptp.if_assn (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc) Uu)) tptp.one_one_assn) (tptp.aa_nat_assn Uub (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uuc) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_rat) (Uub tptp.fun_nat_rat) (Uuc tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_fun765758790203053448at_rat (tptp.aa_fun3638354034882855594at_rat (tptp.aTP_Lamm_nw Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu)) (tptp.aa_nat_rat Uua Uuc)) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc) Uu)) tptp.one_one_rat) (tptp.aa_nat_rat Uub (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uuc) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_nat) (Uub tptp.fun_nat_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aa_fun6854695580826382482at_nat (tptp.aTP_Lamm_ny Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu)) (tptp.aa_nat_nat Uua Uuc)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc) Uu)) tptp.one_one_nat) (tptp.aa_nat_nat Uub (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uuc) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_int) (Uub tptp.fun_nat_int) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun5565043122120104496at_int (tptp.aa_fun5140708168904641446at_int (tptp.aTP_Lamm_oa Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.if_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu)) (tptp.aa_nat_int Uua Uuc)) (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.if_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc) Uu)) tptp.one_one_int) (tptp.aa_nat_int Uub (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uuc) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_Code_integer) (Uub tptp.fun_nat_Code_integer) (Uuc tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aa_fun589076786913273746nteger (tptp.aa_fun3918145391673965625nteger (tptp.aTP_Lamm_nt Uu) Uua) Uub) Uuc) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu) (tptp.aa_nat_Code_integer Uua Uuc)) (tptp.aa_nat_Code_integer Uub Uuc)))) (forall ((Uu tptp.nat) (Uua tptp.fun_na2338080690716861136at_nat) (Uub tptp.fun_na2338080690716861136at_nat) (Uuc tptp.nat)) (= (tptp.aa_nat2240542744625857721at_nat (tptp.aa_fun4141531684813184444at_nat (tptp.aa_fun8230936523094545239at_nat (tptp.aTP_Lamm_ov Uu) Uua) Uub) Uuc) (tptp.if_mul8430962117462786573at_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu) (tptp.aa_nat2240542744625857721at_nat Uua Uuc) (tptp.aa_nat2240542744625857721at_nat Uub Uuc)))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_assn) (Uub tptp.fun_nat_assn) (Uuc tptp.nat)) (= (tptp.aa_nat_assn (tptp.aa_fun785744391571715112t_assn (tptp.aa_fun6591345337174305434t_assn (tptp.aTP_Lamm_nv Uu) Uua) Uub) Uuc) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn (tptp.if_assn (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu)) (tptp.aa_nat_assn Uua Uuc)) (tptp.aa_nat_assn Uub Uuc)))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_rat) (Uub tptp.fun_nat_rat) (Uuc tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_fun765758790203053448at_rat (tptp.aa_fun3638354034882855594at_rat (tptp.aTP_Lamm_nx Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu)) (tptp.aa_nat_rat Uua Uuc)) (tptp.aa_nat_rat Uub Uuc)))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_nat) (Uub tptp.fun_nat_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aa_fun6854695580826382482at_nat (tptp.aTP_Lamm_nz Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu)) (tptp.aa_nat_nat Uua Uuc)) (tptp.aa_nat_nat Uub Uuc)))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_int) (Uub tptp.fun_nat_int) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun5565043122120104496at_int (tptp.aa_fun5140708168904641446at_int (tptp.aTP_Lamm_ob Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.if_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu)) (tptp.aa_nat_int Uua Uuc)) (tptp.aa_nat_int Uub Uuc)))) (forall ((Uu tptp.fun_Co8822979462182099027r_bool) (Uua tptp.fun_Co8499238673658658103nteger) (Uub tptp.fun_Co8499238673658658103nteger) (Uuc tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_fun4435975922079263404nteger (tptp.aa_fun2957433868855875424nteger (tptp.aTP_Lamm_ace Uu) Uua) Uub) Uuc) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_Code_integer_bool Uu Uuc) (tptp.aa_Cod1783974652533396728nteger Uua Uuc)) (tptp.aa_Cod1783974652533396728nteger Uub Uuc)))) (forall ((Uu tptp.fun_Co8822979462182099027r_bool) (Uua tptp.fun_Co4490034186337852034r_assn) (Uub tptp.fun_Co4490034186337852034r_assn) (Uuc tptp.code_integer)) (= (tptp.aa_Code_integer_assn (tptp.aa_fun4119713415300323650r_assn (tptp.aa_fun8067317676786998721r_assn (tptp.aTP_Lamm_ach Uu) Uua) Uub) Uuc) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn (tptp.if_assn (tptp.aa_Code_integer_bool Uu Uuc)) (tptp.aa_Code_integer_assn Uua Uuc)) (tptp.aa_Code_integer_assn Uub Uuc)))) (forall ((Uu tptp.fun_Co8822979462182099027r_bool) (Uua tptp.fun_Code_integer_rat) (Uub tptp.fun_Code_integer_rat) (Uuc tptp.code_integer)) (= (tptp.aa_Code_integer_rat (tptp.aa_fun8169474305930283170er_rat (tptp.aa_fun1894662059565830609er_rat (tptp.aTP_Lamm_aby Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.aa_Code_integer_bool Uu Uuc)) (tptp.aa_Code_integer_rat Uua Uuc)) (tptp.aa_Code_integer_rat Uub Uuc)))) (forall ((Uu tptp.fun_Co8822979462182099027r_bool) (Uua tptp.fun_Code_integer_nat) (Uub tptp.fun_Code_integer_nat) (Uuc tptp.code_integer)) (= (tptp.aa_Code_integer_nat (tptp.aa_fun3076867170244285586er_nat (tptp.aa_fun7635586485349294009er_nat (tptp.aTP_Lamm_abz Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_Code_integer_bool Uu Uuc)) (tptp.aa_Code_integer_nat Uua Uuc)) (tptp.aa_Code_integer_nat Uub Uuc)))) (forall ((Uu tptp.fun_Co8822979462182099027r_bool) (Uua tptp.fun_Code_integer_int) (Uub tptp.fun_Code_integer_int) (Uuc tptp.code_integer)) (= (tptp.aa_Code_integer_int (tptp.aa_fun3291479149765983562er_int (tptp.aa_fun4411173778969602765er_int (tptp.aTP_Lamm_aca Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.if_int (tptp.aa_Code_integer_bool Uu Uuc)) (tptp.aa_Code_integer_int Uua Uuc)) (tptp.aa_Code_integer_int Uub Uuc)))) (forall ((Uu tptp.fun_Pr7757163693017731481t_bool) (Uua tptp.fun_Pr2602117396471556196at_nat) (Uub tptp.fun_Pr2602117396471556196at_nat) (Uuc tptp.product_prod_nat_nat)) (= (tptp.aa_Pro4243173770044397973at_nat (tptp.aa_fun2351638177499875132at_nat (tptp.aa_fun1768432373507419115at_nat (tptp.aTP_Lamm_ih Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_Pro2232559814647311250t_bool Uu Uuc)) (tptp.aa_Pro4243173770044397973at_nat Uua Uuc)) (tptp.aa_Pro4243173770044397973at_nat Uub Uuc)))) (forall ((Uu tptp.fun_Pr803113274115125473t_bool) (Uua tptp.fun_Pr5160692531401422620nt_nat) (Uub tptp.fun_Pr5160692531401422620nt_nat) (Uuc tptp.product_prod_int_int)) (= (tptp.aa_Pro6801748904974264397nt_nat (tptp.aa_fun6016190284160528700nt_nat (tptp.aa_fun1083184158259774627nt_nat (tptp.aTP_Lamm_ig Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_Pro4501881432599481050t_bool Uu Uuc)) (tptp.aa_Pro6801748904974264397nt_nat Uua Uuc)) (tptp.aa_Pro6801748904974264397nt_nat Uub Uuc)))) (forall ((Uu tptp.fun_list_nat_bool) (Uua tptp.fun_list_nat_rat) (Uub tptp.fun_list_nat_rat) (Uuc tptp.list_nat)) (= (tptp.aa_list_nat_rat (tptp.aa_fun1630595088783574696at_rat (tptp.aa_fun6629217458047550682at_rat (tptp.aTP_Lamm_acc Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.aa_list_nat_bool Uu Uuc)) (tptp.aa_list_nat_rat Uua Uuc)) (tptp.aa_list_nat_rat Uub Uuc)))) (forall ((Uu tptp.fun_list_nat_bool) (Uua tptp.fun_list_nat_nat) (Uub tptp.fun_list_nat_nat) (Uuc tptp.list_nat)) (= (tptp.aa_list_nat_nat (tptp.aa_fun8775324257704122008at_nat (tptp.aa_fun7930739032552464066at_nat (tptp.aTP_Lamm_ie Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_list_nat_bool Uu Uuc)) (tptp.aa_list_nat_nat Uua Uuc)) (tptp.aa_list_nat_nat Uub Uuc)))) (forall ((Uu tptp.fun_set_nat_bool) (Uua tptp.fun_set_nat_nat) (Uub tptp.fun_set_nat_nat) (Uuc tptp.set_nat)) (= (tptp.aa_set_nat_nat (tptp.aa_fun3386010016858254564at_nat (tptp.aa_fun8118849421014274228at_nat (tptp.aTP_Lamm_if Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_set_nat_bool Uu Uuc)) (tptp.aa_set_nat_nat Uua Uuc)) (tptp.aa_set_nat_nat Uub Uuc)))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.fun_nat_Code_integer) (Uub tptp.fun_nat_Code_integer) (Uuc tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aa_fun589076786913273746nteger (tptp.aa_fun3918145391673965625nteger (tptp.aTP_Lamm_acf Uu) Uua) Uub) Uuc) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_nat_bool Uu Uuc) (tptp.aa_nat_Code_integer Uua Uuc)) (tptp.aa_nat_Code_integer Uub Uuc)))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.fun_nat_assn) (Uub tptp.fun_nat_assn) (Uuc tptp.nat)) (= (tptp.aa_nat_assn (tptp.aa_fun785744391571715112t_assn (tptp.aa_fun6591345337174305434t_assn (tptp.aTP_Lamm_aci Uu) Uua) Uub) Uuc) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn (tptp.if_assn (tptp.aa_nat_bool Uu Uuc)) (tptp.aa_nat_assn Uua Uuc)) (tptp.aa_nat_assn Uub Uuc)))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.fun_nat_set_nat) (Uub tptp.fun_nat_set_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_set_nat (tptp.aa_fun850356524293783268et_nat (tptp.aa_fun2558789851993377716et_nat (tptp.aTP_Lamm_id Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat (tptp.if_set_nat (tptp.aa_nat_bool Uu Uuc)) (tptp.aa_nat_set_nat Uua Uuc)) (tptp.aa_nat_set_nat Uub Uuc)))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.fun_nat_rat) (Uub tptp.fun_nat_rat) (Uuc tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_fun765758790203053448at_rat (tptp.aa_fun3638354034882855594at_rat (tptp.aTP_Lamm_acb Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.aa_nat_bool Uu Uuc)) (tptp.aa_nat_rat Uua Uuc)) (tptp.aa_nat_rat Uub Uuc)))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.fun_nat_nat) (Uub tptp.fun_nat_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aa_fun6854695580826382482at_nat (tptp.aTP_Lamm_ic Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_nat_bool Uu Uuc)) (tptp.aa_nat_nat Uua Uuc)) (tptp.aa_nat_nat Uub Uuc)))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.fun_nat_int) (Uub tptp.fun_nat_int) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun5565043122120104496at_int (tptp.aa_fun5140708168904641446at_int (tptp.aTP_Lamm_ia Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.if_int (tptp.aa_nat_bool Uu Uuc)) (tptp.aa_nat_int Uua Uuc)) (tptp.aa_nat_int Uub Uuc)))) (forall ((Uu tptp.fun_int_bool) (Uua tptp.fun_int_Code_integer) (Uub tptp.fun_int_Code_integer) (Uuc tptp.int)) (= (tptp.aa_int_Code_integer (tptp.aa_fun5304498221708291146nteger (tptp.aa_fun3938006231294128461nteger (tptp.aTP_Lamm_acd Uu) Uua) Uub) Uuc) (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer (tptp.aa_int_bool Uu Uuc) (tptp.aa_int_Code_integer Uua Uuc)) (tptp.aa_int_Code_integer Uub Uuc)))) (forall ((Uu tptp.fun_int_bool) (Uua tptp.fun_in5957238474111007380at_nat) (Uub tptp.fun_in5957238474111007380at_nat) (Uuc tptp.int)) (= (tptp.aa_int7547510126839136381at_nat (tptp.aa_fun6444483342604292028at_nat (tptp.aa_fun5672742635520905243at_nat (tptp.aTP_Lamm_ij Uu) Uua) Uub) Uuc) (tptp.if_Pro4507677147265585453at_nat (tptp.aa_int_bool Uu Uuc) (tptp.aa_int7547510126839136381at_nat Uua Uuc) (tptp.aa_int7547510126839136381at_nat Uub Uuc)))) (forall ((Uu tptp.fun_int_bool) (Uua tptp.fun_int_assn) (Uub tptp.fun_int_assn) (Uuc tptp.int)) (= (tptp.aa_int_assn (tptp.aa_fun919007281442365664t_assn (tptp.aa_fun7795160494388424622t_assn (tptp.aTP_Lamm_acg Uu) Uua) Uub) Uuc) (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn (tptp.if_assn (tptp.aa_int_bool Uu Uuc)) (tptp.aa_int_assn Uua Uuc)) (tptp.aa_int_assn Uub Uuc)))) (forall ((Uu tptp.fun_int_bool) (Uua tptp.fun_int_rat) (Uub tptp.fun_int_rat) (Uuc tptp.int)) (= (tptp.aa_int_rat (tptp.aa_fun1481061427733998144nt_rat (tptp.aa_fun2191249852558612414nt_rat (tptp.aTP_Lamm_abx Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat (tptp.aa_int_bool Uu Uuc)) (tptp.aa_int_rat Uua Uuc)) (tptp.aa_int_rat Uub Uuc)))) (forall ((Uu tptp.fun_int_bool) (Uua tptp.fun_int_nat) (Uub tptp.fun_int_nat) (Uuc tptp.int)) (= (tptp.aa_int_nat (tptp.aa_fun6506752150744536624nt_nat (tptp.aa_fun5407591398502139302nt_nat (tptp.aTP_Lamm_ib Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_int_bool Uu Uuc)) (tptp.aa_int_nat Uua Uuc)) (tptp.aa_int_nat Uub Uuc)))) (forall ((Uu tptp.fun_int_bool) (Uua tptp.fun_int_int) (Uub tptp.fun_int_int) (Uuc tptp.int)) (= (tptp.aa_int_int (tptp.aa_fun6280345759651049192nt_int (tptp.aa_fun3693603986580398266nt_int (tptp.aTP_Lamm_hz Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.if_int (tptp.aa_int_bool Uu Uuc)) (tptp.aa_int_int Uua Uuc)) (tptp.aa_int_int Uub Uuc)))) (forall ((Uu tptp.fun_int_int) (Uua tptp.fun_int_int) (Uub tptp.set_int) (Uuc tptp.int)) (= (tptp.aa_int_int (tptp.aa_set7310040872927613301nt_int (tptp.aa_fun8076508010538293575nt_int (tptp.aTP_Lamm_lu Uu) Uua) Uub) Uuc) (tptp.groups4538972089207619220nt_int (tptp.aa_int_fun_int_int (tptp.aa_fun5911324870756489105nt_int (tptp.aTP_Lamm_lt Uu) Uua) Uuc) Uub))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.fun_nat_nat) (Uub tptp.set_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_set6537093552120046177at_nat (tptp.aa_fun4561837934398617467at_nat (tptp.aTP_Lamm_ls Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_fun6650658898577385413at_nat (tptp.aTP_Lamm_lr Uu) Uua) Uuc)) Uub))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_Co822469698833053651at_int) (Uub tptp.fun_Co8657364630979331932t_bool) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun3371163242325571225at_int (tptp.aa_fun5074241136823302423at_int (tptp.aTP_Lamm_ti Uu) Uua) Uub) Uuc) (tptp.groups3188404863801439024er_int (tptp.aa_nat1674686023564409748er_int (tptp.aTP_Lamm_th Uua) Uuc) (tptp.collect_Code_integer (tptp.aa_nat6120813132205607877r_bool (tptp.aa_fun8839232882156773436r_bool (tptp.aTP_Lamm_rq Uu) Uub) Uuc))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bool_fun_nat_int) (Uub tptp.fun_bo3288154511880838028t_bool) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun807029333126460483at_int (tptp.aa_fun5144677179269963497at_int (tptp.aTP_Lamm_tf Uu) Uua) Uub) Uuc) (tptp.groups1892458791187145822ol_int (tptp.aa_nat_fun_bool_int (tptp.aTP_Lamm_te Uua) Uuc) (tptp.collect_bool (tptp.aa_nat_fun_bool_bool (tptp.aa_fun4163026448321506586l_bool (tptp.aTP_Lamm_rg Uu) Uub) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_na5492297256294505719er_nat) (Uub tptp.fun_na7774394808840722396r_bool) (Uuc