%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWW470_3 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n010.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 : Fri Sep  1 00:20:56 EDT 2023

% Result   : Theorem 6.65s 6.87s
% Output   : Proof 6.71s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.41  % Problem    : SWW470_3 : TPTP v8.1.2. Released v5.3.0.
% 0.11/0.42  % Command    : do_cvc5 %s %d
% 0.43/0.63  % Computer : n010.cluster.edu
% 0.43/0.63  % Model    : x86_64 x86_64
% 0.43/0.63  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.43/0.63  % Memory   : 8042.1875MB
% 0.43/0.63  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.43/0.63  % CPULimit   : 300
% 0.43/0.63  % WCLimit    : 300
% 0.43/0.63  % DateTime   : Sun Aug 27 19:42:35 EDT 2023
% 0.43/0.63  % CPUTime    : 
% 0.87/1.03  %----Proving TF0_NAR, FOF, or CNF
% 6.65/6.87  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.pnT2rxT3eP/cvc5---1.0.5_10126.p...
% 6.65/6.87  ------- get file name : TPTP file name is SWW470_3
% 6.65/6.87  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_10126.smt2...
% 6.65/6.87  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 6.65/6.87  % SZS status Theorem for SWW470_3
% 6.65/6.87  % SZS output start Proof for SWW470_3
% 6.65/6.87  (
% 6.65/6.87  (let ((_let_1 (tptp.hAPP_f762886889e_bool (tptp.hAPP_f1261923407e_bool tptp.cOMBC_892787026e_bool (tptp.hAPP_f963367678e_bool (tptp.hAPP_f375255701e_bool tptp.cOMBB_145932198bool_a tptp.cOMBS_1378840469l_bool) (tptp.hAPP_f1509969235l_bool (tptp.hAPP_f1178339559l_bool tptp.cOMBB_1355796797bool_a (tptp.hAPP_f1561913689l_bool tptp.cOMBB_188601460_state tptp.fconj)) tptp.p))) (tptp.hAPP_f1759915619e_bool (tptp.hAPP_f2073279419e_bool tptp.cOMBB_160679318_state tptp.fNot) tptp.b)))) (let ((_let_2 (tptp.hAPP_b2019457360e_bool tptp.cOMBK_bool_state tptp.fFalse))) (let ((_let_3 (tptp.hAPP_f762886889e_bool tptp.cOMBK_1458035955bool_a _let_2))) (let ((_let_4 (tptp.hoare_572465367rivs_a tptp.g))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_4 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a (tptp.hoare_1876769875iple_a _let_3 tptp.c _let_1)) tptp.bot_bo214064617a_bool))))) (let ((_let_6 (not _let_5))) (let ((_let_7 (forall ((P tptp.fun_state_bool) (Q tptp.x_a)) (= (tptp.hAPP_a2036067514e_bool (tptp.hAPP_f762886889e_bool tptp.cOMBK_1458035955bool_a P) Q) P)))) (let ((_let_8 (forall ((P tptp.bool) (Q tptp.state)) (= (tptp.hAPP_state_bool (tptp.hAPP_b2019457360e_bool tptp.cOMBK_bool_state P) Q) P)))) (let ((_let_9 (forall ((P tptp.bool) (Q tptp.int)) (= (tptp.hAPP_int_bool (tptp.hAPP_b396694332t_bool tptp.cOMBK_bool_int P) Q) P)))) (let ((_let_10 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_11 (tptp.hAPP_nat_int tptp.semiri1621563631at_int tptp.one_one_nat))) (let ((_let_12 (forall ((Pa tptp.fun_int_bool)) (= (tptp.hAPP_f1805168059t_bool tptp.collect_int Pa) Pa)))) (let ((_let_13 (forall ((X_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool tptp.bot_bot_fun_int_bool X_2)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) tptp.bot_bot_fun_int_bool)))))) (let ((_let_14 (tptp.hAPP_b396694332t_bool tptp.cOMBK_bool_int tptp.fFalse))) (let ((_let_15 (tptp.hAPP_f1805168059t_bool tptp.collect_int _let_14))) (let ((_let_16 (= tptp.bot_bot_fun_int_bool _let_15))) (let ((_let_17 (forall ((A_13 tptp.int)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_13) tptp.bot_bot_fun_int_bool)))))) (let ((_let_18 (forall ((Ga tptp.fun_Ho882550911a_bool) (Ca tptp.com) (Q_1 tptp.fun_a_fun_state_bool) (Pa tptp.fun_a_fun_state_bool)) (=> (forall ((Z_11 tptp.x_a) (S_2 tptp.state)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Pa Z_11) S_2)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hoare_572465367rivs_a Ga) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a (tptp.hoare_1876769875iple_a (tptp.hAPP_f762886889e_bool tptp.cOMBK_1458035955bool_a (tptp.hAPP_s1806633685e_bool (tptp.hAPP_f817621513e_bool tptp.cOMBC_2027030106e_bool tptp.fequal_state) S_2)) Ca (tptp.hAPP_f762886889e_bool tptp.cOMBK_1458035955bool_a (tptp.hAPP_a2036067514e_bool Q_1 Z_11)))) tptp.bot_bo214064617a_bool))))) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hoare_572465367rivs_a Ga) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a (tptp.hoare_1876769875iple_a Pa Ca Q_1)) tptp.bot_bo214064617a_bool))))))) (let ((_let_19 (= _let_14 _let_15))) (let ((_let_20 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_21 (tptp.hBOOL (tptp.hAPP_int_bool tptp.bot_bot_fun_int_bool _let_20)))) (let ((_let_22 (tptp.hAPP_a2036067514e_bool _let_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_90))) (let ((_let_23 (tptp.hBOOL (tptp.hAPP_state_bool _let_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91)))) (let ((_let_24 (= tptp.fFalse (tptp.hAPP_int_bool _let_14 _let_20)))) (let ((_let_25 (= _let_2 _let_22))) (let ((_let_26 (= tptp.fFalse (tptp.hAPP_state_bool _let_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91)))) (let ((_let_27 (ASSUME :args (_let_16)))) (let ((_let_28 (forall ((Pa tptp.fun_int_bool)) (= Pa (tptp.hAPP_f1805168059t_bool tptp.collect_int Pa))))) (let ((_let_29 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_30 (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int _let_20) tptp.bot_bot_fun_int_bool)))) (let ((_let_31 (= _let_30 _let_21))) (let ((_let_32 (not _let_21))) (let ((_let_33 (_let_13))) (let ((_let_34 (ASSUME :args _let_33))) (let ((_let_35 (_let_17))) (let ((_let_36 (ASSUME :args _let_35))) (let ((_let_37 (not _let_23))) (let ((_let_38 (or _let_37 (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_4 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a (tptp.hoare_1876769875iple_a (tptp.hAPP_f762886889e_bool tptp.cOMBK_1458035955bool_a (tptp.hAPP_s1806633685e_bool (tptp.hAPP_f817621513e_bool tptp.cOMBC_2027030106e_bool tptp.fequal_state) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91)) tptp.c (tptp.hAPP_f762886889e_bool tptp.cOMBK_1458035955bool_a (tptp.hAPP_a2036067514e_bool _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_90)))) tptp.bot_bo214064617a_bool)))))) (let ((_let_39 (forall ((Z_11 tptp.x_a) (S_2 tptp.state)) (or (not (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool (tptp.hAPP_f762886889e_bool tptp.cOMBK_1458035955bool_a (tptp.hAPP_b2019457360e_bool tptp.cOMBK_bool_state tptp.fFalse)) Z_11) S_2))) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hoare_572465367rivs_a