tptp.code_integer)) (= (tptp.aa_Code_integer_nat (tptp.aa_fun490956603642643274er_nat (tptp.aa_fun3698671732857677092er_nat (tptp.aTP_Lamm_ts Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_Cod8670293052248272184at_nat (tptp.aTP_Lamm_sq Uua) Uuc)) (tptp.collect_nat (tptp.aa_Cod2498268374540730821t_bool (tptp.aa_fun6816041618782723900t_bool (tptp.aTP_Lamm_sr Uu) Uub) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_fun_int_nat) (Uub tptp.fun_nat_fun_int_bool) (Uuc tptp.int)) (= (tptp.aa_int_nat (tptp.aa_fun8682134193436059786nt_nat (tptp.aa_fun2690579329546488917nt_nat (tptp.aTP_Lamm_tq Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_int_fun_nat_nat (tptp.aTP_Lamm_sm Uua) Uuc)) (tptp.collect_nat (tptp.aa_int_fun_nat_bool (tptp.aa_fun8184653438340336124t_bool (tptp.aTP_Lamm_rz Uu) Uub) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_fun_bool_nat) (Uub tptp.fun_na9137082442855928016l_bool) (Uuc tptp.bool)) (= (tptp.aa_bool_nat (tptp.aa_fun8887362042153257964ol_nat (tptp.aa_fun8325916554501496444ol_nat (tptp.aTP_Lamm_to Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_bool_fun_nat_nat (tptp.aTP_Lamm_si Uua) Uuc)) (tptp.collect_nat (tptp.aa_bool_fun_nat_bool (tptp.aa_fun4762308584704297754t_bool (tptp.aTP_Lamm_sj Uu) Uub) Uuc))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_Co3009391273526075439nt_int) (Uub tptp.fun_Co8197081679332685312t_bool) (Uuc tptp.int)) (= (tptp.aa_int_int (tptp.aa_fun7408359038690759577nt_int (tptp.aa_fun3657818423959754427nt_int (tptp.aTP_Lamm_tm Uu) Uua) Uub) Uuc) (tptp.groups3188404863801439024er_int (tptp.aa_int1390634949194299888er_int (tptp.aTP_Lamm_sd Uua) Uuc) (tptp.collect_Code_integer (tptp.aa_int3865899974016033897r_bool (tptp.aa_fun4269100936724824892r_bool (tptp.aTP_Lamm_se Uu) Uub) Uuc))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bool_fun_int_int) (Uub tptp.fun_bo2827871560234191408t_bool) (Uuc tptp.int)) (= (tptp.aa_int_int (tptp.aa_fun4844225129491648835nt_int (tptp.aa_fun4909036969399236677nt_int (tptp.aTP_Lamm_tk Uu) Uua) Uub) Uuc) (tptp.groups1892458791187145822ol_int (tptp.aa_int_fun_bool_int (tptp.aTP_Lamm_ru Uua) Uuc) (tptp.collect_bool (tptp.aa_int_fun_bool_bool (tptp.aa_fun6035399485891414554l_bool (tptp.aTP_Lamm_rv Uu) Uub) Uuc))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_Co3312552843764780407at_nat) (Uub tptp.fun_Co8657364630979331932t_bool) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun7549014261834767933at_nat (tptp.aa_fun5721305349739569687at_nat (tptp.aTP_Lamm_tc Uu) Uua) Uub) Uuc) (tptp.groups3190895334310489300er_nat (tptp.aa_nat5852537043073606456er_nat (tptp.aTP_Lamm_rp Uua) Uuc) (tptp.collect_Code_integer (tptp.aa_nat6120813132205607877r_bool (tptp.aa_fun8839232882156773436r_bool (tptp.aTP_Lamm_rq Uu) Uub) Uuc))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_fun_nat_nat) (Uub tptp.fun_int_fun_nat_bool) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun4133023758092209198at_nat (tptp.aa_fun7384697781603784697at_nat (tptp.aTP_Lamm_ta Uu) Uua) Uub) Uuc) (tptp.groups1707563613775114915nt_nat (tptp.aa_nat_fun_int_nat (tptp.aTP_Lamm_rk Uua) Uuc) (tptp.collect_int (tptp.aa_nat_fun_int_bool (tptp.aa_fun3035398748895483388t_bool (tptp.aTP_Lamm_rl Uu) Uub) Uuc))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bool_fun_nat_nat) (Uub tptp.fun_bo3288154511880838028t_bool) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun4984880352635657191at_nat (tptp.aa_fun8028557108643889at_nat (tptp.aTP_Lamm_sy Uu) Uua) Uub) Uuc) (tptp.groups1894949261696196098ol_nat (tptp.aa_nat_fun_bool_nat (tptp.aTP_Lamm_rf Uua) Uuc) (tptp.collect_bool (tptp.aa_nat_fun_bool_bool (tptp.aa_fun4163026448321506586l_bool (tptp.aTP_Lamm_rg Uu) Uub) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_na5492297256294505719er_nat) (Uub tptp.fun_na7774394808840722396r_bool) (Uuc tptp.code_integer)) (= (tptp.aa_Code_integer_nat (tptp.aa_fun490956603642643274er_nat (tptp.aa_fun3698671732857677092er_nat (tptp.aTP_Lamm_ss Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_Cod8670293052248272184at_nat (tptp.aTP_Lamm_sq Uua) Uuc)) (tptp.collect_nat (tptp.aa_Cod2498268374540730821t_bool (tptp.aa_fun6816041618782723900t_bool (tptp.aTP_Lamm_sr Uu) Uub) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_fun_int_nat) (Uub tptp.fun_nat_fun_int_bool) (Uuc tptp.int)) (= (tptp.aa_int_nat (tptp.aa_fun8682134193436059786nt_nat (tptp.aa_fun2690579329546488917nt_nat (tptp.aTP_Lamm_sn Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_int_fun_nat_nat (tptp.aTP_Lamm_sm Uua) Uuc)) (tptp.collect_nat (tptp.aa_int_fun_nat_bool (tptp.aa_fun8184653438340336124t_bool (tptp.aTP_Lamm_rz Uu) Uub) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_fun_bool_nat) (Uub tptp.fun_na9137082442855928016l_bool) (Uuc tptp.bool)) (= (tptp.aa_bool_nat (tptp.aa_fun8887362042153257964ol_nat (tptp.aa_fun8325916554501496444ol_nat (tptp.aTP_Lamm_sk Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_bool_fun_nat_nat (tptp.aTP_Lamm_si Uua) Uuc)) (tptp.collect_nat (tptp.aa_bool_fun_nat_bool (tptp.aa_fun4762308584704297754t_bool (tptp.aTP_Lamm_sj Uu) Uub) Uuc))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_Co3009391273526075439nt_int) (Uub tptp.fun_Co8197081679332685312t_bool) (Uuc tptp.int)) (= (tptp.aa_int_int (tptp.aa_fun7408359038690759577nt_int (tptp.aa_fun3657818423959754427nt_int (tptp.aTP_Lamm_sf Uu) Uua) Uub) Uuc) (tptp.groups7234854612051535045er_int (tptp.aa_int1390634949194299888er_int (tptp.aTP_Lamm_sd Uua) Uuc) (tptp.collect_Code_integer (tptp.aa_int3865899974016033897r_bool (tptp.aa_fun4269100936724824892r_bool (tptp.aTP_Lamm_se Uu) Uub) Uuc))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bool_fun_int_int) (Uub tptp.fun_bo2827871560234191408t_bool) (Uuc tptp.int)) (= (tptp.aa_int_int (tptp.aa_fun4844225129491648835nt_int (tptp.aa_fun4909036969399236677nt_int (tptp.aTP_Lamm_rw Uu) Uua) Uub) Uuc) (tptp.groups5766010803219694601ol_int (tptp.aa_int_fun_bool_int (tptp.aTP_Lamm_ru Uua) Uuc) (tptp.collect_bool (tptp.aa_int_fun_bool_bool (tptp.aa_fun6035399485891414554l_bool (tptp.aTP_Lamm_rv Uu) Uub) Uuc))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_Co3312552843764780407at_nat) (Uub tptp.fun_Co8657364630979331932t_bool) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun7549014261834767933at_nat (tptp.aa_fun5721305349739569687at_nat (tptp.aTP_Lamm_rr Uu) Uua) Uub) Uuc) (tptp.groups7237345082560585321er_nat (tptp.aa_nat5852537043073606456er_nat (tptp.aTP_Lamm_rp Uua) Uuc) (tptp.collect_Code_integer (tptp.aa_nat6120813132205607877r_bool (tptp.aa_fun8839232882156773436r_bool (tptp.aTP_Lamm_rq Uu) Uub) Uuc))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_fun_nat_nat) (Uub tptp.fun_int_fun_nat_bool) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun4133023758092209198at_nat (tptp.aa_fun7384697781603784697at_nat (tptp.aTP_Lamm_rm Uu) Uua) Uub) Uuc) (tptp.groups4541462559716669496nt_nat (tptp.aa_nat_fun_int_nat (tptp.aTP_Lamm_rk Uua) Uuc) (tptp.collect_int (tptp.aa_nat_fun_int_bool (tptp.aa_fun3035398748895483388t_bool (tptp.aTP_Lamm_rl Uu) Uub) Uuc))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bool_fun_nat_nat) (Uub tptp.fun_bo3288154511880838028t_bool) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun4984880352635657191at_nat (tptp.aa_fun8028557108643889at_nat (tptp.aTP_Lamm_rh Uu) Uua) Uub) Uuc) (tptp.groups5768501273728744877ol_nat (tptp.aa_nat_fun_bool_nat (tptp.aTP_Lamm_rf Uua) Uuc) (tptp.collect_bool (tptp.aa_nat_fun_bool_bool (tptp.aa_fun4163026448321506586l_bool (tptp.aTP_Lamm_rg Uu) Uub) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_fun_int_int) (Uub tptp.fun_nat_fun_int_bool) (Uuc tptp.int)) (= (tptp.aa_int_int (tptp.aa_fun4504283173926863078nt_int (tptp.aa_fun5512849559334105941nt_int (tptp.aTP_Lamm_sa Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_mu Uua) Uuc)) (tptp.collect_nat (tptp.aa_int_fun_nat_bool (tptp.aa_fun8184653438340336124t_bool (tptp.aTP_Lamm_rz Uu) Uub) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_fun_nat_nat) (Uub tptp.fun_nat_fun_nat_bool) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun4644938397070871434at_nat (tptp.aa_fun7390876557192650417at_nat (tptp.aTP_Lamm_sw Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_lk Uua) Uuc)) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aa_fun3051233943552222972t_bool (tptp.aTP_Lamm_sv Uu) Uub) Uuc))))) (forall ((Uu tptp.code_natural) (Uua tptp.code_natural) (Uub tptp.code_natural) (Uuc tptp.code_natural)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 tptp.one)))))))))))))))))))))))) (= (tptp.aa_Cod6808739660676082561atural (tptp.aa_Cod4292056611156568242atural (tptp.aa_Cod8811915439870959971atural (tptp.aTP_Lamm_aoy Uu) Uua) Uub) Uuc) (tptp.produc4480994950612372183atural (tptp.produc3574140220909816553atural (tptp.inc_shift (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 _let_1))))))))) Uu) Uuc) (tptp.produc3574140220909816553atural Uub (tptp.inc_shift (tptp.aa_num_Code_natural tptp.numera5444537566228673987atural (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 _let_1))))))))) Uua)))))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat) (Uuc tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Uua))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Uu))) (= (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat (tptp.aa_nat4158579785191972357at_nat (tptp.aTP_Lamm_amq Uu) Uua) Uub) Uuc) (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_2 Uub)) (tptp.aa_nat_nat _let_1 Uuc))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_2 Uuc)) (tptp.aa_nat_nat _let_1 Uub))))))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.set_Pr1261947904930325089at_nat) (Uub tptp.nat) (Uuc tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat Uu Uuc))) (let ((_let_2 (tptp.aa_nat_nat Uu Uub))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aa_set1256819327649670340t_bool (tptp.aTP_Lamm_ahu Uu) Uua) Uub) Uuc)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_2) _let_1)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_2) _let_1)) (tptp.pp (tptp.aa_set3135850010578026034t_bool (tptp.member8440522571783428010at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat Uub) Uuc)) Uua)))))))) (forall ((Uu tptp.fun_int_nat) (Uua tptp.set_Pr958786334691620121nt_int) (Uub tptp.int) (Uuc tptp.int)) (let ((_let_1 (tptp.aa_int_nat Uu Uuc))) (let ((_let_2 (tptp.aa_int_nat Uu Uub))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aa_set8965632145344517972t_bool (tptp.aTP_Lamm_ahv Uu) Uua) Uub) Uuc)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_2) _let_1)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_2) _let_1)) (tptp.member5262025264175285858nt_int (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Uub) Uuc) Uua))))))) (forall ((Uu tptp.fun_int_option_int) (Uua tptp.fun_Pr803113274115125473t_bool) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aa_fun7489457930223801746t_bool (tptp.aTP_Lamm_aht Uu) Uua) Uub) Uuc)) (and (= (tptp.aa_int_option_int Uu Uub) (tptp.aa_int_option_int tptp.some_int Uuc)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool Uua (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Uub) Uuc)))))) (forall ((Uu tptp.fun_fu6675107418524772179et_nat) (Uua tptp.fun_Pr3073222722562426257t_bool) (Uub tptp.fun_Pr6001797050664311790t_bool) (Uuc tptp.produc3658429121746597890et_nat)) (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool (tptp.aa_fun6808777976510360636t_bool (tptp.aa_fun8271251865843499800t_bool (tptp.aTP_Lamm_aho Uu) Uua) Uub) Uuc)) (and (= (tptp.aa_fun3443883199727375236et_nat Uu Uub) (tptp.some_P624177172695371229et_nat Uuc)) (tptp.pp (tptp.aa_Pro7454463142485379962t_bool Uua (tptp.aa_Pro1252775905504286431et_nat (tptp.aa_fun324524810586414160et_nat tptp.produc8148480564485311129et_nat Uub) Uuc)))))) (forall ((Uu tptp.fun_fu1965482174671583728et_nat) (Uua tptp.fun_Pr229822445725053876t_bool) (Uub tptp.fun_Pr6001797050664311790t_bool) (Uuc tptp.produc6108883039684432031et_nat)) (= (tptp.pp (tptp.aa_Pro7454463142485379962t_bool (tptp.aa_fun1003322038264691679t_bool (tptp.aa_fun6031285004062638814t_bool (tptp.aTP_Lamm_ahp Uu) Uua) Uub) Uuc)) (and (= (tptp.aa_fun5342968722616283297et_nat Uu Uub) (tptp.some_P7593219549526818170et_nat Uuc)) (tptp.pp (tptp.aa_Pro6092667153363046813t_bool Uua (tptp.aa_Pro4782578008252579993et_nat (tptp.aa_fun2587632456826484618et_nat tptp.produc3083477295402903094et_nat Uub) Uuc)))))) (forall ((Uu tptp.fun_fu4756305112005770350nt_int) (Uua tptp.fun_Pr6019674992625747500t_bool) (Uub tptp.fun_Pr9164807099015279978e_term) (Uuc tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun5300525129335604105t_bool (tptp.aa_fun414483183390545080t_bool (tptp.aTP_Lamm_ahq Uu) Uua) Uub) Uuc)) (and (= (tptp.aa_fun2000036126570120791nt_int Uu Uub) (tptp.some_P4184893108420464158nt_int Uuc)) (tptp.pp (tptp.aa_Pro5031108791230793749t_bool Uua (tptp.aa_Pro3513184699142849729nt_int (tptp.aa_fun1388719692539776744nt_int tptp.produc1560874099174258678nt_int Uub) Uuc)))))) (forall ((Uu tptp.fun_fu3249470265263746970nt_int) (Uua tptp.fun_Pr5504123824928244736t_bool) (Uub tptp.fun_in6429348457993719614e_term) (Uuc tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun4446166836006121821t_bool (tptp.aa_fun8816120322678784096t_bool (tptp.aTP_Lamm_ahr Uu) Uua) Uub) Uuc)) (and (= (tptp.aa_fun4554338130361792899nt_int Uu Uub) (tptp.some_P4184893108420464158nt_int Uuc)) (tptp.pp (tptp.aa_Pro7591400126937138665t_bool Uua (tptp.aa_Pro835648289009615341nt_int (tptp.aa_fun7940596247606734144nt_int tptp.produc4852315488734385442nt_int Uub) Uuc)))))) (forall ((Uu tptp.fun_a_1313742400928293293it_nat) (Uua tptp.fun_Pr2906233850362575543t_bool) (Uub tptp.a) (Uuc tptp.produc6653097349344004940it_nat)) (= (tptp.pp (tptp.aa_Pro3182513528956304653t_bool (tptp.aa_a_f736957945511644770t_bool (tptp.aa_fun302308005641782372t_bool (tptp.aTP_Lamm_ahs Uu) Uua) Uub) Uuc)) (and (= (tptp.aa_a_o5231022909227610846it_nat Uu Uub) (tptp.some_P1054239925786823975it_nat Uuc)) (tptp.pp (tptp.aa_Pro8278066377857552544t_bool Uua (tptp.aa_Pro8078911840264235907it_nat (tptp.aa_a_f2234720956197727492it_nat tptp.produc9178034014595674355it_nat Uub) Uuc)))))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aa_nat2010205248571845816nteger (tptp.aa_Cod3140087502949435154nteger (tptp.aTP_Lamm_acq Uu) Uua) Uub) Uuc) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uub) Uuc))) (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger Uu) Uuc))) (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.rat) (Uua tptp.rat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aTP_Lamm_aco Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uub) Uuc))) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat Uu) Uuc))) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aa_int431785320988601264at_int (tptp.aTP_Lamm_acp Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uub) Uuc))) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int Uu) Uuc))) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aa_nat2010205248571845816nteger (tptp.aa_Cod3140087502949435154nteger (tptp.aTP_Lamm_acn Uu) Uua) Uub) Uuc) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uub) Uuc))) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Uu) Uuc))) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.rat) (Uua tptp.rat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aTP_Lamm_acl Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uub) Uuc))) (tptp.aa_nat_rat (tptp.power_power_rat Uu) Uuc))) (tptp.aa_nat_rat (tptp.power_power_rat Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_nat3783148529270815480at_nat (tptp.aTP_Lamm_acj Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uub) Uuc))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Uu) Uuc))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aa_int431785320988601264at_int (tptp.aTP_Lamm_acm Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uub) Uuc))) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Uu) Uuc))) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.code_integer) (Uua tptp.nat) (Uub tptp.code_integer) (Uuc tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aa_Cod1578151519121547077nteger (tptp.aa_nat2351529209232473362nteger (tptp.aTP_Lamm_aio Uu) Uua) Uub) Uuc) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) (tptp.aa_nat_nat tptp.suc Uuc)))) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Uu) Uuc)))) (forall ((Uu tptp.rat) (Uua tptp.nat) (Uub tptp.rat) (Uuc tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_nat298952458717073160at_rat (tptp.aTP_Lamm_aip Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) (tptp.aa_nat_nat tptp.suc Uuc)))) (tptp.aa_nat_rat (tptp.power_power_rat Uu) Uuc)))) (forall ((Uu tptp.int) (Uua tptp.nat) (Uub tptp.int) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int (tptp.aa_nat6704147566042551216at_int (tptp.aTP_Lamm_aiq Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) (tptp.aa_nat_nat tptp.suc Uuc)))) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Uu) Uuc)))) (forall ((Uu tptp.fun_list_nat_bool) (Uua tptp.set_list_nat) (Uub tptp.fun_bool_bool) (Uuc tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_fun8098540714523660868l_bool (tptp.aa_set6964050860520458327l_bool (tptp.aTP_Lamm_jn Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.member_bool Uuc (tptp.image_list_nat_bool Uu Uua))) (tptp.pp (tptp.aa_bool_bool Uub Uuc))))) (forall ((Uu tptp.fun_bool_bool) (Uua tptp.set_bool) (Uub tptp.fun_bool_bool) (Uuc tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_fun8098540714523660868l_bool (tptp.aa_set6656371295676988350l_bool (tptp.aTP_Lamm_iv Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.member_bool Uuc (tptp.image_bool_bool Uu Uua))) (tptp.pp (tptp.aa_bool_bool Uub Uuc))))) (forall ((Uu tptp.fun_bool_nat) (Uua tptp.set_bool) (Uub tptp.fun_nat_bool) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun3878383735219268284t_bool (tptp.aa_set5798912244828377086t_bool (tptp.aTP_Lamm_jb Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) (tptp.image_bool_nat Uu Uua))) (tptp.pp (tptp.aa_nat_bool Uub Uuc))))) (forall ((Uu tptp.fun_bool_int) (Uua tptp.set_bool) (Uub tptp.fun_int_bool) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun5146555767781538748t_bool (tptp.aa_set507720255357849342t_bool (tptp.aTP_Lamm_jh Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uuc) (tptp.image_bool_int Uu Uua))) (tptp.pp (tptp.aa_int_bool Uub Uuc))))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.set_nat) (Uub tptp.fun_bool_bool) (Uuc tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_fun8098540714523660868l_bool (tptp.aa_set2341586533381200199l_bool (tptp.aTP_Lamm_ix Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.member_bool Uuc (tptp.image_nat_bool Uu Uua))) (tptp.pp (tptp.aa_bool_bool Uub Uuc))))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.set_nat) (Uub tptp.fun_nat_bool) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun3878383735219268284t_bool (tptp.aa_set2548965808111510023t_bool (tptp.aTP_Lamm_jd Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) (tptp.image_nat_nat Uu Uua))) (tptp.pp (tptp.aa_nat_bool Uub Uuc))))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.set_nat) (Uub tptp.fun_int_bool) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun5146555767781538748t_bool (tptp.aa_set6481145855495758087t_bool (tptp.aTP_Lamm_jj Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uuc) (tptp.image_nat_int Uu Uua))) (tptp.pp (tptp.aa_int_bool Uub Uuc))))) (forall ((Uu tptp.fun_int_bool) (Uua tptp.set_int) (Uub tptp.fun_bool_bool) (Uuc tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_fun8098540714523660868l_bool (tptp.aa_set8137165717292330403l_bool (tptp.aTP_Lamm_iz Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.member_bool Uuc (tptp.image_int_bool Uu Uua))) (tptp.pp (tptp.aa_bool_bool Uub Uuc))))) (forall ((Uu tptp.fun_int_nat) (Uua tptp.set_int) (Uub tptp.fun_nat_bool) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun3878383735219268284t_bool (tptp.aa_set527285886755939t_bool (tptp.aTP_Lamm_jf Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) (tptp.image_int_nat Uu Uua))) (tptp.pp (tptp.aa_nat_bool Uub Uuc))))) (forall ((Uu tptp.fun_int_int) (Uua tptp.set_int) (Uub tptp.fun_int_bool) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun5146555767781538748t_bool (tptp.aa_set3932707333271004003t_bool (tptp.aTP_Lamm_jl Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uuc) (tptp.image_int_int Uu Uua))) (tptp.pp (tptp.aa_int_bool Uub Uuc))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_Co8310303586393106575r_bool) (Uub tptp.code_integer) (Uuc tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool (tptp.aa_fun2374795795022016636r_bool (tptp.aTP_Lamm_alt Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Uuc) Uu)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool Uua Uub) Uuc))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_bo284609390884453567r_bool) (Uub tptp.bool) (Uuc tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_boo5858427943822696632r_bool (tptp.aa_fun5712573584333027516r_bool (tptp.aTP_Lamm_alf Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Uuc) Uu)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_boo5858427943822696632r_bool Uua Uub) Uuc))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_na7774394808840722396r_bool) (Uub tptp.nat) (Uuc tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_nat6120813132205607877r_bool (tptp.aa_fun5933071796644114364r_bool (tptp.aTP_Lamm_so Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Uuc) Uu)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_nat6120813132205607877r_bool Uua Uub) Uuc))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_in5519481650651148416r_bool) (Uub tptp.int) (Uuc tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_int3865899974016033897r_bool (tptp.aa_fun9015013955937593532r_bool (tptp.aTP_Lamm_alm Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Uuc) Uu)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_int3865899974016033897r_bool Uua Uub) Uuc))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_Co3748208068438171869l_bool) (Uub tptp.code_integer) (Uuc tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_Cod8494480694608518558l_bool (tptp.aa_fun473675042869869048l_bool (tptp.aTP_Lamm_alp Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.member_bool Uuc Uu)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_Cod8494480694608518558l_bool Uua Uub) Uuc))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bo1841576699660343469l_bool) (Uub tptp.bool) (Uuc tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool (tptp.aa_fun1447330757145981436l_bool (tptp.aTP_Lamm_alc Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.member_bool Uuc Uu)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool Uua Uub) Uuc))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_na9137082442855928016l_bool) (Uub tptp.nat) (Uuc tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_nat_fun_bool_bool (tptp.aa_fun1387864478824611934l_bool (tptp.aTP_Lamm_sg Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.member_bool Uuc Uu)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_nat_fun_bool_bool Uua Uub) Uuc))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_in3865155034416861484l_bool) (Uub tptp.int) (Uuc tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_int_fun_bool_bool (tptp.aa_fun3617675969253937942l_bool (tptp.aTP_Lamm_ali Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.member_bool Uuc Uu)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_int_fun_bool_bool Uua Uub) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_Co8657364630979331932t_bool) (Uub tptp.code_integer) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_Cod2498268374540730821t_bool (tptp.aa_fun498830667440607164t_bool (tptp.aTP_Lamm_rn Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_Cod2498268374540730821t_bool Uua Uub) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_bo3288154511880838028t_bool) (Uub tptp.bool) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_bool_fun_nat_bool (tptp.aa_fun7537470554201192406t_bool (tptp.aTP_Lamm_rd Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_bool_fun_nat_bool Uua Uub) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_fun_nat_bool) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aa_fun3051233943552222972t_bool (tptp.aTP_Lamm_st Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool Uua Uub) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_int_fun_nat_bool) (Uub tptp.int) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool (tptp.aa_fun3602880909931171836t_bool (tptp.aTP_Lamm_ri Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool Uua Uub) Uuc))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_Co8197081679332685312t_bool) (Uub tptp.code_integer) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_Cod8597349444926882409t_bool (tptp.aa_fun6946700965406361788t_bool (tptp.aTP_Lamm_sb Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uuc) Uu)) (tptp.pp (tptp.aa_int_bool (tptp.aa_Cod8597349444926882409t_bool Uua Uub) Uuc))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_bo2827871560234191408t_bool) (Uub tptp.bool) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_bool_fun_int_bool (tptp.aa_fun4998116011708744478t_bool (tptp.aTP_Lamm_rs Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uuc) Uu)) (tptp.pp (tptp.aa_int_bool (tptp.aa_bool_fun_int_bool Uua Uub) Uuc))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_nat_fun_int_bool) (Uub tptp.nat) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_nat_fun_int_bool (tptp.aa_fun7617171277304647676t_bool (tptp.aTP_Lamm_rx Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uuc) Uu)) (tptp.pp (tptp.aa_int_bool (tptp.aa_nat_fun_int_bool Uua Uub) Uuc))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_fun_int_bool) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aa_fun8168818243683596540t_bool (tptp.aTP_Lamm_alk Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uuc) Uu)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool Uua Uub) Uuc))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_Co8310303586393106575r_bool) (Uub tptp.code_integer) (Uuc tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool (tptp.aa_fun2374795795022016636r_bool (tptp.aTP_Lamm_als Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Uuc) Uu)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool Uua Uuc) Uub))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_Co3748208068438171869l_bool) (Uub tptp.bool) (Uuc tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_boo5858427943822696632r_bool (tptp.aa_fun6233448402170926554r_bool (tptp.aTP_Lamm_alo Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Uuc) Uu)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_Cod8494480694608518558l_bool Uua Uuc) Uub))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_Co8657364630979331932t_bool) (Uub tptp.nat) (Uuc tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_nat6120813132205607877r_bool (tptp.aa_fun8839232882156773436r_bool (tptp.aTP_Lamm_rq Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Uuc) Uu)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_Cod2498268374540730821t_bool Uua Uuc) Uub))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_Co8197081679332685312t_bool) (Uub tptp.int) (Uuc tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_int3865899974016033897r_bool (tptp.aa_fun4269100936724824892r_bool (tptp.aTP_Lamm_se Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Uuc) Uu)) (tptp.pp (tptp.aa_int_bool (tptp.aa_Cod8597349444926882409t_bool Uua Uuc) Uub))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bo284609390884453567r_bool) (Uub tptp.code_integer) (Uuc tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_Cod8494480694608518558l_bool (tptp.aa_fun9176172261886745818l_bool (tptp.aTP_Lamm_ada Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.member_bool Uuc Uu)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_boo5858427943822696632r_bool Uua Uuc) Uub))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bo1841576699660343469l_bool) (Uub tptp.bool) (Uuc tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool (tptp.aa_fun1447330757145981436l_bool (tptp.aTP_Lamm_alb Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.member_bool Uuc Uu)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool Uua Uuc) Uub))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bo3288154511880838028t_bool) (Uub tptp.nat) (Uuc tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_nat_fun_bool_bool (tptp.aa_fun4163026448321506586l_bool (tptp.aTP_Lamm_rg Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.member_bool Uuc Uu)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_bool_fun_nat_bool Uua Uuc) Uub))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bo2827871560234191408t_bool) (Uub tptp.int) (Uuc tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_int_fun_bool_bool (tptp.aa_fun6035399485891414554l_bool (tptp.aTP_Lamm_rv Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.member_bool Uuc Uu)) (tptp.pp (tptp.aa_int_bool (tptp.aa_bool_fun_int_bool Uua