tptp.g) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a (tptp.hoare_1876769875iple_a (tptp.hAPP_f762886889e_bool tptp.cOMBK_1458035955bool_a (tptp.hAPP_s1806633685e_bool (tptp.hAPP_f817621513e_bool tptp.cOMBC_2027030106e_bool tptp.fequal_state) S_2)) tptp.c (tptp.hAPP_f762886889e_bool tptp.cOMBK_1458035955bool_a (tptp.hAPP_a2036067514e_bool (tptp.hAPP_f762886889e_bool (tptp.hAPP_f1261923407e_bool tptp.cOMBC_892787026e_bool (tptp.hAPP_f963367678e_bool (tptp.hAPP_f375255701e_bool tptp.cOMBB_145932198bool_a tptp.cOMBS_1378840469l_bool) (tptp.hAPP_f1509969235l_bool (tptp.hAPP_f1178339559l_bool tptp.cOMBB_1355796797bool_a (tptp.hAPP_f1561913689l_bool tptp.cOMBB_188601460_state tptp.fconj)) tptp.p))) (tptp.hAPP_f1759915619e_bool (tptp.hAPP_f2073279419e_bool tptp.cOMBB_160679318_state tptp.fNot) tptp.b)) Z_11)))) tptp.bot_bo214064617a_bool))))))) (let ((_let_40 (not _let_38))) (let ((_let_41 (not _let_39))) (let ((_let_42 (or _let_41 _let_5))) (let ((_let_43 (forall ((Ga tptp.fun_Ho882550911a_bool) (Ca tptp.com) (Q_1 tptp.fun_a_fun_state_bool) (Pa tptp.fun_a_fun_state_bool)) (or (not (forall ((Z_11 tptp.x_a) (S_2 tptp.state)) (or (not (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Pa Z_11) S_2))) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hoare_572465367rivs_a Ga) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a (tptp.hoare_1876769875iple_a (tptp.hAPP_f762886889e_bool tptp.cOMBK_1458035955bool_a (tptp.hAPP_s1806633685e_bool (tptp.hAPP_f817621513e_bool tptp.cOMBC_2027030106e_bool tptp.fequal_state) S_2)) Ca (tptp.hAPP_f762886889e_bool tptp.cOMBK_1458035955bool_a (tptp.hAPP_a2036067514e_bool Q_1 Z_11)))) tptp.bot_bo214064617a_bool)))))) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hoare_572465367rivs_a Ga) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a (tptp.hoare_1876769875iple_a Pa Ca Q_1)) tptp.bot_bo214064617a_bool))))))) (let ((_let_44 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_45 (or))) (let ((_let_46 (_let_41))) (let ((_let_47 (forall ((P tptp.bool) (Q tptp.int)) (= P (tptp.hAPP_int_bool (tptp.hAPP_b396694332t_bool tptp.cOMBK_bool_int P) Q))))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (forall ((P tptp.fun_state_bool) (Q tptp.x_a)) (= P (tptp.hAPP_a2036067514e_bool (tptp.hAPP_f762886889e_bool tptp.cOMBK_1458035955bool_a P) Q))))) (let ((_let_50 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_51 (forall ((P tptp.bool) (Q tptp.state)) (= P (tptp.hAPP_state_bool (tptp.hAPP_b2019457360e_bool tptp.cOMBK_bool_state P) Q))))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_53 (not _let_26))) (let ((_let_54 (not _let_25))) (let ((_let_55 (not _let_24))) (let ((_let_56 (not _let_19))) (let ((_let_57 (not _let_16))) (let ((_let_58 (ASSUME :args (_let_32)))) (let ((_let_59 (ASSUME :args (_let_19)))) (let ((_let_60 (ASSUME :args (_let_24)))) (let ((_let_61 (ASSUME :args (_let_26)))) (let ((_let_62 (ASSUME :args (_let_25)))) (let ((_let_63 (ASSUME :args (_let_23)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_58 _let_27 _let_59 _let_60 _let_61 _let_62 _let_63) :args (_let_16 _let_19 _let_32 _let_23 _let_24 _let_25 _let_26)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_63)) (CONG (TRANS (CONG (SYMM _let_62) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91)) :args (APPLY_UF tptp.hAPP_state_bool)) (SYMM _let_61) (SYMM (SYMM _let_60)) (CONG (TRANS (SYMM (SYMM _let_59)) (SYMM _let_27)) (REFL :args (_let_20)) :args (APPLY_UF tptp.hAPP_int_bool))) :args (APPLY_UF tptp.hBOOL)) (FALSE_INTRO _let_58))) :args (_let_32 _let_16 _let_19 _let_24 _let_26 _let_25 _let_23)) :args ((not (and _let_16 _let_19 _let_32 _let_23 _let_24 _let_25 _let_26)) SB_LITERAL))) (CONG (REFL :args (_let_57)) (REFL :args (_let_56)) (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_21))) (REFL :args (_let_37)) (REFL :args (_let_55)) (REFL :args (_let_54)) (REFL :args (_let_53)) :args _let_45)) :args ((or _let_57 _let_21 _let_56 _let_37 _let_55 _let_54 _let_53))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (tptp.fFalse SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP_state_bool (tptp.hAPP_b2019457360e_bool tptp.cOMBK_bool_state P) Q)))) :args (_let_51))) _let_52 :args (_let_26 false _let_51)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_50 :args (_let_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_90 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP_a2036067514e_bool (tptp.hAPP_f762886889e_bool tptp.cOMBK_1458035955bool_a P) Q)))) :args (_let_49))) _let_50 :args (_let_25 false _let_49)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (tptp.fFalse _let_20 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP_int_bool (tptp.hAPP_b396694332t_bool tptp.cOMBK_bool_int P) Q)))) :args (_let_47))) _let_48 :args (_let_24 false _let_47)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 0)) (CONG (REFL :args (_let_38)) (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_23))) :args _let_45)) :args ((or _let_23 _let_38))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_46)) :args _let_46)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_39))) (REFL :args (_let_40)) :args _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_42)) :args ((or _let_5 _let_41 (not _let_42)))) (ASSUME :args (_let_6)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (tptp.g tptp.c _let_1 _let_3 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP_f500854239l_bool (tptp.hoare_572465367rivs_a Ga) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a (tptp.hoare_1876769875iple_a Pa Ca Q_1)) tptp.bot_bo214064617a_bool))))) :args (_let_43))) _let_44 :args (_let_42 false _let_43)) :args (_let_41 true _let_5 false _let_42)) :args (_let_40 true _let_39)) :args (_let_23 true _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_31)) :args ((or _let_30 _let_32 (not _let_31)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (_let_20 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hAPP_i2112223885l_bool tptp.member_int A_13)))) :args _let_35)) _let_36 :args ((not _let_30) false _let_17)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_34 :args (_let_20 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hAPP_i2112223885l_bool tptp.member_int X_2)))) :args _let_33))) _let_34 :args (_let_31 false _let_13)) :args (_let_32 true _let_30 false _let_31)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_29 :args (_let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hAPP_f1805168059t_bool tptp.collect_int Pa)))) :args (_let_28))) _let_29 :args (_let_19 false _let_28)) _let_27 :args (false false _let_26 false _let_25 false _let_24 false _let_23 true _let_21 false _let_19 false _let_16)) :args ((forall ((Ga tptp.fun_Ho882550911a_bool)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hoare_572465367rivs_a Ga) tptp.bot_bo214064617a_bool))) (forall ((Fun1_2 tptp.fun_a_fun_state_bool) (Com_2 tptp.com) (Fun2_2 tptp.fun_a_fun_state_bool) (Fun1_1 tptp.fun_a_fun_state_bool) (Com_1 tptp.com) (Fun2_1 tptp.fun_a_fun_state_bool)) (= (= (tptp.hoare_1876769875iple_a Fun1_2 Com_2 Fun2_2) (tptp.hoare_1876769875iple_a Fun1_1 Com_1 Fun2_1)) (and (= Fun1_2 Fun1_1) (= Com_2 Com_1) (= Fun2_2 Fun2_1)))) (forall ((Ga tptp.fun_Ho882550911a_bool) (G_1 tptp.fun_Ho882550911a_bool) (Ts tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hoare_572465367rivs_a Ga))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hoare_572465367rivs_a G_1) Ts)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 G_1)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 Ts)))))) (forall ((Ts tptp.fun_Ho882550911a_bool) (Ga tptp.fun_Ho882550911a_bool) (T_2 tptp.hoare_2076525193iple_a)) (let ((_let_1 (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a T_2))) (let ((_let_2 (tptp.hoare_572465367rivs_a Ga))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_2 (tptp.hAPP_f642208769a_bool _let_1 tptp.bot_bo214064617a_bool))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_2 Ts)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_2 (tptp.hAPP_f642208769a_bool _let_1 Ts)))))))) (forall ((Ga tptp.fun_Ho882550911a_bool) (Pa tptp.fun_a_fun_state_bool) (Ca tptp.com) (Q_1 tptp.fun_a_fun_state_bool) (C_5 tptp.bool)) (let ((_let_1 (tptp.hoare_572465367rivs_a Ga))) (=> (=> (tptp.hBOOL C_5) (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a (tptp.hoare_1876769875iple_a Pa Ca Q_1)) tptp.bot_bo214064617a_bool)))) (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a (tptp.hoare_1876769875iple_a (tptp.hAPP_b540892988e_bool (tptp.hAPP_f1824947087e_bool tptp.cOMBC_41962815e_bool (tptp.hAPP_f340725611e_bool (tptp.hAPP_f1006724181e_bool tptp.cOMBB_1348041619bool_a tptp.cOMBC_231445413l_bool) (tptp.hAPP_f1509969235l_bool (tptp.hAPP_f1178339559l_bool tptp.cOMBB_1355796797bool_a (tptp.hAPP_f1561913689l_bool tptp.cOMBB_188601460_state tptp.fconj)) Pa))) C_5) Ca Q_1)) tptp.bot_bo214064617a_bool)))))) _let_18 (forall ((Q_1 tptp.fun_a_fun_state_bool) (Ga tptp.fun_Ho882550911a_bool) (Pa tptp.fun_a_fun_state_bool) (Ca tptp.com) (Q_3 tptp.fun_a_fun_state_bool)) (let ((_let_1 (tptp.hoare_572465367rivs_a Ga))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a (tptp.hoare_1876769875iple_a Pa Ca Q_3)) tptp.bot_bo214064617a_bool))) (=> (forall ((Z_11 tptp.x_a) (S_2 tptp.state)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Q_3 Z_11) S_2)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Q_1 Z_11) S_2)))) (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a (tptp.hoare_1876769875iple_a Pa Ca Q_1)) tptp.bot_bo214064617a_bool))))))) (forall ((Pa tptp.fun_a_fun_state_bool) (Ga tptp.fun_Ho882550911a_bool) (P_2 tptp.fun_a_fun_state_bool) (Ca tptp.com) (Q_1 tptp.fun_a_fun_state_bool)) (let ((_let_1 (tptp.hoare_572465367rivs_a Ga))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a (tptp.hoare_1876769875iple_a P_2 Ca Q_1)) tptp.bot_bo214064617a_bool))) (=> (forall ((Z_11 tptp.x_a) (S_2 tptp.state)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Pa Z_11) S_2)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool P_2 Z_11) S_2)))) (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a (tptp.hoare_1876769875iple_a Pa Ca Q_1)) tptp.bot_bo214064617a_bool))))))) (forall ((Q_1 tptp.fun_a_fun_state_bool) (Pa tptp.fun_a_fun_state_bool) (Ga tptp.fun_Ho882550911a_bool) (P_2 tptp.fun_a_fun_state_bool) (Ca tptp.com) (Q_3 tptp.fun_a_fun_state_bool)) (let ((_let_1 (tptp.hoare_572465367rivs_a Ga))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a (tptp.hoare_1876769875iple_a P_2 Ca Q_3)) tptp.bot_bo214064617a_bool))) (=> (forall ((Z_11 tptp.x_a) (S_2 tptp.state)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Pa Z_11) S_2)) (forall ((S_3 tptp.state)) (=> (forall ((Z_12 tptp.x_a)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool P_2 Z_12) S_2)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Q_3 Z_12) S_3)))) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Q_1 Z_11) S_3)))))) (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a (tptp.hoare_1876769875iple_a Pa Ca Q_1)) tptp.bot_bo214064617a_bool))))))) (forall ((A_13 tptp.nat) (Ba tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat A_13))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Ba) A))) (=> (not (= A_13 Ba)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)))))) (forall ((A_13 tptp.hoare_2076525193iple_a) (Ba tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a A_13))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a Ba) A))) (=> (not (= A_13 Ba)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 A)))))) (forall ((A_13 tptp.int) (Ba tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int A_13))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int Ba) A))) (=> (not (= A_13 Ba)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A)))))) (forall ((Ba tptp.nat) (A_13 tptp.nat) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat A_13))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B))) (= A_13 Ba)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Ba) B)))))) (forall ((Ba tptp.hoare_2076525193iple_a) (A_13 tptp.hoare_2076525193iple_a) (B tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a A_13))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 B))) (= A_13 Ba)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a Ba) B)))))) (forall ((Ba tptp.int) (A_13 tptp.int) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int A_13))) (=> (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B))) (= A_13 Ba)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int Ba) B)))))) (forall ((A_13 tptp.hoare_2076525193iple_a)) (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a A_13) tptp.bot_bo214064617a_bool)))) (forall ((A_13 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_13) tptp.bot_bot_fun_nat_bool)))) _let_17 (forall ((A_13 tptp.nat)) (= (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_n1699378549t_bool tptp.fequal_nat A_13)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) tptp.bot_bot_fun_nat_bool))) (forall ((A_13 tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_f642208769a_bool tptp.collec977865374iple_a (tptp.hAPP_H2077279219a_bool tptp.fequal1589671816iple_a A_13)) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) tptp.bot_bo214064617a_bool))) (forall ((A_13 tptp.int)) (= (tptp.hAPP_f1805168059t_bool tptp.collect_int (tptp.hAPP_i1948725293t_bool tptp.fequal_int A_13)) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) tptp.bot_bot_fun_int_bool))) (forall ((A_13 tptp.nat)) (= (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.fequal_nat) A_13)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) tptp.bot_bot_fun_nat_bool))) (forall ((A_13 tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_f642208769a_bool tptp.collec977865374iple_a (tptp.hAPP_H2077279219a_bool (tptp.hAPP_f877684549a_bool tptp.cOMBC_1047656090a_bool tptp.fequal1589671816iple_a) A_13)) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) tptp.bot_bo214064617a_bool))) (forall ((A_13 tptp.int)) (= (tptp.hAPP_f1805168059t_bool tptp.collect_int (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool tptp.fequal_int) A_13)) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) tptp.bot_bot_fun_int_bool))) (forall ((Pa tptp.fun_nat_bool) (A_13 tptp.nat)) (let ((_let_1 (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fconj) (tptp.hAPP_n1699378549t_bool tptp.fequal_nat A_13))) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool Pa A_13)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) tptp.bot_bot_fun_nat_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bot_fun_nat_bool)))))) (forall ((Pa tptp.fun_Ho882550911a_bool) (A_13 tptp.hoare_2076525193iple_a)) (let ((_let_1 (tptp.hAPP_f642208769a_bool tptp.collec977865374iple_a (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1004093413a_bool tptp.cOMBS_1108095524l_bool (tptp.hAPP_f268025233l_bool (tptp.hAPP_f1261090107l_bool tptp.cOMBB_345279363iple_a tptp.fconj) (tptp.hAPP_H2077279219a_bool tptp.fequal1589671816iple_a A_13))) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_H454055633a_bool Pa A_13)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) tptp.bot_bo214064617a_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo214064617a_bool)))))) (forall ((Pa tptp.fun_int_bool) (A_13 tptp.int)) (let ((_let_1 (tptp.hAPP_f1805168059t_bool tptp.collect_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_i1948725293t_bool tptp.fequal_int A_13))) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool Pa A_13)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) tptp.bot_bot_fun_int_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bot_fun_int_bool)))))) (forall ((Pa tptp.fun_nat_bool) (A_13 tptp.nat)) (let ((_let_1 (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fconj) (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.fequal_nat) A_13))) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_nat_bool Pa A_13)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) tptp.bot_bot_fun_nat_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bot_fun_nat_bool)))))) (forall ((Pa tptp.fun_Ho882550911a_bool) (A_13 tptp.hoare_2076525193iple_a)) (let ((_let_1 (tptp.hAPP_f642208769a_bool tptp.collec977865374iple_a (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1004093413a_bool tptp.cOMBS_1108095524l_bool (tptp.hAPP_f268025233l_bool (tptp.hAPP_f1261090107l_bool tptp.cOMBB_345279363iple_a tptp.fconj) (tptp.hAPP_H2077279219a_bool (tptp.hAPP_f877684549a_bool tptp.cOMBC_1047656090a_bool tptp.fequal1589671816iple_a) A_13))) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_H454055633a_bool Pa A_13)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) tptp.bot_bo214064617a_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bo214064617a_bool)))))) (forall ((Pa tptp.fun_int_bool) (A_13 tptp.int)) (let ((_let_1 (tptp.hAPP_f1805168059t_bool tptp.collect_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool tptp.fequal_int) A_13))) Pa)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool Pa A_13)))) (and (=> _let_2 (= _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) tptp.bot_bot_fun_int_bool))) (=> (not _let_2) (= _let_1 tptp.bot_bot_fun_int_bool)))))) (forall ((A_13 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (=> (= A tptp.bot_bo214064617a_bool) (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a A_13) A))))) (forall ((A_13 tptp.nat) (A tptp.fun_nat_bool)) (=> (= A tptp.bot_bot_fun_nat_bool) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_13) A))))) (forall ((A_13 tptp.int) (A tptp.fun_int_bool)) (=> (= A tptp.bot_bot_fun_int_bool) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_13) A))))) (forall ((Pa tptp.fun_Ho882550911a_bool)) (= (= (tptp.hAPP_f642208769a_bool tptp.collec977865374iple_a Pa) tptp.bot_bo214064617a_bool) (forall ((X_2 tptp.hoare_2076525193iple_a)) (not (tptp.hBOOL (tptp.hAPP_H454055633a_bool Pa X_2)))))) (forall ((Pa tptp.fun_int_bool)) (= (= (tptp.hAPP_f1805168059t_bool tptp.collect_int Pa) tptp.bot_bot_fun_int_bool) (forall ((X_2 tptp.int)) (not (tptp.hBOOL (tptp.hAPP_int_bool Pa X_2)))))) (forall ((Pa tptp.fun_nat_bool)) (= (= (tptp.hAPP_f800510211t_bool tptp.collect_nat Pa) tptp.bot_bot_fun_nat_bool) (forall ((X_2 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool Pa X_2)))))) (forall ((Ca tptp.hoare_2076525193iple_a)) (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a Ca) tptp.bot_bo214064617a_bool)))) (forall ((Ca tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Ca) tptp.bot_bot_fun_nat_bool)))) (forall ((Ca tptp.int)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Ca) tptp.bot_bot_fun_int_bool)))) (forall ((Pa tptp.fun_Ho882550911a_bool)) (= (= tptp.bot_bo214064617a_bool (tptp.hAPP_f642208769a_bool tptp.collec977865374iple_a Pa)) (forall ((X_2 tptp.hoare_2076525193iple_a)) (not (tptp.hBOOL (tptp.hAPP_H454055633a_bool Pa X_2)))))) (forall ((Pa tptp.fun_int_bool)) (= (= tptp.bot_bot_fun_int_bool (tptp.hAPP_f1805168059t_bool tptp.collect_int Pa)) (forall ((X_2 tptp.int)) (not (tptp.hBOOL (tptp.hAPP_int_bool Pa X_2)))))) (forall ((Pa tptp.fun_nat_bool)) (= (= tptp.bot_bot_fun_nat_bool (tptp.hAPP_f800510211t_bool tptp.collect_nat Pa)) (forall ((X_2 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool Pa