Uuc) Uub))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_na7774394808840722396r_bool) (Uub tptp.code_integer) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_Cod2498268374540730821t_bool (tptp.aa_fun6816041618782723900t_bool (tptp.aTP_Lamm_sr Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_nat6120813132205607877r_bool Uua Uuc) Uub))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_na9137082442855928016l_bool) (Uub tptp.bool) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_bool_fun_nat_bool (tptp.aa_fun4762308584704297754t_bool (tptp.aTP_Lamm_sj Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_nat_fun_bool_bool Uua Uuc) Uub))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_fun_nat_bool) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aa_fun3051233943552222972t_bool (tptp.aTP_Lamm_sv Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool Uua Uuc) Uub))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_fun_int_bool) (Uub tptp.int) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool (tptp.aa_fun8184653438340336124t_bool (tptp.aTP_Lamm_rz Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (tptp.pp (tptp.aa_int_bool (tptp.aa_nat_fun_int_bool Uua Uuc) Uub))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_in5519481650651148416r_bool) (Uub tptp.code_integer) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_Cod8597349444926882409t_bool (tptp.aa_fun2469241947764354620t_bool (tptp.aTP_Lamm_adc Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uuc) Uu)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_int3865899974016033897r_bool Uua Uuc) Uub))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_in3865155034416861484l_bool) (Uub tptp.bool) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_bool_fun_int_bool (tptp.aa_fun2580392495071267866t_bool (tptp.aTP_Lamm_alh Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uuc) Uu)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_int_fun_bool_bool Uua Uuc) Uub))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_fun_nat_bool) (Uub tptp.nat) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_nat_fun_int_bool (tptp.aa_fun3035398748895483388t_bool (tptp.aTP_Lamm_rl Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uuc) Uu)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool Uua Uuc) Uub))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_fun_int_bool) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aa_fun8168818243683596540t_bool (tptp.aTP_Lamm_adb Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uuc) Uu)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool Uua Uuc) Uub))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_Code_integer_nat) (Uub tptp.code_integer) (Uuc tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool (tptp.aa_fun3949617354051801383r_bool (tptp.aTP_Lamm_adm Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Uuc) Uu)) (= (tptp.aa_Code_integer_nat Uua Uuc) (tptp.aa_Code_integer_nat Uua Uub))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bo7282069421189217543nteger) (Uub tptp.bool) (Uuc tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool (tptp.aa_fun7305734610747869602l_bool (tptp.aTP_Lamm_adf Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.member_bool Uuc Uu)) (= (tptp.aa_bool_Code_integer Uua Uuc) (tptp.aa_bool_Code_integer Uua Uub))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bool_nat) (Uub tptp.bool) (Uuc tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool (tptp.aa_fun5754907045972229615l_bool (tptp.aTP_Lamm_add Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.member_bool Uuc Uu)) (= (tptp.aa_bool_nat Uua Uuc) (tptp.aa_bool_nat Uua Uub))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bool_int) (Uub tptp.bool) (Uuc tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool (tptp.aa_fun4343082806956354195l_bool (tptp.aTP_Lamm_ade Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.member_bool Uuc Uu)) (= (tptp.aa_bool_int Uua Uuc) (tptp.aa_bool_int Uua Uub))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_Code_integer) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aa_fun2111297154760714689t_bool (tptp.aTP_Lamm_adi Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (= (tptp.aa_nat_Code_integer Uua Uuc) (tptp.aa_nat_Code_integer Uua Uub))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aa_fun3777555276967886990t_bool (tptp.aTP_Lamm_adg Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (= (tptp.aa_nat_nat Uua Uuc) (tptp.aa_nat_nat Uua Uub))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_int) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aa_fun2605284095902351154t_bool (tptp.aTP_Lamm_adh Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (= (tptp.aa_nat_int Uua Uuc) (tptp.aa_nat_int Uua Uub))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_Code_integer) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aa_fun8056663032588759469t_bool (tptp.aTP_Lamm_adl Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uuc) Uu)) (= (tptp.aa_int_Code_integer Uua Uuc) (tptp.aa_int_Code_integer Uua Uub))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_nat) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aa_fun2912556895731619962t_bool (tptp.aTP_Lamm_adj Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uuc) Uu)) (= (tptp.aa_int_nat Uua Uuc) (tptp.aa_int_nat Uua Uub))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_int) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aa_fun1740285714666084126t_bool (tptp.aTP_Lamm_adk Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uuc) Uu)) (= (tptp.aa_int_int Uua Uuc) (tptp.aa_int_int Uua Uub))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_Code_integer_nat) (Uub tptp.nat) (Uuc tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_nat6120813132205607877r_bool (tptp.aa_fun3279747613005586548r_bool (tptp.aTP_Lamm_wm Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Uuc) Uu)) (= (tptp.aa_Code_integer_nat Uua Uuc) Uub)))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_Code_integer_int) (Uub tptp.int) (Uuc tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_int3865899974016033897r_bool (tptp.aa_fun1275183216929564604r_bool (tptp.aTP_Lamm_ws Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Uuc) Uu)) (= (tptp.aa_Code_integer_int Uua Uuc) Uub)))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bool_nat) (Uub tptp.nat) (Uuc tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_nat_fun_bool_bool (tptp.aa_fun6446435369898359566l_bool (tptp.aTP_Lamm_wi Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.member_bool Uuc Uu)) (= (tptp.aa_bool_nat Uua Uuc) Uub)))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bool_int) (Uub tptp.int) (Uuc tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_int_fun_bool_bool (tptp.aa_fun5833344538494674374l_bool (tptp.aTP_Lamm_wo Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.member_bool Uuc Uu)) (= (tptp.aa_bool_int Uua Uuc) Uub)))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_Code_integer) (Uub tptp.code_integer) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_Cod2498268374540730821t_bool (tptp.aa_fun7122322691611174516t_bool (tptp.aTP_Lamm_yy Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (= (tptp.aa_nat_Code_integer Uua Uuc) Uub)))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aa_fun3777555276967886990t_bool (tptp.aTP_Lamm_wv Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (= (tptp.aa_nat_nat Uua Uuc) Uub)))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_int) (Uub tptp.int) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool (tptp.aa_fun2712483305291392982t_bool (tptp.aTP_Lamm_wq Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (= (tptp.aa_nat_int Uua Uuc) Uub)))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_Code_integer) (Uub tptp.code_integer) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_Cod8597349444926882409t_bool (tptp.aa_fun6079510497903818172t_bool (tptp.aTP_Lamm_zc Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uuc) Uu)) (= (tptp.aa_int_Code_integer Uua Uuc) Uub)))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_nat) (Uub tptp.nat) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_nat_fun_int_bool (tptp.aa_fun2805357686342578134t_bool (tptp.aTP_Lamm_wk Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uuc) Uu)) (= (tptp.aa_int_nat Uua Uuc) Uub)))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_int) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aa_fun1740285714666084126t_bool (tptp.aTP_Lamm_wy Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uuc) Uu)) (= (tptp.aa_int_int Uua Uuc) Uub)))) (forall ((Uu tptp.code_integer) (Uua tptp.nat) (Uub tptp.code_integer) (Uuc tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aa_Cod1578151519121547077nteger (tptp.aa_nat2351529209232473362nteger (tptp.aTP_Lamm_ail Uu) Uua) Uub) Uuc) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Uu) Uuc)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) Uuc))))) (forall ((Uu tptp.rat) (Uua tptp.nat) (Uub tptp.rat) (Uuc tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_nat298952458717073160at_rat (tptp.aTP_Lamm_aim Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat Uu) Uuc)) (tptp.aa_nat_rat (tptp.power_power_rat Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) Uuc))))) (forall ((Uu tptp.int) (Uua tptp.nat) (Uub tptp.int) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int (tptp.aa_nat6704147566042551216at_int (tptp.aTP_Lamm_ain Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Uu) Uuc)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) Uuc))))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_nat3783148529270815480at_nat (tptp.aTP_Lamm_abn Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uuc)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aa_int2327297053056786951t_bool (tptp.aTP_Lamm_any Uu) Uua) Uub) Uuc)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uu) Uuc)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uua) Uub))))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aa_nat8637530788439456283t_bool (tptp.aTP_Lamm_amv Uu) Uua) Uub) Uuc)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) Uuc)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uub) Uua))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aa_int2327297053056786951t_bool (tptp.aTP_Lamm_anw Uu) Uua) Uub) Uuc)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uu) Uuc)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uua) Uub))))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aa_nat8637530788439456283t_bool (tptp.aTP_Lamm_amt Uu) Uua) Uub) Uuc)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) Uuc)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uub) Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat (tptp.aa_nat4158579785191972357at_nat (tptp.aTP_Lamm_amx Uu) Uua) Uub) Uuc) (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) Uub)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) Uuc)))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat (tptp.aa_nat4158579785191972357at_nat (tptp.aTP_Lamm_amz Uu) Uua) Uub) Uuc) (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.product_Pair_nat_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) Uuc)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) Uub)))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aa_nat8637530788439456283t_bool (tptp.aTP_Lamm_aos Uu) Uua) Uub) Uuc)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uub) Uua)))) (forall ((Uu tptp.fun_list_nat_bool) (Uua tptp.set_list_nat) (Uub tptp.fun_bool_bool) (Uuc tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool (tptp.aa_fun7225089676084268943t_bool (tptp.aa_set4768573287508199762t_bool (tptp.aTP_Lamm_jo Uu) Uua) Uub) Uuc)) (and (tptp.member_list_nat Uuc Uua) (tptp.pp (tptp.aa_bool_bool Uub (tptp.aa_list_nat_bool Uu Uuc)))))) (forall ((Uu tptp.fun_bool_bool) (Uua tptp.set_bool) (Uub tptp.fun_bool_bool) (Uuc tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_fun8098540714523660868l_bool (tptp.aa_set6656371295676988350l_bool (tptp.aTP_Lamm_iw Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.member_bool Uuc Uua)) (tptp.pp (tptp.aa_bool_bool Uub (tptp.aa_bool_bool Uu Uuc)))))) (forall ((Uu tptp.fun_bool_nat) (Uua tptp.set_bool) (Uub tptp.fun_nat_bool) (Uuc tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_fun6062112079508222567l_bool (tptp.aa_set3283638209543405755l_bool (tptp.aTP_Lamm_jc Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.member_bool Uuc Uua)) (tptp.pp (tptp.aa_nat_bool Uub (tptp.aa_bool_nat Uu Uuc)))))) (forall ((Uu tptp.fun_bool_int) (Uua tptp.set_bool) (Uub tptp.fun_int_bool) (Uuc tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_fun9099954163972356363l_bool (tptp.aa_set6321480294007539551l_bool (tptp.aTP_Lamm_ji Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.member_bool Uuc Uua)) (tptp.pp (tptp.aa_int_bool Uub (tptp.aa_bool_int Uu Uuc)))))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.set_nat) (Uub tptp.fun_bool_bool) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun5996870036960543647t_bool (tptp.aa_set2681322491556877426t_bool (tptp.aTP_Lamm_iy Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uua)) (tptp.pp (tptp.aa_bool_bool Uub (tptp.aa_nat_bool Uu Uuc)))))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.set_nat) (Uub tptp.fun_nat_bool) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun3878383735219268284t_bool (tptp.aa_set2548965808111510023t_bool (tptp.aTP_Lamm_je Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uua)) (tptp.pp (tptp.aa_nat_bool Uub (tptp.aa_nat_nat Uu Uuc)))))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.set_nat) (Uub tptp.fun_int_bool) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun8270846734250162968t_bool (tptp.aa_set6941428807142404707t_bool (tptp.aTP_Lamm_jk Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uua)) (tptp.pp (tptp.aa_int_bool Uub (tptp.aa_nat_int Uu Uuc)))))) (forall ((Uu tptp.fun_int_bool) (Uua tptp.set_int) (Uub tptp.fun_bool_bool) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun2872579070491919427t_bool (tptp.aa_set820588111078594490t_bool (tptp.aTP_Lamm_ja Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uuc) Uua)) (tptp.pp (tptp.aa_bool_bool Uub (tptp.aa_int_bool Uu Uuc)))))) (forall ((Uu tptp.fun_int_nat) (Uua tptp.set_int) (Uub tptp.fun_nat_bool) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun754092768750644064t_bool (tptp.aa_set8763616371094885127t_bool (tptp.aTP_Lamm_jg Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uuc) Uua)) (tptp.pp (tptp.aa_nat_bool Uub (tptp.aa_int_nat Uu Uuc)))))) (forall ((Uu