X_2)))))) (forall ((A tptp.fun_Ho882550911a_bool)) (= (exists ((X_2 tptp.hoare_2076525193iple_a)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_2) A))) (not (= A tptp.bot_bo214064617a_bool)))) (forall ((A tptp.fun_nat_bool)) (= (exists ((X_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A))) (not (= A tptp.bot_bot_fun_nat_bool)))) (forall ((A tptp.fun_int_bool)) (= (exists ((X_2 tptp.int)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) A))) (not (= A tptp.bot_bot_fun_int_bool)))) (forall ((A tptp.fun_Ho882550911a_bool)) (= (forall ((X_2 tptp.hoare_2076525193iple_a)) (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_2) A)))) (= A tptp.bot_bo214064617a_bool))) (forall ((A tptp.fun_nat_bool)) (= (forall ((X_2 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)))) (= A tptp.bot_bot_fun_nat_bool))) (forall ((A tptp.fun_int_bool)) (= (forall ((X_2 tptp.int)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) A)))) (= A tptp.bot_bot_fun_int_bool))) (= tptp.bot_bo214064617a_bool (tptp.hAPP_f642208769a_bool tptp.collec977865374iple_a (tptp.hAPP_b1299643615a_bool tptp.cOMBK_861658160iple_a tptp.fFalse))) _let_16 (= tptp.bot_bot_fun_nat_bool (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_b1013836512t_bool tptp.cOMBK_bool_nat tptp.fFalse))) (forall ((A_13 tptp.nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_13) A)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) A) A))) (forall ((A_13 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a A_13) A)) (= (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) A) A))) (forall ((A_13 tptp.int) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_13) A)) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) A) A))) (forall ((Ba tptp.nat) (A_13 tptp.nat) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat A_13))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Ba) B)))))) (forall ((Ba tptp.hoare_2076525193iple_a) (A_13 tptp.hoare_2076525193iple_a) (B tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a A_13))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a Ba) B)))))) (forall ((Ba tptp.int) (A_13 tptp.int) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int A_13))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int Ba) B)))))) (forall ((B tptp.fun_nat_bool) (X_1 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1))) (let ((_let_2 (tptp.hAPP_n215258509l_bool tptp.member_nat X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_2 A))) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_2 B))) (= (= (tptp.hAPP_f800510211t_bool _let_1 A) (tptp.hAPP_f800510211t_bool _let_1 B)) (= A B))))))) (forall ((B tptp.fun_Ho882550911a_bool) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1))) (let ((_let_2 (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_2 A))) (=> (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_2 B))) (= (= (tptp.hAPP_f642208769a_bool _let_1 A) (tptp.hAPP_f642208769a_bool _let_1 B)) (= A B))))))) (forall ((B tptp.fun_int_bool) (X_1 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1))) (let ((_let_2 (tptp.hAPP_i2112223885l_bool tptp.member_int X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_2 A))) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_2 B))) (= (= (tptp.hAPP_f1805168059t_bool _let_1 A) (tptp.hAPP_f1805168059t_bool _let_1 B)) (= A B))))))) (forall ((Y_1 tptp.nat) (A tptp.fun_nat_bool) (X_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Y_1) A) X_1)) (or (= Y_1 X_1) (tptp.hBOOL (tptp.hAPP_nat_bool A X_1))))) (forall ((Y_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (X_1 tptp.hoare_2076525193iple_a)) (= (tptp.hBOOL (tptp.hAPP_H454055633a_bool (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a Y_1) A) X_1)) (or (= Y_1 X_1) (tptp.hBOOL (tptp.hAPP_H454055633a_bool A X_1))))) (forall ((Y_1 tptp.int) (A tptp.fun_int_bool) (X_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int Y_1) A) X_1)) (or (= Y_1 X_1) (tptp.hBOOL (tptp.hAPP_int_bool A X_1))))) (forall ((A_13 tptp.nat) (Ba tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat A_13))) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Ba) A))) (or (= A_13 Ba) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)))))) (forall ((A_13 tptp.hoare_2076525193iple_a) (Ba tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a A_13))) (= (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a Ba) A))) (or (= A_13 Ba) (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 A)))))) (forall ((A_13 tptp.int) (Ba tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int A_13))) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int Ba) A))) (or (= A_13 Ba) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A)))))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1))) (let ((_let_2 (tptp.hAPP_n1512601776t_bool tptp.insert_nat Y_1))) (= (tptp.hAPP_f800510211t_bool _let_1 (tptp.hAPP_f800510211t_bool _let_2 A)) (tptp.hAPP_f800510211t_bool _let_2 (tptp.hAPP_f800510211t_bool _let_1 A)))))) (forall ((X_1 tptp.hoare_2076525193iple_a) (Y_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1))) (let ((_let_2 (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a Y_1))) (= (tptp.hAPP_f642208769a_bool _let_1 (tptp.hAPP_f642208769a_bool _let_2 A)) (tptp.hAPP_f642208769a_bool _let_2 (tptp.hAPP_f642208769a_bool _let_1 A)))))) (forall ((X_1 tptp.int) (Y_1 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1))) (let ((_let_2 (tptp.hAPP_i1529485324t_bool tptp.insert_int Y_1))) (= (tptp.hAPP_f1805168059t_bool _let_1 (tptp.hAPP_f1805168059t_bool _let_2 A)) (tptp.hAPP_f1805168059t_bool _let_2 (tptp.hAPP_f1805168059t_bool _let_1 A)))))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1))) (let ((_let_2 (tptp.hAPP_f800510211t_bool _let_1 A))) (= (tptp.hAPP_f800510211t_bool _let_1 _let_2) _let_2)))) (forall ((X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1))) (let ((_let_2 (tptp.hAPP_f642208769a_bool _let_1 A))) (= (tptp.hAPP_f642208769a_bool _let_1 _let_2) _let_2)))) (forall ((X_1 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1))) (let ((_let_2 (tptp.hAPP_f1805168059t_bool _let_1 A))) (= (tptp.hAPP_f1805168059t_bool _let_1 _let_2) _let_2)))) (forall ((A_13 tptp.nat) (Pa tptp.fun_nat_bool)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) (tptp.hAPP_f800510211t_bool tptp.collect_nat Pa)) (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fimplies) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f894608603t_bool tptp.cOMBB_bool_bool_nat tptp.fNot) (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.fequal_nat) A_13)))) Pa)))) (forall ((A_13 tptp.hoare_2076525193iple_a) (Pa tptp.fun_Ho882550911a_bool)) (= (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) (tptp.hAPP_f642208769a_bool tptp.collec977865374iple_a Pa)) (tptp.hAPP_f642208769a_bool tptp.collec977865374iple_a (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1004093413a_bool tptp.cOMBS_1108095524l_bool (tptp.hAPP_f268025233l_bool (tptp.hAPP_f1261090107l_bool tptp.cOMBB_345279363iple_a tptp.fimplies) (tptp.hAPP_f642208769a_bool (tptp.hAPP_f629438041a_bool tptp.cOMBB_361863589iple_a tptp.fNot) (tptp.hAPP_H2077279219a_bool (tptp.hAPP_f877684549a_bool tptp.cOMBC_1047656090a_bool tptp.fequal1589671816iple_a) A_13)))) Pa)))) (forall ((A_13 tptp.int) (Pa tptp.fun_int_bool)) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) (tptp.hAPP_f1805168059t_bool tptp.collect_int Pa)) (tptp.hAPP_f1805168059t_bool tptp.collect_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fimplies) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f627970963t_bool tptp.cOMBB_bool_bool_int tptp.fNot) (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool tptp.fequal_int) A_13)))) Pa)))) (forall ((A_13 tptp.nat) (B tptp.fun_nat_bool)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) B) (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fdisj) (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.fequal_nat) A_13))) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat) B))))) (forall ((A_13 tptp.hoare_2076525193iple_a) (B tptp.fun_Ho882550911a_bool)) (= (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) B) (tptp.hAPP_f642208769a_bool tptp.collec977865374iple_a (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1004093413a_bool tptp.cOMBS_1108095524l_bool (tptp.hAPP_f268025233l_bool (tptp.hAPP_f1261090107l_bool tptp.cOMBB_345279363iple_a tptp.fdisj) (tptp.hAPP_H2077279219a_bool (tptp.hAPP_f877684549a_bool tptp.cOMBC_1047656090a_bool tptp.fequal1589671816iple_a) A_13))) (tptp.hAPP_f642208769a_bool (tptp.hAPP_f325481667a_bool tptp.cOMBC_1529670358l_bool tptp.member276146780iple_a) B))))) (forall ((A_13 tptp.int) (B tptp.fun_int_bool)) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) B) (tptp.hAPP_f1805168059t_bool tptp.collect_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fdisj) (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool tptp.fequal_int) A_13))) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f202917053t_bool tptp.cOMBC_94739984l_bool tptp.member_int) B))))) (forall ((A_13 tptp.nat) (B tptp.fun_nat_bool)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_13) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) B)))) (forall ((A_13 tptp.hoare_2076525193iple_a) (B tptp.fun_Ho882550911a_bool)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a A_13) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) B)))) (forall ((A_13 tptp.int) (B tptp.fun_int_bool)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_13) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) B)))) (forall ((X_2 tptp.nat) (Xa tptp.fun_nat_bool)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_2) Xa) (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fdisj) (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.fequal_nat) X_2))) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat) Xa))))) (forall ((X_2 tptp.hoare_2076525193iple_a) (Xa tptp.fun_Ho882550911a_bool)) (= (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_2) Xa) (tptp.hAPP_f642208769a_bool tptp.collec977865374iple_a (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1004093413a_bool tptp.cOMBS_1108095524l_bool (tptp.hAPP_f268025233l_bool (tptp.hAPP_f1261090107l_bool tptp.cOMBB_345279363iple_a tptp.fdisj) (tptp.hAPP_H2077279219a_bool (tptp.hAPP_f877684549a_bool tptp.cOMBC_1047656090a_bool tptp.fequal1589671816iple_a) X_2))) (tptp.hAPP_f642208769a_bool (tptp.hAPP_f325481667a_bool tptp.cOMBC_1529670358l_bool tptp.member276146780iple_a) Xa))))) (forall ((X_2 tptp.int) (Xa tptp.fun_int_bool)) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_2) Xa) (tptp.hAPP_f1805168059t_bool tptp.collect_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fdisj) (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool tptp.fequal_int) X_2))) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f202917053t_bool tptp.cOMBC_94739984l_bool tptp.member_int) Xa))))) (forall ((A_13 tptp.nat) (Ba tptp.nat)) (=> (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) tptp.bot_bot_fun_nat_bool) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Ba) tptp.bot_bot_fun_nat_bool)) (= A_13 Ba))) (forall ((A_13 tptp.hoare_2076525193iple_a) (Ba tptp.hoare_2076525193iple_a)) (=> (= (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) tptp.bot_bo214064617a_bool) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a Ba) tptp.bot_bo214064617a_bool)) (= A_13 Ba))) (forall ((A_13 tptp.int) (Ba tptp.int)) (=> (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) tptp.bot_bot_fun_int_bool) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int Ba) tptp.bot_bot_fun_int_bool)) (= A_13 Ba))) (forall ((Ba tptp.nat) (A_13 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Ba) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) tptp.bot_bot_fun_nat_bool))) (= Ba A_13))) (forall ((Ba tptp.hoare_2076525193iple_a) (A_13 tptp.hoare_2076525193iple_a)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a Ba) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) tptp.bot_bo214064617a_bool))) (= Ba A_13))) (forall ((Ba tptp.int) (A_13 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Ba) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) tptp.bot_bot_fun_int_bool))) (= Ba A_13))) (forall ((A_13 tptp.nat) (Ba tptp.nat) (Ca tptp.nat) (D_1 tptp.nat)) (= (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Ba) tptp.bot_bot_fun_nat_bool)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Ca) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat D_1) tptp.bot_bot_fun_nat_bool))) (or (and (= A_13 Ca) (= Ba D_1)) (and (= A_13 D_1) (= Ba Ca))))) (forall ((A_13 tptp.hoare_2076525193iple_a) (Ba tptp.hoare_2076525193iple_a) (Ca tptp.hoare_2076525193iple_a) (D_1 tptp.hoare_2076525193iple_a)) (= (= (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a