tptp.fun_int_int) (Uua tptp.set_int) (Uub tptp.fun_int_bool) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun5146555767781538748t_bool (tptp.aa_set3932707333271004003t_bool (tptp.aTP_Lamm_jm Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uuc) Uua)) (tptp.pp (tptp.aa_int_bool Uub (tptp.aa_int_int Uu Uuc)))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_Co8499238673658658103nteger) (Uub tptp.fun_Co8499238673658658103nteger) (Uuc tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_fun6999757421500609566r_bool (tptp.aa_fun4344203112627146752r_bool (tptp.aTP_Lamm_uw Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Uuc) Uu)) (not (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger Uua Uuc)) (tptp.aa_Cod1783974652533396728nteger Uub Uuc)) tptp.one_one_Code_integer))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_Co4490034186337852034r_assn) (Uub tptp.fun_Co4490034186337852034r_assn) (Uuc tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_fun8795547071341169043r_bool (tptp.aa_fun7758107644544034538r_bool (tptp.aTP_Lamm_ve Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Uuc) Uu)) (not (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.aa_Code_integer_assn Uua Uuc)) (tptp.aa_Code_integer_assn Uub Uuc)) tptp.one_one_assn))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bo7282069421189217543nteger) (Uub tptp.fun_bo7282069421189217543nteger) (Uuc tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_fun7063430368917475406l_bool (tptp.aa_fun8946763977956929170l_bool (tptp.aTP_Lamm_uq Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.member_bool Uuc Uu)) (not (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_bool_Code_integer Uua Uuc)) (tptp.aa_bool_Code_integer Uub Uuc)) tptp.one_one_Code_integer))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bool_assn) (Uub tptp.fun_bool_assn) (Uuc tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_fun4109262947370446873l_bool (tptp.aa_fun3956630383439263058l_bool (tptp.aTP_Lamm_uy Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.member_bool Uuc Uu)) (not (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.aa_bool_assn Uua Uuc)) (tptp.aa_bool_assn Uub Uuc)) tptp.one_one_assn))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bool_rat) (Uub tptp.fun_bool_rat) (Uuc tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_fun4510340986217973961l_bool (tptp.aa_fun5608642267463484754l_bool (tptp.aTP_Lamm_vg Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.member_bool Uuc Uu)) (not (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_bool_rat Uua Uuc)) (tptp.aa_bool_rat Uub Uuc)) tptp.one_one_rat))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_Code_integer) (Uub tptp.fun_nat_Code_integer) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun1752071697927428280t_bool (tptp.aa_fun4813323487062687079t_bool (tptp.aTP_Lamm_us Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (not (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer Uua Uuc)) (tptp.aa_nat_Code_integer Uub Uuc)) tptp.one_one_Code_integer))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_assn) (Uub tptp.fun_nat_assn) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun1272683333798124589t_bool (tptp.aa_fun7103831392407232081t_bool (tptp.aTP_Lamm_va Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (not (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.aa_nat_assn Uua Uuc)) (tptp.aa_nat_assn Uub Uuc)) tptp.one_one_assn))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_rat) (Uub tptp.fun_nat_rat) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun5637262893798792573t_bool (tptp.aa_fun2107527232086395633t_bool (tptp.aTP_Lamm_vi Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (not (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat Uua Uuc)) (tptp.aa_nat_rat Uub Uuc)) tptp.one_one_rat))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_Code_integer) (Uub tptp.fun_int_Code_integer) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun3610984093196804608t_bool (tptp.aa_fun2519502641837456723t_bool (tptp.aTP_Lamm_uu Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uuc) Uu)) (not (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_int_Code_integer Uua Uuc)) (tptp.aa_int_Code_integer Uub Uuc)) tptp.one_one_Code_integer))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_assn) (Uub tptp.fun_int_assn) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun1414614411059211637t_bool (tptp.aa_fun5523883950577104445t_bool (tptp.aTP_Lamm_vc Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uuc) Uu)) (not (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn tptp.times_times_assn (tptp.aa_int_assn Uua Uuc)) (tptp.aa_int_assn Uub Uuc)) tptp.one_one_assn))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_Co8499238673658658103nteger) (Uub tptp.fun_Co8499238673658658103nteger) (Uuc tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_fun6999757421500609566r_bool (tptp.aa_fun4344203112627146752r_bool (tptp.aTP_Lamm_uc Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Uuc) Uu)) (not (= (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger Uua Uuc)) (tptp.aa_Cod1783974652533396728nteger Uub Uuc)) tptp.zero_z3403309356797280102nteger))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_Code_integer_rat) (Uub tptp.fun_Code_integer_rat) (Uuc tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_fun6870034422411604195r_bool (tptp.aa_fun5917639483493975434r_bool (tptp.aTP_Lamm_uk Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set1374477347934578310r_bool (tptp.member_Code_integer Uuc) Uu)) (not (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_Code_integer_rat Uua Uuc)) (tptp.aa_Code_integer_rat Uub Uuc)) tptp.zero_zero_rat))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bo7282069421189217543nteger) (Uub tptp.fun_bo7282069421189217543nteger) (Uuc tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_fun7063430368917475406l_bool (tptp.aa_fun8946763977956929170l_bool (tptp.aTP_Lamm_tw Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.member_bool Uuc Uu)) (not (= (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_bool_Code_integer Uua Uuc)) (tptp.aa_bool_Code_integer Uub Uuc)) tptp.zero_z3403309356797280102nteger))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bool_rat) (Uub tptp.fun_bool_rat) (Uuc tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_fun4510340986217973961l_bool (tptp.aa_fun5608642267463484754l_bool (tptp.aTP_Lamm_ue Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.member_bool Uuc Uu)) (not (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_bool_rat Uua Uuc)) (tptp.aa_bool_rat Uub Uuc)) tptp.zero_zero_rat))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bool_nat) (Uub tptp.fun_bool_nat) (Uuc tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_fun7969004623323359937l_bool (tptp.aa_fun1357226766775296850l_bool (tptp.aTP_Lamm_um Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.member_bool Uuc Uu)) (not (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_bool_nat Uua Uuc)) (tptp.aa_bool_nat Uub Uuc)) tptp.zero_zero_nat))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_Code_integer) (Uub tptp.fun_nat_Code_integer) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun1752071697927428280t_bool (tptp.aa_fun4813323487062687079t_bool (tptp.aTP_Lamm_ty Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (not (= (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_nat_Code_integer Uua Uuc)) (tptp.aa_nat_Code_integer Uub Uuc)) tptp.zero_z3403309356797280102nteger))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_rat) (Uub tptp.fun_nat_rat) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun5637262893798792573t_bool (tptp.aa_fun2107527232086395633t_bool (tptp.aTP_Lamm_ug Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (not (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat Uua Uuc)) (tptp.aa_nat_rat Uub Uuc)) tptp.zero_zero_rat))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_nat) (Uub tptp.fun_nat_nat) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun1783405840085286277t_bool (tptp.aa_fun5267048652646918913t_bool (tptp.aTP_Lamm_uo Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (not (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat Uua Uuc)) (tptp.aa_nat_nat Uub Uuc)) tptp.zero_zero_nat))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_Code_integer) (Uub tptp.fun_int_Code_integer) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun3610984093196804608t_bool (tptp.aa_fun2519502641837456723t_bool (tptp.aTP_Lamm_ua Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uuc) Uu)) (not (= (tptp.aa_Cod1783974652533396728nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_int_Code_integer Uua Uuc)) (tptp.aa_int_Code_integer Uub Uuc)) tptp.zero_z3403309356797280102nteger))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_rat) (Uub tptp.fun_int_rat) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun258058769140594373t_bool (tptp.aa_fun465274253410646749t_bool (tptp.aTP_Lamm_ui Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_int_bool (tptp.member_int Uuc) Uu)) (not (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_int_rat Uua Uuc)) (tptp.aa_int_rat Uub Uuc)) tptp.zero_zero_rat))))) (forall ((Uu tptp.fun_bo7282069421189217543nteger) (Uua tptp.code_integer) (Uub tptp.list_bool) (Uuc tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aa_lis7128949495651308427nteger (tptp.aa_Cod4918889179898416383nteger (tptp.aTP_Lamm_aiw Uu) Uua) Uub) Uuc) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_bool_Code_integer Uu (tptp.aa_nat_bool (tptp.nth_bool Uub) Uuc))) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Uua) Uuc)))) (forall ((Uu tptp.fun_bool_rat) (Uua tptp.rat) (Uub tptp.list_bool) (Uuc tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_lis1392928297027365766at_rat (tptp.aa_rat954805563275384383at_rat (tptp.aTP_Lamm_aiz Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_bool_rat Uu (tptp.aa_nat_bool (tptp.nth_bool Uub) Uuc))) (tptp.aa_nat_rat (tptp.power_power_rat Uua) Uuc)))) (forall ((Uu tptp.fun_nat_Code_integer) (Uua tptp.code_integer) (Uub tptp.list_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aa_lis7000467330633774408nteger (tptp.aa_Cod9048065728759425570nteger (tptp.aTP_Lamm_aiv Uu) Uua) Uub) Uuc) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer Uu (tptp.aa_nat_nat (tptp.nth_nat Uub) Uuc))) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Uua) Uuc)))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.rat) (Uub tptp.list_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_lis7014846069874721091at_rat (tptp.aa_rat4396832037704353944at_rat (tptp.aTP_Lamm_aiy Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat Uu (tptp.aa_nat_nat (tptp.nth_nat Uub) Uuc))) (tptp.aa_nat_rat (tptp.power_power_rat Uua) Uuc)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat) (Uub tptp.list_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_lis1299702591413342011at_nat (tptp.aa_nat9125522253416007816at_nat (tptp.aTP_Lamm_ajd Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat Uu (tptp.aa_nat_nat (tptp.nth_nat Uub) Uuc))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Uua) Uuc)))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.int) (Uub tptp.list_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_lis6345223608758921111at_int (tptp.aa_int7844622935458978624at_int (tptp.aTP_Lamm_ajb Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int Uu (tptp.aa_nat_nat (tptp.nth_nat Uub) Uuc))) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Uua) Uuc)))) (forall ((Uu tptp.fun_int_Code_integer) (Uua tptp.code_integer) (Uub tptp.list_int) (Uuc tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aa_lis2169558292809893284nteger (tptp.aa_Cod4217156690935544446nteger (tptp.aTP_Lamm_aiu Uu) Uua) Uub) Uuc) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_int_Code_integer Uu (tptp.aa_nat_int (tptp.nth_int Uub) Uuc))) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Uua) Uuc)))) (forall ((Uu tptp.fun_int_rat) (Uua tptp.rat) (Uub tptp.list_int) (Uuc tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_lis1742918661435654559at_rat (tptp.aa_rat8348276666120063220at_rat (tptp.aTP_Lamm_aix Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_int_rat Uu (tptp.aa_nat_int (tptp.nth_int Uub) Uuc))) (tptp.aa_nat_rat (tptp.power_power_rat Uua) Uuc)))) (forall ((Uu tptp.fun_int_nat) (Uua tptp.nat) (Uub tptp.list_int) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_lis5251147219829051287at_nat (tptp.aa_nat3853594844976941284at_nat (tptp.aTP_Lamm_ajc Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_int_nat Uu (tptp.aa_nat_int (tptp.nth_int Uub) Uuc))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Uua) Uuc)))) (forall ((Uu tptp.fun_int_int) (Uua tptp.int) (Uub tptp.list_int) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_lis1073296200319854579at_int (tptp.aa_int2572695527019912092at_int (tptp.aTP_Lamm_aja Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int Uu (tptp.aa_nat_int (tptp.nth_int Uub) Uuc))) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Uua) Uuc)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.fun_nat_nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_fun6650658898577385413at_nat (tptp.aTP_Lamm_lr Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat Uu Uub)) (tptp.aa_nat_nat Uua Uuc)))) (forall ((Uu tptp.fun_int_int) (Uua tptp.fun_int_int) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.aa_fun5911324870756489105nt_int (tptp.aTP_Lamm_lt Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int Uu Uub)) (tptp.aa_int_int Uua Uuc)))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_na5492297256294505719er_nat) (Uub 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(tptp.aa_Code_integer_int (tptp.aa_fun531554186711482826er_int (tptp.aa_fun2196751070425669740er_int (tptp.aTP_Lamm_tl Uu) Uua) Uub) Uuc) (tptp.groups1705073143266064639nt_int (tptp.aa_Cod5491795744640130032nt_int Uua Uuc) (tptp.collect_int (tptp.aa_Cod8597349444926882409t_bool (tptp.aa_fun6946700965406361788t_bool (tptp.aTP_Lamm_sb Uu) Uub) Uuc))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_nat_fun_int_nat) (Uub tptp.fun_nat_fun_int_bool) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun7682780481535005230at_nat (tptp.aa_fun503657754853467129at_nat (tptp.aTP_Lamm_tp Uu) Uua) Uub) Uuc) (tptp.groups1707563613775114915nt_nat (tptp.aa_nat_fun_int_nat Uua Uuc) (tptp.collect_int (tptp.aa_nat_fun_int_bool (tptp.aa_fun7617171277304647676t_bool (tptp.aTP_Lamm_rx