Ba) tptp.bot_bo214064617a_bool)) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a Ca) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a D_1) tptp.bot_bo214064617a_bool))) (or (and (= A_13 Ca) (= Ba D_1)) (and (= A_13 D_1) (= Ba Ca))))) (forall ((A_13 tptp.int) (Ba tptp.int) (Ca tptp.int) (D_1 tptp.int)) (= (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int Ba) tptp.bot_bot_fun_int_bool)) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int Ca) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int D_1) tptp.bot_bot_fun_int_bool))) (or (and (= A_13 Ca) (= Ba D_1)) (and (= A_13 D_1) (= Ba Ca))))) (forall ((Ba tptp.nat) (A_13 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Ba) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) tptp.bot_bot_fun_nat_bool))) (= Ba A_13))) (forall ((Ba tptp.hoare_2076525193iple_a) (A_13 tptp.hoare_2076525193iple_a)) (= (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a Ba) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) tptp.bot_bo214064617a_bool))) (= Ba A_13))) (forall ((Ba tptp.int) (A_13 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Ba) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) tptp.bot_bot_fun_int_bool))) (= Ba A_13))) (forall ((A_13 tptp.nat) (A tptp.fun_nat_bool)) (not (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) A) tptp.bot_bot_fun_nat_bool))) (forall ((A_13 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (not (= (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) A) tptp.bot_bo214064617a_bool))) (forall ((A_13 tptp.int) (A tptp.fun_int_bool)) (not (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) A) tptp.bot_bot_fun_int_bool))) (forall ((A_13 tptp.nat) (A tptp.fun_nat_bool)) (not (= tptp.bot_bot_fun_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) A)))) (forall ((A_13 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (not (= tptp.bot_bo214064617a_bool (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) A)))) (forall ((A_13 tptp.int) (A tptp.fun_int_bool)) (not (= tptp.bot_bot_fun_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) A)))) (forall ((X_1 tptp.nat)) (= (tptp.hAPP_f22106695ol_nat tptp.the_elem_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) tptp.bot_bot_fun_nat_bool)) X_1)) (forall ((X_1 tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_f2009966983iple_a tptp.the_el2146174248iple_a (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1) tptp.bot_bo214064617a_bool)) X_1)) (forall ((X_1 tptp.int)) (= (tptp.hAPP_f1594865479ol_int tptp.the_elem_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) tptp.bot_bot_fun_int_bool)) X_1)) (forall ((X_1 tptp.hoare_2076525193iple_a)) (= (tptp.hBOOL (tptp.hAPP_H454055633a_bool tptp.bot_bo214064617a_bool X_1)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool tptp.bot_bot_fun_int_bool X_1)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool tptp.bot_bot_fun_nat_bool X_1)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_2 tptp.hoare_2076525193iple_a)) (= (tptp.hBOOL (tptp.hAPP_H454055633a_bool tptp.bot_bo214064617a_bool X_2)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool tptp.bot_bot_fun_int_bool X_2)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((X_2 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool tptp.bot_bot_fun_nat_bool X_2)) (tptp.hBOOL tptp.bot_bot_bool))) (forall ((Ga tptp.fun_Ho882550911a_bool) (Pa tptp.fun_a_fun_state_bool)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hoare_572465367rivs_a Ga) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a (tptp.hoare_1876769875iple_a Pa tptp.skip Pa)) tptp.bot_bo214064617a_bool)))) (forall ((D_1 tptp.com) (R_1 tptp.fun_a_fun_state_bool) (Ga tptp.fun_Ho882550911a_bool) (Pa tptp.fun_a_fun_state_bool) (Ca tptp.com) (Q_1 tptp.fun_a_fun_state_bool)) (let ((_let_1 (tptp.hoare_572465367rivs_a Ga))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a (tptp.hoare_1876769875iple_a Pa Ca Q_1)) tptp.bot_bo214064617a_bool))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a (tptp.hoare_1876769875iple_a Q_1 D_1 R_1)) tptp.bot_bo214064617a_bool))) (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a (tptp.hoare_1876769875iple_a Pa (tptp.semi Ca D_1) R_1)) tptp.bot_bo214064617a_bool))))))) (forall ((Y_1 tptp.hoare_2076525193iple_a)) (not (forall ((Fun1 tptp.fun_a_fun_state_bool) (Com tptp.com) (Fun2 tptp.fun_a_fun_state_bool)) (not (= Y_1 (tptp.hoare_1876769875iple_a Fun1 Com Fun2)))))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (not (forall ((B_35 tptp.fun_nat_bool)) (=> (= A (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) B_35)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) B_35))))))) (forall ((X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A)) (not (forall ((B_35 tptp.fun_Ho882550911a_bool)) (=> (= A (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1) B_35)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) B_35))))))) (forall ((X_1 tptp.int) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (not (forall ((B_35 tptp.fun_int_bool)) (=> (= A (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) B_35)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) B_35))))))) (forall ((A_13 tptp.nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_13) A)) (exists ((B_35 tptp.fun_nat_bool)) (and (= A (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) B_35)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_13) B_35))))))) (forall ((A_13 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a A_13) A)) (exists ((B_35 tptp.fun_Ho882550911a_bool)) (and (= A (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) B_35)) (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a A_13) B_35))))))) (forall ((A_13 tptp.int) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_13) A)) (exists ((B_35 tptp.fun_int_bool)) (and (= A (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) B_35)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_13) B_35))))))) (forall ((A tptp.fun_Ho882550911a_bool)) (=> (forall ((Y_21 tptp.hoare_2076525193iple_a)) (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a Y_21) A)))) (= A tptp.bot_bo214064617a_bool))) (forall ((A tptp.fun_nat_bool)) (=> (forall ((Y_21 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Y_21) A)))) (= A tptp.bot_bot_fun_nat_bool))) (forall ((A tptp.fun_int_bool)) (=> (forall ((Y_21 tptp.int)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Y_21) A)))) (= A