Uu) Uub) Uuc))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_bool_fun_int_int) (Uub tptp.fun_bo2827871560234191408t_bool) (Uuc tptp.bool)) (= (tptp.aa_bool_int (tptp.aa_fun2977339950115259112ol_int (tptp.aa_fun6505924867870464892ol_int (tptp.aTP_Lamm_tj Uu) Uua) Uub) Uuc) (tptp.groups1705073143266064639nt_int (tptp.aa_bool_fun_int_int Uua Uuc) (tptp.collect_int (tptp.aa_bool_fun_int_bool (tptp.aa_fun4998116011708744478t_bool (tptp.aTP_Lamm_rs Uu) Uub) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_Co3312552843764780407at_nat) (Uub tptp.fun_Co8657364630979331932t_bool) (Uuc tptp.code_integer)) (= (tptp.aa_Code_integer_nat (tptp.aa_fun2949368542467568330er_nat (tptp.aa_fun8366171557965857828er_nat (tptp.aTP_Lamm_tb Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_Cod8670293052248272184at_nat Uua Uuc)) (tptp.collect_nat (tptp.aa_Cod2498268374540730821t_bool (tptp.aa_fun498830667440607164t_bool (tptp.aTP_Lamm_rn Uu) Uub) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_Co822469698833053651at_int) (Uub tptp.fun_Co8657364630979331932t_bool) (Uuc tptp.code_integer)) (= (tptp.aa_Code_integer_int (tptp.aa_fun7994889559813147430er_int (tptp.aa_fun6206124202175859492er_int (tptp.aTP_Lamm_tg Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_Cod4492442032739075476at_int Uua Uuc)) (tptp.collect_nat (tptp.aa_Cod2498268374540730821t_bool (tptp.aa_fun498830667440607164t_bool (tptp.aTP_Lamm_rn Uu) Uub) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_int_fun_nat_nat) (Uub tptp.fun_int_fun_nat_bool) (Uuc tptp.int)) (= (tptp.aa_int_nat (tptp.aa_fun5132377469993263754nt_nat (tptp.aa_fun348247319442030677nt_nat (tptp.aTP_Lamm_sz Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_int_fun_nat_nat Uua Uuc)) (tptp.collect_nat (tptp.aa_int_fun_nat_bool (tptp.aa_fun3602880909931171836t_bool (tptp.aTP_Lamm_ri Uu) Uub) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_bool_fun_nat_nat) (Uub tptp.fun_bo3288154511880838028t_bool) (Uuc tptp.bool)) (= (tptp.aa_bool_nat (tptp.aa_fun7928520491197679664ol_nat (tptp.aa_fun5318524179215677308ol_nat (tptp.aTP_Lamm_sx Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat (tptp.aa_bool_fun_nat_nat Uua Uuc)) (tptp.collect_nat (tptp.aa_bool_fun_nat_bool (tptp.aa_fun7537470554201192406t_bool (tptp.aTP_Lamm_rd Uu) Uub) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_bool_fun_nat_int) (Uub tptp.fun_bo3288154511880838028t_bool) (Uuc tptp.bool)) (= (tptp.aa_bool_int (tptp.aa_fun3750669471688482956ol_int (tptp.aa_fun5436235457428229244ol_int (tptp.aTP_Lamm_td Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int (tptp.aa_bool_fun_nat_int Uua Uuc)) (tptp.collect_nat (tptp.aa_bool_fun_nat_bool (tptp.aa_fun7537470554201192406t_bool (tptp.aTP_Lamm_rd Uu) Uub) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_fun_nat_nat) (Uub tptp.fun_nat_fun_nat_bool) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun4644938397070871434at_nat (tptp.aa_fun7390876557192650417at_nat (tptp.aTP_Lamm_su Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat Uua Uuc)) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aa_fun3051233943552222972t_bool (tptp.aTP_Lamm_st Uu) Uub) Uuc))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_na5492297256294505719er_nat) (Uub tptp.fun_na7774394808840722396r_bool) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun8701945955350064829at_nat (tptp.aa_fun5063706727594296087at_nat (tptp.aTP_Lamm_sp Uu) Uua) Uub) Uuc) (tptp.groups7237345082560585321er_nat (tptp.aa_nat5852537043073606456er_nat Uua Uuc) (tptp.collect_Code_integer (tptp.aa_nat6120813132205607877r_bool (tptp.aa_fun5933071796644114364r_bool (tptp.aTP_Lamm_so Uu) Uub) Uuc))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_nat_fun_bool_nat) (Uub tptp.fun_na9137082442855928016l_bool) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun4035688661005363499at_nat (tptp.aa_fun2816605880368898353at_nat (tptp.aTP_Lamm_sh Uu) Uua) Uub) Uuc) (tptp.groups5768501273728744877ol_nat (tptp.aa_nat_fun_bool_nat Uua Uuc) (tptp.collect_bool (tptp.aa_nat_fun_bool_bool (tptp.aa_fun1387864478824611934l_bool (tptp.aTP_Lamm_sg Uu) Uub) Uuc))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_Co3009391273526075439nt_int) (Uub tptp.fun_Co8197081679332685312t_bool) (Uuc tptp.code_integer)) (= (tptp.aa_Code_integer_int (tptp.aa_fun531554186711482826er_int (tptp.aa_fun2196751070425669740er_int (tptp.aTP_Lamm_sc Uu) Uua) Uub) Uuc) (tptp.groups4538972089207619220nt_int (tptp.aa_Cod5491795744640130032nt_int Uua Uuc) (tptp.collect_int (tptp.aa_Cod8597349444926882409t_bool (tptp.aa_fun6946700965406361788t_bool (tptp.aTP_Lamm_sb Uu) Uub) Uuc))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_nat_fun_int_nat) (Uub tptp.fun_nat_fun_int_bool) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun7682780481535005230at_nat (tptp.aa_fun503657754853467129at_nat (tptp.aTP_Lamm_sl Uu) Uua) Uub) Uuc) (tptp.groups4541462559716669496nt_nat (tptp.aa_nat_fun_int_nat Uua Uuc) (tptp.collect_int (tptp.aa_nat_fun_int_bool (tptp.aa_fun7617171277304647676t_bool (tptp.aTP_Lamm_rx Uu) Uub) Uuc))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_nat_fun_int_int) (Uub tptp.fun_nat_fun_int_bool) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun3504929462025808522at_int (tptp.aa_fun3325927984641084153at_int (tptp.aTP_Lamm_ry Uu) Uua) Uub) Uuc) (tptp.groups4538972089207619220nt_int (tptp.aa_nat_fun_int_int Uua Uuc) (tptp.collect_int (tptp.aa_nat_fun_int_bool (tptp.aa_fun7617171277304647676t_bool (tptp.aTP_Lamm_rx Uu) Uub) Uuc))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_bool_fun_int_int) (Uub tptp.fun_bo2827871560234191408t_bool) (Uuc tptp.bool)) (= (tptp.aa_bool_int (tptp.aa_fun2977339950115259112ol_int (tptp.aa_fun6505924867870464892ol_int (tptp.aTP_Lamm_rt Uu) Uua) Uub) Uuc) (tptp.groups4538972089207619220nt_int (tptp.aa_bool_fun_int_int Uua Uuc) (tptp.collect_int (tptp.aa_bool_fun_int_bool (tptp.aa_fun4998116011708744478t_bool (tptp.aTP_Lamm_rs Uu) Uub) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_Co3312552843764780407at_nat) (Uub tptp.fun_Co8657364630979331932t_bool) (Uuc tptp.code_integer)) (= (tptp.aa_Code_integer_nat (tptp.aa_fun2949368542467568330er_nat (tptp.aa_fun8366171557965857828er_nat (tptp.aTP_Lamm_ro Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_Cod8670293052248272184at_nat Uua Uuc)) (tptp.collect_nat (tptp.aa_Cod2498268374540730821t_bool (tptp.aa_fun498830667440607164t_bool (tptp.aTP_Lamm_rn Uu) Uub) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_int_fun_nat_nat) (Uub tptp.fun_int_fun_nat_bool) (Uuc tptp.int)) (= (tptp.aa_int_nat (tptp.aa_fun5132377469993263754nt_nat (tptp.aa_fun348247319442030677nt_nat (tptp.aTP_Lamm_rj Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_int_fun_nat_nat Uua Uuc)) (tptp.collect_nat (tptp.aa_int_fun_nat_bool (tptp.aa_fun3602880909931171836t_bool (tptp.aTP_Lamm_ri Uu) Uub) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_bool_fun_nat_nat) (Uub tptp.fun_bo3288154511880838028t_bool) (Uuc tptp.bool)) (= (tptp.aa_bool_nat (tptp.aa_fun7928520491197679664ol_nat (tptp.aa_fun5318524179215677308ol_nat (tptp.aTP_Lamm_re Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_bool_fun_nat_nat Uua Uuc)) (tptp.collect_nat (tptp.aa_bool_fun_nat_bool (tptp.aa_fun7537470554201192406t_bool (tptp.aTP_Lamm_rd Uu) Uub) Uuc))))) (forall ((Uu tptp.bool) (Uua tptp.fun_int_fun_int_bool) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aa_fun8168818243683596540t_bool (tptp.aTP_Lamm_aib Uu) Uua) Uub) Uuc)) (and (tptp.pp Uu) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool Uua Uub) Uuc))))) (forall ((Uu tptp.fun_a_2990225006182978344t_unit) (Uua tptp.a) (Uub tptp.heap_e7401611519738050253t_unit) (Uuc tptp.nat)) (= (tptp.aa_nat3804989708481012326it_nat (tptp.aa_hea5083147195637387702it_nat (tptp.aa_a_f112692477493148739it_nat (tptp.aTP_Lamm_ahh Uu) Uua) Uub) Uuc) (tptp.heap_T3616969660504097270t_unit Uuc (tptp.aa_hea684056619475940329it_nat (tptp.heap_T875086893843062177t_unit (tptp.aa_a_H4862568901524997081t_unit Uu Uua)) Uub)))) (forall ((Uu tptp.fun_a_6093291656547882009Heap_a) (Uua tptp.a) (Uub tptp.heap_e7401611519738050253t_unit) (Uuc tptp.nat)) (= (tptp.aa_nat3190776082673941207it_nat (tptp.aa_hea414212936809421479it_nat (tptp.aa_a_f1761598956578211508it_nat (tptp.aTP_Lamm_ahd Uu) Uua) Uub) Uuc) (tptp.heap_T7616092557645711335rame_a Uuc (tptp.aa_hea4724376117875161946it_nat (tptp.heap_Time_execute_a (tptp.aa_a_H8829438773920479562Heap_a Uu Uua)) Uub)))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_nat) (Uub tptp.fun_nat_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aa_fun6854695580826382482at_nat (tptp.aTP_Lamm_xs Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat Uua) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aa_fun3777555276967886990t_bool (tptp.aTP_Lamm_wv Uu) Uub) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_int) (Uub tptp.fun_nat_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun1613598493704395220at_int (tptp.aa_fun1189263540488932170at_int (tptp.aTP_Lamm_xt Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int Uua) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aa_fun3777555276967886990t_bool (tptp.aTP_Lamm_wv Uu) Uub) Uuc))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_Code_integer_int) (Uub tptp.fun_Code_integer_int) (Uuc tptp.int)) (= (tptp.aa_int_int (tptp.aa_fun2480750449653600025nt_int (tptp.aa_fun6168136379806246172nt_int (tptp.aTP_Lamm_xq Uu) Uua) Uub) Uuc) (tptp.groups3188404863801439024er_int Uua (tptp.collect_Code_integer (tptp.aa_int3865899974016033897r_bool (tptp.aa_fun1275183216929564604r_bool (tptp.aTP_Lamm_ws Uu) Uub) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_nat) (Uub tptp.fun_nat_int) (Uuc tptp.int)) (= (tptp.aa_int_nat (tptp.aa_fun1518875816675579952nt_nat (tptp.aa_fun3769689747080337738nt_nat (tptp.aTP_Lamm_xr Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat Uua) (tptp.collect_nat (tptp.aa_int_fun_nat_bool (tptp.aa_fun2712483305291392982t_bool (tptp.aTP_Lamm_wq Uu) Uub) Uuc))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bool_int) (Uub tptp.fun_bool_int) (Uuc tptp.int)) (= (tptp.aa_int_int (tptp.aa_fun707691183620917999nt_int (tptp.aa_fun7930693643136840740nt_int (tptp.aTP_Lamm_xp Uu) Uua) Uub) Uuc) (tptp.groups1892458791187145822ol_int Uua (tptp.collect_bool (tptp.aa_int_fun_bool_bool (tptp.aa_fun5833344538494674374l_bool (tptp.aTP_Lamm_wo Uu) Uub) Uuc))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_Code_integer_nat) (Uub tptp.fun_Code_integer_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun1707803128846032901at_nat (tptp.aa_fun2075405564639334828at_nat (tptp.aTP_Lamm_xm Uu) Uua) Uub) Uuc) (tptp.groups3190895334310489300er_nat Uua (tptp.collect_Code_integer (tptp.aa_nat6120813132205607877r_bool (tptp.aa_fun3279747613005586548r_bool (tptp.aTP_Lamm_wm Uu) Uub) Uuc))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_Code_integer_int) (Uub tptp.fun_Code_integer_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun6753324146191612001at_int (tptp.aa_fun29770176697515108at_int (tptp.aTP_Lamm_xo Uu) Uua) Uub) Uuc) (tptp.groups3188404863801439024er_int Uua (tptp.collect_Code_integer (tptp.aa_nat6120813132205607877r_bool (tptp.aa_fun3279747613005586548r_bool (tptp.aTP_Lamm_wm Uu) Uub) Uuc))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_nat) (Uub tptp.fun_int_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5507398438843482068at_nat (tptp.aa_fun3220669823809117514at_nat (tptp.aTP_Lamm_xl Uu) Uua) Uub) Uuc) (tptp.groups1707563613775114915nt_nat Uua (tptp.collect_int (tptp.aa_nat_fun_int_bool (tptp.aa_fun2805357686342578134t_bool (tptp.aTP_Lamm_wk Uu) Uub) Uuc))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bool_nat) (Uub tptp.fun_bool_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun9158115899668126683at_nat (tptp.aa_fun3360519976762538604at_nat (tptp.aTP_Lamm_xk Uu) Uua) Uub) Uuc) (tptp.groups1894949261696196098ol_nat Uua (tptp.collect_bool (tptp.aa_nat_fun_bool_bool (tptp.aa_fun6446435369898359566l_bool (tptp.aTP_Lamm_wi Uu) Uub) Uuc))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bool_int) (Uub tptp.fun_bool_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun4980264880158929975at_int (tptp.aa_fun1792327440028109676at_int (tptp.aTP_Lamm_xn Uu) Uua) Uub) Uuc) (tptp.groups1892458791187145822ol_int Uua (tptp.collect_bool (tptp.aa_nat_fun_bool_bool (tptp.aa_fun6446435369898359566l_bool (tptp.aTP_Lamm_wi Uu) Uub) Uuc))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_Code_integer) (Uub tptp.fun_int_int) (Uuc tptp.code_integer)) (= (tptp.aa_Code_integer_int (tptp.aa_fun2092574682676764953er_int (tptp.aa_fun9146121993134396956er_int (tptp.aTP_Lamm_aae Uu) Uua) Uub) Uuc) (tptp.groups1705073143266064639nt_int Uub (tptp.collect_int (tptp.aa_Cod8597349444926882409t_bool (tptp.aa_fun6079510497903818172t_bool (tptp.aTP_Lamm_zc Uu) Uua) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_Code_integer) (Uub tptp.fun_nat_nat) (Uuc tptp.code_integer)) (= (tptp.aa_Code_integer_nat (tptp.aa_fun2720235278490593797er_nat (tptp.aa_fun676797813428960940er_nat (tptp.aTP_Lamm_aab Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat Uub) (tptp.collect_nat (tptp.aa_Cod2498268374540730821t_bool (tptp.aa_fun7122322691611174516t_bool (tptp.aTP_Lamm_yy Uu) Uua) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_Code_integer) (Uub tptp.fun_nat_int) (Uuc tptp.code_integer)) (= (tptp.aa_Code_integer_int (tptp.aa_fun2934847258012291773er_int (tptp.aa_fun2579177667528128868er_int (tptp.aTP_Lamm_aad Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_int (tptp.groups705719431365010083at_int Uub) (tptp.collect_nat (tptp.aa_Cod2498268374540730821t_bool (tptp.aa_fun7122322691611174516t_bool (tptp.aTP_Lamm_yy Uu) Uua) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_nat) (Uub tptp.fun_nat_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aa_fun6854695580826382482at_nat (tptp.aTP_Lamm_aai Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat Uub) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aa_fun3777555276967886990t_bool (tptp.aTP_Lamm_wv Uu) Uua) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_int) (Uub tptp.fun_nat_nat) (Uuc tptp.int)) (= (tptp.aa_int_nat (tptp.aa_fun6790803225114646484nt_nat (tptp.aa_fun5866268260113680714nt_nat (tptp.aTP_Lamm_aac Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat Uub) (tptp.collect_nat (tptp.aa_int_fun_nat_bool (tptp.aa_fun2712483305291392982t_bool (tptp.aTP_Lamm_wq Uu) Uua) Uuc))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_Code_integer_nat) (Uub tptp.fun_Code_integer_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun1707803128846032901at_nat (tptp.aa_fun2075405564639334828at_nat (tptp.aTP_Lamm_aah Uu) Uua) Uub) Uuc) (tptp.groups3190895334310489300er_nat Uub (tptp.collect_Code_integer (tptp.aa_nat6120813132205607877r_bool (tptp.aa_fun3279747613005586548r_bool (tptp.aTP_Lamm_wm Uu) Uua) Uuc))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_Code_integer_nat) (Uub tptp.fun_Code_integer_int) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun1481396737752545469at_int (tptp.aa_fun3536767048123317348at_int (tptp.aTP_Lamm_aak Uu) Uua) Uub) Uuc) (tptp.groups3188404863801439024er_int Uub (tptp.collect_Code_integer (tptp.aa_nat6120813132205607877r_bool (tptp.aa_fun3279747613005586548r_bool (tptp.aTP_Lamm_wm Uu) Uua) Uuc))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_nat) (Uub tptp.fun_int_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5507398438843482068at_nat (tptp.aa_fun3220669823809117514at_nat (tptp.aTP_Lamm_aag Uu) Uua) Uub) Uuc) (tptp.groups1707563613775114915nt_nat Uub (tptp.collect_int (tptp.aa_nat_fun_int_bool (tptp.aa_fun2805357686342578134t_bool (tptp.aTP_Lamm_wk Uu) Uua) Uuc))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bool_nat) (Uub tptp.fun_bool_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun9158115899668126683at_nat (tptp.aa_fun3360519976762538604at_nat (tptp.aTP_Lamm_aaf Uu) Uua) Uub) Uuc) (tptp.groups1894949261696196098ol_nat Uub (tptp.collect_bool (tptp.aa_nat_fun_bool_bool (tptp.aa_fun6446435369898359566l_bool (tptp.aTP_Lamm_wi Uu) Uua) Uuc))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bool_nat) (Uub tptp.fun_bool_int) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun8931709508574639251at_int (tptp.aa_fun4821881460246521124at_int (tptp.aTP_Lamm_aaj Uu) Uua) Uub) Uuc) (tptp.groups1892458791187145822ol_int Uub (tptp.collect_bool (tptp.aa_nat_fun_bool_bool (tptp.aa_fun6446435369898359566l_bool (tptp.aTP_Lamm_wi Uu) Uua) Uuc))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_int) (Uub tptp.fun_int_int) (Uuc tptp.int)) (= (tptp.aa_int_int (tptp.aa_fun6280345759651049192nt_int (tptp.aa_fun3693603986580398266nt_int (tptp.aTP_Lamm_wz Uu) Uua) Uub) Uuc) (tptp.groups4538972089207619220nt_int Uua (tptp.collect_int (tptp.aa_int_fun_int_bool (tptp.aa_fun1740285714666084126t_bool (tptp.aTP_Lamm_wy Uu) Uub) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_nat) (Uub tptp.fun_nat_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aa_fun6854695580826382482at_nat (tptp.aTP_Lamm_ww Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat Uua) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aa_fun3777555276967886990t_bool (tptp.aTP_Lamm_wv Uu) Uub) Uuc))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_Code_integer_int) (Uub tptp.fun_Code_integer_int) (Uuc tptp.int)) (= (tptp.aa_int_int (tptp.aa_fun2480750449653600025nt_int (tptp.aa_fun6168136379806246172nt_int (tptp.aTP_Lamm_wt Uu) Uua) Uub) Uuc) (tptp.groups7234854612051535045er_int Uua (tptp.collect_Code_integer (tptp.aa_int3865899974016033897r_bool (tptp.aa_fun1275183216929564604r_bool (tptp.aTP_Lamm_ws Uu) Uub) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_nat) (Uub tptp.fun_nat_int) (Uuc tptp.int)) (= (tptp.aa_int_nat (tptp.aa_fun1518875816675579952nt_nat (tptp.aa_fun3769689747080337738nt_nat (tptp.aTP_Lamm_wu Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat Uua) (tptp.collect_nat (tptp.aa_int_fun_nat_bool (tptp.aa_fun2712483305291392982t_bool (tptp.aTP_Lamm_wq Uu) Uub) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_int) (Uub tptp.fun_nat_int) (Uuc tptp.int)) (= (tptp.aa_int_int (tptp.aa_fun6564396834021159052nt_int (tptp.aa_fun7327629743597663234nt_int (tptp.aTP_Lamm_wr Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int Uua) (tptp.collect_nat (tptp.aa_int_fun_nat_bool (tptp.aa_fun2712483305291392982t_bool (tptp.aTP_Lamm_wq Uu) Uub) Uuc))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bool_int) (Uub tptp.fun_bool_int) (Uuc tptp.int)) (= (tptp.aa_int_int (tptp.aa_fun707691183620917999nt_int (tptp.aa_fun7930693643136840740nt_int (tptp.aTP_Lamm_wp Uu) Uua) Uub) Uuc) (tptp.groups5766010803219694601ol_int Uua (tptp.collect_bool (tptp.aa_int_fun_bool_bool (tptp.aa_fun5833344538494674374l_bool (tptp.aTP_Lamm_wo Uu) Uub) Uuc))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_Code_integer_nat) (Uub tptp.fun_Code_integer_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun1707803128846032901at_nat (tptp.aa_fun2075405564639334828at_nat (tptp.aTP_Lamm_wn Uu) Uua) Uub) Uuc) (tptp.groups7237345082560585321er_nat Uua (tptp.collect_Code_integer (tptp.aa_nat6120813132205607877r_bool (tptp.aa_fun3279747613005586548r_bool (tptp.aTP_Lamm_wm Uu) Uub) Uuc))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_nat) (Uub tptp.fun_int_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5507398438843482068at_nat (tptp.aa_fun3220669823809117514at_nat (tptp.aTP_Lamm_wl Uu) Uua) Uub) Uuc) (tptp.groups4541462559716669496nt_nat Uua (tptp.collect_int (tptp.aa_nat_fun_int_bool (tptp.aa_fun2805357686342578134t_bool (tptp.aTP_Lamm_wk Uu) Uub) Uuc))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_int) (Uub tptp.fun_int_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun1329547419334285360at_int (tptp.aa_fun6778609820326443010at_int (tptp.aTP_Lamm_wx Uu) Uua) Uub) Uuc) (tptp.groups4538972089207619220nt_int Uua (tptp.collect_int (tptp.aa_nat_fun_int_bool (tptp.aa_fun2805357686342578134t_bool (tptp.aTP_Lamm_wk Uu) Uub) Uuc))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bool_nat) (Uub tptp.fun_bool_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun9158115899668126683at_nat (tptp.aa_fun3360519976762538604at_nat (tptp.aTP_Lamm_wj Uu) Uua) Uub) Uuc) (tptp.groups5768501273728744877ol_nat Uua (tptp.collect_bool (tptp.aa_nat_fun_bool_bool (tptp.aa_fun6446435369898359566l_bool (tptp.aTP_Lamm_wi Uu) Uub) Uuc))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_Code_integer) (Uub tptp.fun_int_int) (Uuc tptp.code_integer)) (= (tptp.aa_Code_integer_int (tptp.aa_fun2092574682676764953er_int (tptp.aa_fun9146121993134396956er_int (tptp.aTP_Lamm_zd Uu) Uua) Uub) Uuc) (tptp.groups4538972089207619220nt_int Uub (tptp.collect_int (tptp.aa_Cod8597349444926882409t_bool (tptp.aa_fun6079510497903818172t_bool (tptp.aTP_Lamm_zc Uu) Uua) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_Code_integer) (Uub tptp.fun_nat_nat) (Uuc tptp.code_integer)) (= (tptp.aa_Code_integer_nat (tptp.aa_fun2720235278490593797er_nat (tptp.aa_fun676797813428960940er_nat (tptp.aTP_Lamm_yz Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat Uub) (tptp.collect_nat (tptp.aa_Cod2498268374540730821t_bool (tptp.aa_fun7122322691611174516t_bool (tptp.aTP_Lamm_yy Uu) Uua) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_nat) (Uub tptp.fun_nat_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aa_fun6854695580826382482at_nat (tptp.aTP_Lamm_zh Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat Uub) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aa_fun3777555276967886990t_bool (tptp.aTP_Lamm_wv Uu) Uua) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_int) (Uub tptp.fun_nat_nat) (Uuc tptp.int)) (= (tptp.aa_int_nat (tptp.aa_fun6790803225114646484nt_nat (tptp.aa_fun5866268260113680714nt_nat (tptp.aTP_Lamm_za Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat Uub) (tptp.collect_nat (tptp.aa_int_fun_nat_bool (tptp.aa_fun2712483305291392982t_bool (tptp.aTP_Lamm_wq Uu) Uua) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_int) (Uub tptp.fun_nat_int) (Uuc tptp.int)) (= (tptp.aa_int_int (tptp.aa_fun6564396834021159052nt_int (tptp.aa_fun7327629743597663234nt_int (tptp.aTP_Lamm_zj Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_int (tptp.groups3539618377306564664at_int Uub) (tptp.collect_nat (tptp.aa_int_fun_nat_bool (tptp.aa_fun2712483305291392982t_bool (tptp.aTP_Lamm_wq Uu) Uua) Uuc))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bool_int) (Uub tptp.fun_bool_int) (Uuc tptp.int)) (= (tptp.aa_int_int (tptp.aa_fun707691183620917999nt_int (tptp.aa_fun7930693643136840740nt_int (tptp.aTP_Lamm_zi Uu) Uua) Uub) Uuc) (tptp.groups5766010803219694601ol_int Uub (tptp.collect_bool (tptp.aa_int_fun_bool_bool (tptp.aa_fun5833344538494674374l_bool (tptp.aTP_Lamm_wo Uu) Uua) Uuc))))) (forall ((Uu tptp.set_Code_integer) (Uua tptp.fun_Code_integer_nat) (Uub tptp.fun_Code_integer_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun1707803128846032901at_nat (tptp.aa_fun2075405564639334828at_nat (tptp.aTP_Lamm_zg Uu) Uua) Uub) Uuc) (tptp.groups7237345082560585321er_nat Uub (tptp.collect_Code_integer (tptp.aa_nat6120813132205607877r_bool (tptp.aa_fun3279747613005586548r_bool (tptp.aTP_Lamm_wm Uu) Uua) Uuc))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_nat) (Uub tptp.fun_int_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5507398438843482068at_nat (tptp.aa_fun3220669823809117514at_nat (tptp.aTP_Lamm_zf Uu) Uua) Uub) Uuc) (tptp.groups4541462559716669496nt_nat Uub (tptp.collect_int (tptp.aa_nat_fun_int_bool (tptp.aa_fun2805357686342578134t_bool (tptp.aTP_Lamm_wk Uu) Uua) Uuc))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_nat) (Uub tptp.fun_int_int) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun5280992047749994636at_int (tptp.aa_fun4682031307293100034at_int (tptp.aTP_Lamm_zb Uu) Uua) Uub) Uuc) (tptp.groups4538972089207619220nt_int Uub (tptp.collect_int (tptp.aa_nat_fun_int_bool (tptp.aa_fun2805357686342578134t_bool (tptp.aTP_Lamm_wk Uu) Uua) Uuc))))) (forall ((Uu tptp.set_bool) (Uua tptp.fun_bool_nat) (Uub tptp.fun_bool_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun9158115899668126683at_nat (tptp.aa_fun3360519976762538604at_nat (tptp.aTP_Lamm_ze Uu) Uua) Uub) Uuc) (tptp.groups5768501273728744877ol_nat Uub (tptp.collect_bool (tptp.aa_nat_fun_bool_bool (tptp.aa_fun6446435369898359566l_bool (tptp.aTP_Lamm_wi Uu) Uua) Uuc))))) (forall ((Uu tptp.fun_Pr2478283820680522243nt_int) (Uua tptp.fun_in1696471567231710611nt_int) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int (tptp.aa_fun4152872853588681340nt_int (tptp.aTP_Lamm_agj Uu) Uua) Uub) Uuc) (tptp.aa_Pro6970504127699319548nt_int Uu (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int Uua Uub) Uuc)))) (forall ((Uu tptp.fun_Pr803113274115125473t_bool) (Uua tptp.fun_in1696471567231710611nt_int) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aa_fun395975271853239642t_bool (tptp.aTP_Lamm_agf Uu) Uua) Uub) Uuc)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool Uu (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int Uua Uub) Uuc))))) (forall ((Uu tptp.fun_Pr982841511892225912nt_int) (Uua tptp.fun_in1696471567231710611nt_int) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.aa_fun7461304428735181397nt_int (tptp.aTP_Lamm_agg Uu) Uua) Uub) Uuc) (tptp.aa_Pro6799258434465214121nt_int Uu (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int Uua Uub) Uuc)))) (forall ((Uu tptp.fun_bo7720638723722887333nt_int) (Uua tptp.fun_int_fun_int_bool) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int (tptp.aa_fun9101259627203045662nt_int (tptp.aTP_Lamm_agh Uu) Uua) Uub) Uuc) (tptp.aa_boo6976928504896087454nt_int Uu (tptp.aa_int_bool (tptp.aa_int_fun_int_bool Uua Uub) Uuc)))) (forall ((Uu tptp.fun_bool_bool) (Uua tptp.fun_int_fun_int_bool) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aa_fun8168818243683596540t_bool (tptp.aTP_Lamm_agb Uu) Uua) Uub) Uuc)) (tptp.pp (tptp.aa_bool_bool Uu (tptp.aa_int_bool (tptp.aa_int_fun_int_bool Uua Uub) Uuc))))) (forall ((Uu tptp.fun_bool_int) (Uua tptp.fun_int_fun_int_bool) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.aa_fun5341983444565040691nt_int (tptp.aTP_Lamm_agc Uu) Uua) Uub) Uuc) (tptp.aa_bool_int Uu (tptp.aa_int_bool (tptp.aa_int_fun_int_bool Uua Uub) Uuc)))) (forall ((Uu tptp.fun_in4211310926729683942nt_int) (Uua tptp.fun_int_fun_int_int) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int (tptp.aa_fun1034830265760468567nt_int (tptp.aTP_Lamm_agi Uu) Uua) Uub) Uuc) (tptp.aa_int7462565939943104719nt_int Uu (tptp.aa_int_int (tptp.aa_int_fun_int_int Uua Uub) Uuc)))) (forall ((Uu tptp.fun_int_bool) (Uua tptp.fun_int_fun_int_int) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aa_fun980369494830392501t_bool (tptp.aTP_Lamm_agd Uu) Uua) Uub) Uuc)) (tptp.pp (tptp.aa_int_bool Uu (tptp.aa_int_int (tptp.aa_int_fun_int_int Uua Uub) Uuc))))) (forall ((Uu tptp.fun_int_int) (Uua tptp.fun_int_fun_int_int) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.aa_fun6119123525526402106nt_int (tptp.aTP_Lamm_age Uu) Uua) Uub) Uuc) (tptp.aa_int_int Uu (tptp.aa_int_int (tptp.aa_int_fun_int_int Uua Uub) Uuc)))) (forall ((Uu tptp.fun_fu6897202038601531823t_bool) (Uua tptp.fun_na4786964484885125043t_bool) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool (tptp.aa_fun3491305611276047780t_bool (tptp.aTP_Lamm_agk Uu) Uua) Uub) Uuc) (tptp.aa_fun830836278467416944t_bool Uu (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool Uua Uub) Uuc)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_nat3783148529270815480at_nat (tptp.aTP_Lamm_abo Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uub) Uua)) (tptp.aa_nat_nat tptp.suc Uuc))))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aa_nat1293065384339088724at_int (tptp.aTP_Lamm_abr Uu) Uua) Uub) Uuc) (tptp.aa_nat_int Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uub) Uua)) (tptp.aa_nat_nat tptp.suc Uuc))))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_nat3783148529270815480at_nat (tptp.aTP_Lamm_jz Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uub) Uua)) Uuc)))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aa_nat1293065384339088724at_int (tptp.aTP_Lamm_nr Uu) Uua) Uub) Uuc) (tptp.aa_nat_int Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uub) Uua)) Uuc)))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int (tptp.aa_int1966403025003302569nt_int (tptp.aTP_Lamm_aod Uu) Uua) Uub) Uuc) (tptp.aa_Pro6970504127699319548nt_int tptp.normalize (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uu) Uuc)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uub) Uua))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uua) Uuc))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int (tptp.aa_int1966403025003302569nt_int (tptp.aTP_Lamm_aob Uu) Uua) Uub) Uuc) (tptp.aa_Pro6970504127699319548nt_int tptp.normalize (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uu) Uuc)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uub) Uua))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uua) Uuc))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int (tptp.aa_int1966403025003302569nt_int (tptp.aTP_Lamm_ans Uu) Uua) Uub) Uuc) (tptp.aa_Pro6970504127699319548nt_int tptp.normalize (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uu) Uub)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uua) Uuc))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int (tptp.aa_int1966403025003302569nt_int (tptp.aTP_Lamm_anu Uu) Uua) Uub) Uuc) (tptp.aa_Pro6970504127699319548nt_int tptp.normalize (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uu) Uuc)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uua) Uub))))) (forall ((Uu tptp.nat) (Uua tptp.rat) (Uub tptp.rat) (Uuc tptp.rat) (Uud tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_rat3146053865535587600at_rat (tptp.aa_rat7467449789483521253at_rat (tptp.aTP_Lamm_mc Uu) Uua) Uub) Uuc) Uud) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uud)) Uua)) tptp.one_one_rat)) Uud)) (tptp.aa_nat_rat (tptp.power_power_rat Uub) Uud))) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Uub) Uuc)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uud))))) (forall ((Uu tptp.nat) (Uua tptp.rat) (Uub tptp.rat) (Uuc tptp.rat) (Uud tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_rat3146053865535587600at_rat (tptp.aa_rat7467449789483521253at_rat (tptp.aTP_Lamm_mb Uu) Uua) Uub) Uuc) Uud) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uu)) Uua)) Uud)) (tptp.aa_nat_rat (tptp.power_power_rat Uub) Uud))) (tptp.aa_nat_rat (tptp.power_power_rat Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uud))))) (forall ((Uu tptp.nat) (Uua tptp.rat) (Uub tptp.rat) (Uuc tptp.rat) (Uud tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_rat3146053865535587600at_rat (tptp.aa_rat7467449789483521253at_rat (tptp.aTP_Lamm_mi Uu) Uua) Uub) Uuc) Uud) (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.times_times_rat (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat Uua)) Uud)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat Uub)) Uud))) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat tptp.plus_plus_rat Uub) Uuc)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uud))))) (forall ((Uu tptp.code_integer) (Uua tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aTP_Lamm_aka Uu) Uua) Uu)) (forall ((Uu tptp.rat) (Uua tptp.list_nat)) (= (tptp.aa_list_nat_rat (tptp.aTP_Lamm_akc Uu) Uua) Uu)) (forall ((Uu tptp.rat) (Uua tptp.set_nat)) (= (tptp.aa_set_nat_rat (tptp.aTP_Lamm_akb Uu) Uua) Uu)) (forall ((Uu tptp.rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_ajz Uu) Uua) Uu)) (forall ((Uu tptp.nat) (Uua tptp.list_nat)) (= (tptp.aa_list_nat_nat (tptp.aTP_Lamm_ajt Uu) Uua) Uu)) (forall ((Uu tptp.nat) (Uua tptp.set_nat)) (= (tptp.aa_set_nat_nat (tptp.aTP_Lamm_ajs Uu) Uua) Uu)) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_ajw Uu) Uua) Uu)) (forall ((Uu tptp.int) (Uua tptp.list_nat)) (= (tptp.aa_list_nat_int (tptp.aTP_Lamm_ajv Uu) Uua) Uu)) (forall ((Uu tptp.int) (Uua tptp.set_nat)) (= (tptp.aa_set_nat_int (tptp.aTP_Lamm_aju Uu) Uua) Uu)) (forall ((Uu tptp.int) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.aTP_Lamm_ajx Uu) Uua) Uu)) (forall ((Uu tptp.int) (Uua tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.aTP_Lamm_ajy Uu) Uua) Uu)) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_nb Uu) Uua)) true)) (forall ((Uu tptp.int) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_nc Uu) Uua)) true)) (forall ((Uu tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.aTP_Lamm_fr Uu) Uu)) (forall ((Uu tptp.assn)) (= (tptp.aa_assn_assn tptp.aTP_Lamm_fs Uu) Uu)) (forall ((Uu tptp.rat)) (= (tptp.aa_rat_rat tptp.aTP_Lamm_ft Uu) Uu)) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_nat tptp.aTP_Lamm_fu Uu) Uu)) (forall ((Uu tptp.int)) (= (tptp.aa_int_int tptp.aTP_Lamm_fv Uu) Uu)) (forall ((Uu tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.aTP_Lamm_fw Uu) tptp.zero_z3403309356797280102nteger)) (forall ((Uu tptp.rat)) (= (tptp.aa_rat_rat tptp.aTP_Lamm_fx Uu) tptp.zero_zero_rat)) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_nat tptp.aTP_Lamm_fy Uu) tptp.zero_zero_nat)) (forall ((Uu tptp.int)) (= (tptp.aa_int_int tptp.aTP_Lamm_fz Uu) tptp.zero_zero_int)) (forall ((Uu tptp.list_nat)) (= (tptp.aa_list_nat_nat tptp.aTP_Lamm_alx Uu) tptp.one_one_nat)) (forall ((Uu tptp.set_nat)) (= (tptp.aa_set_nat_nat tptp.aTP_Lamm_alw Uu) tptp.one_one_nat)) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_nat tptp.aTP_Lamm_mj Uu) tptp.one_one_nat)) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_int tptp.aTP_Lamm_mk Uu) tptp.one_one_int)) (forall ((Uu tptp.int)) (= (tptp.aa_int_int tptp.aTP_Lamm_ml Uu) tptp.one_one_int)) (forall ((Uu tptp.heap_e7401611519738050253t_unit)) (= (tptp.aa_hea684056619475940329it_nat tptp.aTP_Lamm_fk Uu) tptp.none_P9117596204409417319it_nat)) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_option_nat tptp.aTP_Lamm_er Uu) tptp.none_nat)) (forall ((Uu tptp.produc3658429121746597890et_nat)) (= (tptp.pp (tptp.aa_Pro2991721470636411351t_bool tptp.aTP_Lamm_eo Uu)) false)) (forall ((Uu tptp.product_prod_nat_nat)) (= (tptp.pp (tptp.aa_Pro2232559814647311250t_bool tptp.aTP_Lamm_be Uu)) false)) (forall ((Uu tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool tptp.aTP_Lamm_bb Uu)) false)) (forall ((Uu tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool tptp.aTP_Lamm_bc Uu)) false)) (forall ((Uu tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool tptp.aTP_Lamm_bf Uu)) false)) (forall ((Uu tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool tptp.aTP_Lamm_bd Uu)) false)) (forall ((Uu tptp.num)) (= (tptp.pp (tptp.aa_num_bool tptp.aTP_Lamm_et Uu)) false)) (forall ((Uu tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool tptp.aTP_Lamm_bg Uu)) false)) (forall ((Uu tptp.int)) (= (tptp.pp (tptp.aa_int_bool tptp.aTP_Lamm_bh Uu)) false)) (forall ((Uu tptp.num)) (= (tptp.pp (tptp.aa_num_bool tptp.aTP_Lamm_es Uu)) true)) (forall ((Uu tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool tptp.aTP_Lamm_amh Uu)) true)) (forall ((P tptp.bool)) (or (tptp.pp P) (tptp.pp (tptp.aa_bool_bool tptp.fNot P)))) (forall ((P tptp.bool)) (or (not (tptp.pp (tptp.aa_bool_bool tptp.fNot P))) (not (tptp.pp P)))) (tptp.pp tptp.fTrue) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fconj P) Q))) (tptp.pp Q))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fconj P) Q))) (tptp.pp P))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.pp P)) (not (tptp.pp Q)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fconj P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fdisj P) Q))) (tptp.pp P) (tptp.pp Q))) (forall ((Q tptp.bool) (P tptp.bool)) (or (not (tptp.pp Q)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fdisj P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.pp P)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fdisj P) Q)))) (not (tptp.pp tptp.fFalse)) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.if_int tptp.fFalse) X) Y) Y)) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.if_int tptp.fTrue) X) Y) X)) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat tptp.fFalse) X) Y) Y)) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat tptp.fTrue) X) Y) X)) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num (tptp.if_num tptp.fFalse) X) Y) Y)) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num (tptp.if_num tptp.fTrue) X) Y) X)) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat tptp.fFalse) X) Y) Y)) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.aa_rat_rat (tptp.aa_rat_fun_rat_rat (tptp.if_rat tptp.fTrue) X) Y) X)) (forall ((X tptp.int) (Y tptp.int)) (or (not (= X Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int X) Y)))) (forall ((X tptp.int) (Y tptp.int)) (or (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int X) Y))) (= X Y))) (forall ((X tptp.nat) (Y tptp.nat)) (or (not (= X Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat X) Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (or (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat X) Y))) (= X Y))) (forall ((X tptp.num) (Y tptp.num)) (or (not (= X Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.fequal_num X) Y)))) (forall ((X tptp.num) (Y tptp.num)) (or (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.fequal_num X) Y))) (= X Y))) (forall ((X tptp.rat) (Y tptp.rat)) (or (not (= X Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.fequal_rat X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (or (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.fequal_rat X) Y))) (= X Y))) (forall ((X tptp.bool) (Y tptp.bool)) (or (not (= X Y)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fequal_bool X) Y)))) (forall ((X tptp.bool) (Y tptp.bool)) (or (not (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fequal_bool X) Y))) (= X Y))) (forall ((X tptp.assn) (Y tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn (tptp.if_assn tptp.fFalse) X) Y) Y)) (forall ((X tptp.assn) (Y tptp.assn)) (= (tptp.aa_assn_assn (tptp.aa_ass954072293579886259n_assn (tptp.if_assn tptp.fTrue) X) Y) X)) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer tptp.fFalse X) Y) Y)) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.if_Code_integer tptp.fTrue X) Y) X)) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat (tptp.if_set_nat tptp.fFalse) X) Y) Y)) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (tptp.aa_set_nat_set_nat (tptp.aa_set2309701074089104077et_nat (tptp.if_set_nat tptp.fTrue) X) Y) X)) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (or (not (= X Y)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer X) Y)))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (or (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer X) Y))) (= X Y))) (forall ((X tptp.code_natural) (Y tptp.code_natural)) (or (not (= X Y)) (tptp.pp (tptp.aa_Code_natural_bool (tptp.fequal_Code_natural X) Y)))) (forall ((X tptp.code_natural) (Y tptp.code_natural)) (or (not (tptp.pp (tptp.aa_Code_natural_bool (tptp.fequal_Code_natural X) Y))) (= X Y))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (or (not (= X Y)) (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.fequal_set_nat X) Y)))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (or (not (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set5116768664143533222t_bool tptp.fequal_set_nat X) Y))) (= X Y))) (forall ((X tptp.list_nat) (Y tptp.list_nat)) (or (not (= X Y)) (tptp.pp (tptp.aa_list_nat_bool (tptp.fequal_list_nat X) Y)))) (forall ((X tptp.list_nat) (Y tptp.list_nat)) (or (not (tptp.pp (tptp.aa_list_nat_bool (tptp.fequal_list_nat X) Y))) (= X Y))) (forall ((X tptp.fun_int_int) (Y tptp.fun_int_int)) (= (tptp.if_fun_int_int tptp.fFalse X Y) Y)) (forall ((X tptp.fun_int_int) (Y tptp.fun_int_int)) (= (tptp.if_fun_int_int tptp.fTrue X Y) X)) (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (tptp.aa_Pro6970504127699319548nt_int (tptp.if_Pro3027730157355071871nt_int tptp.fFalse X) Y) Y)) (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (tptp.aa_Pro6970504127699319548nt_int (tptp.if_Pro3027730157355071871nt_int tptp.fTrue X) Y) X)) (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (tptp.aa_Pro262675715343573244at_nat (tptp.aa_Pro8023792847356852296at_nat (tptp.if_Pro6206227464963214023at_nat tptp.fFalse) X) Y) Y)) (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (tptp.aa_Pro262675715343573244at_nat (tptp.aa_Pro8023792847356852296at_nat (tptp.if_Pro6206227464963214023at_nat tptp.fTrue) X) Y) X)) (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (or (not (= X Y)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool tptp.fequal6010348034681699726nt_int X) Y)))) (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (or (not (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool tptp.fequal6010348034681699726nt_int X) Y))) (= X Y))) (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (or (not (= X Y)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool tptp.fequal9188845342289841878at_nat X) Y)))) (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (or (not (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool tptp.fequal9188845342289841878at_nat X) Y))) (= X Y))) (forall ((X tptp.multis2468970476368604999at_nat) (Y tptp.multis2468970476368604999at_nat)) (= (tptp.if_mul8430962117462786573at_nat tptp.fFalse X Y) Y)) (forall ((X tptp.multis2468970476368604999at_nat) (Y tptp.multis2468970476368604999at_nat)) (= (tptp.if_mul8430962117462786573at_nat tptp.fTrue X Y) X)) (forall ((X tptp.produc8923325533196201883nteger) (Y tptp.produc8923325533196201883nteger)) (= (tptp.if_Pro6119634080678213985nteger tptp.fFalse X Y) Y)) (forall ((X tptp.produc8923325533196201883nteger) (Y tptp.produc8923325533196201883nteger)) (= (tptp.if_Pro6119634080678213985nteger tptp.fTrue X Y) X)) (forall ((X tptp.produc3260487557148687353it_nat) (Y tptp.produc3260487557148687353it_nat)) (or (not (= X Y)) (tptp.pp (tptp.aa_Pro8278066377857552544t_bool (tptp.fequal7405809337025681252it_nat X) Y)))) (forall ((X tptp.produc3260487557148687353it_nat) (Y tptp.produc3260487557148687353it_nat)) (or (not (tptp.pp (tptp.aa_Pro8278066377857552544t_bool (tptp.fequal7405809337025681252it_nat X) Y))) (= X Y))) (forall ((X tptp.produc859450856879609959at_nat) (Y tptp.produc859450856879609959at_nat)) (= (tptp.if_Pro4507677147265585453at_nat tptp.fFalse X Y) Y)) (forall ((X tptp.produc859450856879609959at_nat) (Y tptp.produc859450856879609959at_nat)) (= (tptp.if_Pro4507677147265585453at_nat tptp.fTrue X Y) X)) (forall ((X tptp.option3562590408128118217it_nat) (Y tptp.option3562590408128118217it_nat)) (= (tptp.if_opt6883606601682554499it_nat tptp.fFalse X Y) Y)) (forall ((X tptp.option3562590408128118217it_nat) (Y tptp.option3562590408128118217it_nat)) (= (tptp.if_opt6883606601682554499it_nat tptp.fTrue X Y) X)) (forall ((X tptp.produc8664842809031399944it_nat) (Y tptp.produc8664842809031399944it_nat)) (or (not (= X Y)) (tptp.pp (tptp.aa_Pro8715207439678120785t_bool (tptp.fequal1407654770548522611it_nat X) Y)))) (forall ((X tptp.produc8664842809031399944it_nat) (Y tptp.produc8664842809031399944it_nat)) (or (not (tptp.pp (tptp.aa_Pro8715207439678120785t_bool (tptp.fequal1407654770548522611it_nat X) Y))) (= X Y))) (forall ((P tptp.bool)) (or (= P tptp.fTrue) (= P tptp.fFalse))) (forall ((X tptp.option8956607266484857688it_nat) (Y tptp.option8956607266484857688it_nat)) (= (tptp.if_opt1729522071442692626it_nat tptp.fFalse X Y) Y)) (forall ((X tptp.option8956607266484857688it_nat) (Y tptp.option8956607266484857688it_nat)) (= (tptp.if_opt1729522071442692626it_nat tptp.fTrue X Y) X)) _let_5 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 27.92/28.26 )
% 27.92/28.26 % SZS output end Proof for ITP213_1
% 27.92/28.26 % cvc5---1.0.5 exiting
% 27.92/28.26 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------