tptp.bot_bot_fun_int_bool))) (forall ((Q_1 tptp.fun_a_fun_state_bool) (Ga tptp.fun_Ho882550911a_bool) (Ca tptp.com) (Pa tptp.fun_a_fun_state_bool)) (=> (forall ((Z_11 tptp.x_a) (S_2 tptp.state)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Pa Z_11) S_2)) (exists ((P_1 tptp.fun_a_fun_state_bool) (Q_2 tptp.fun_a_fun_state_bool)) (and (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hoare_572465367rivs_a Ga) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a (tptp.hoare_1876769875iple_a P_1 Ca Q_2)) tptp.bot_bo214064617a_bool))) (forall ((S_3 tptp.state)) (=> (forall ((Z_12 tptp.x_a)) (=> (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool P_1 Z_12) S_2)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Q_2 Z_12) S_3)))) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_a2036067514e_bool Q_1 Z_11) S_3)))))))) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hoare_572465367rivs_a Ga) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a (tptp.hoare_1876769875iple_a Pa Ca Q_1)) tptp.bot_bo214064617a_bool))))) (forall ((A tptp.fun_nat_bool)) (= (not (= A tptp.bot_bot_fun_nat_bool)) (exists ((X_2 tptp.nat) (B_35 tptp.fun_nat_bool)) (and (= A (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_2) B_35)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) B_35))))))) (forall ((A tptp.fun_Ho882550911a_bool)) (= (not (= A tptp.bot_bo214064617a_bool)) (exists ((X_2 tptp.hoare_2076525193iple_a) (B_35 tptp.fun_Ho882550911a_bool)) (and (= A (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_2) B_35)) (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_2) B_35))))))) (forall ((A tptp.fun_int_bool)) (= (not (= A tptp.bot_bot_fun_int_bool)) (exists ((X_2 tptp.int) (B_35 tptp.fun_int_bool)) (and (= A (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_2) B_35)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) B_35))))))) (forall ((Com1_2 tptp.com) (Com2_2 tptp.com)) (not (= (tptp.semi Com1_2 Com2_2) tptp.skip))) (forall ((Com1_2 tptp.com) (Com2_2 tptp.com)) (not (= tptp.skip (tptp.semi Com1_2 Com2_2)))) (forall ((X_28 tptp.fun_nat_bool)) (= (tptp.hAPP_f22106695ol_nat tptp.the_elem_nat X_28) (tptp.hAPP_f22106695ol_nat tptp.the_nat (tptp.hAPP_f158894502t_bool (tptp.hAPP_f1777703707t_bool tptp.cOMBB_955900739ol_nat (tptp.hAPP_f103356543l_bool tptp.fequal_fun_nat_bool X_28)) (tptp.hAPP_f1570313510t_bool (tptp.hAPP_f688831301t_bool tptp.cOMBC_178881787t_bool tptp.insert_nat) tptp.bot_bot_fun_nat_bool))))) (forall ((X_28 tptp.fun_Ho882550911a_bool)) (= (tptp.hAPP_f2009966983iple_a tptp.the_el2146174248iple_a X_28) (tptp.hAPP_f2009966983iple_a tptp.the_Ho1456473914iple_a (tptp.hAPP_f338738851a_bool (tptp.hAPP_f1827400025a_bool tptp.cOMBB_1676209667iple_a (tptp.hAPP_f256727871l_bool tptp.fequal291249344a_bool X_28)) (tptp.hAPP_f219434403a_bool (tptp.hAPP_f1824299331a_bool tptp.cOMBC_175592824a_bool tptp.insert1582918915iple_a) tptp.bot_bo214064617a_bool))))) (forall ((X_28 tptp.fun_int_bool)) (= (tptp.hAPP_f1594865479ol_int tptp.the_elem_int X_28) (tptp.hAPP_f1594865479ol_int tptp.the_int (tptp.hAPP_f2119767738t_bool (tptp.hAPP_f423804115t_bool tptp.cOMBB_1418110531ol_int (tptp.hAPP_f284875647l_bool tptp.fequal_fun_int_bool X_28)) (tptp.hAPP_f1048215610t_bool (tptp.hAPP_f472159229t_bool tptp.cOMBC_1683390479t_bool tptp.insert_int) tptp.bot_bot_fun_int_bool))))) (forall ((Com1_1 tptp.com) (Com2_1 tptp.com) (Com1 tptp.com) (Com2 tptp.com)) (= (= (tptp.semi Com1_1 Com2_1) (tptp.semi Com1 Com2)) (and (= Com1_1 Com1) (= Com2_1 Com2)))) (forall ((F tptp.fun_nat_fun_nat_nat) (A_13 tptp.nat) (Ba tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.finite_fold1Set_nat F (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) tptp.bot_bot_fun_nat_bool)) Ba)) (= A_13 Ba))) (forall ((F tptp.fun_Ho483360497iple_a) (A_13 tptp.hoare_2076525193iple_a) (Ba tptp.hoare_2076525193iple_a)) (= (tptp.hBOOL (tptp.hAPP_H454055633a_bool (tptp.finite100168025iple_a F (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) tptp.bot_bo214064617a_bool)) Ba)) (= A_13 Ba))) (forall ((F tptp.fun_int_fun_int_int) (A_13 tptp.int) (Ba tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.finite_fold1Set_int F (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) tptp.bot_bot_fun_int_bool)) Ba)) (= A_13 Ba))) (forall ((X_1 tptp.nat) (F tptp.fun_nat_fun_nat_nat) (F_1 tptp.fun_fun_nat_bool_nat)) (=> (tptp.hBOOL (tptp.finite988810631ne_nat F F_1)) (= (tptp.hAPP_f22106695ol_nat F_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) tptp.bot_bot_fun_nat_bool)) X_1))) (forall ((X_1 tptp.hoare_2076525193iple_a) (F tptp.fun_Ho483360497iple_a) (F_1 tptp.fun_fu253747899iple_a)) (=> (tptp.hBOOL (tptp.finite232328454iple_a F F_1)) (= (tptp.hAPP_f2009966983iple_a F_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1) tptp.bot_bo214064617a_bool)) X_1))) (forall ((X_1 tptp.int) (F tptp.fun_int_fun_int_int) (F_1 tptp.fun_fun_int_bool_int)) (=> (tptp.hBOOL (tptp.finite1626084323ne_int F F_1)) (= (tptp.hAPP_f1594865479ol_int F_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) tptp.bot_bot_fun_int_bool)) X_1))) (forall ((X_2 tptp.hoare_2076525193iple_a)) (= (tptp.hBOOL (tptp.hAPP_H454055633a_bool tptp.bot_bo214064617a_bool X_2)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_2) tptp.bot_bo214064617a_bool)))) (forall ((X_2 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool tptp.bot_bot_fun_nat_bool X_2)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) tptp.bot_bot_fun_nat_bool)))) _let_13 (forall ((Ga tptp.fun_Ho882550911a_bool) (Pa tptp.fun_a_fun_state_bool) (X_28 tptp.vname) (A_13 tptp.fun_state_nat)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hoare_572465367rivs_a Ga) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a (tptp.hoare_1876769875iple_a (tptp.hAPP_f100967412e_bool (tptp.hAPP_f1460451647e_bool tptp.cOMBC_524597097e_bool (tptp.hAPP_f1406200875e_bool (tptp.hAPP_f635443597e_bool tptp.cOMBB_2139825703bool_a tptp.cOMBB_844853809_state) Pa)) (tptp.hAPP_f871651461_state (tptp.hAPP_f851239890_state tptp.cOMBS_777315357_state (tptp.hAPP_v365393659_state (tptp.hAPP_f1542232213_state tptp.cOMBC_1193272608_state tptp.update) X_28)) A_13)) (tptp.ass X_28 A_13) Pa)) tptp.bot_bo214064617a_bool)))) (forall ((F tptp.fun_nat_fun_nat_nat) (A_13 tptp.nat)) (= (tptp.hAPP_f22106695ol_nat (tptp.finite_fold1_nat F) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) tptp.bot_bot_fun_nat_bool)) A_13)) (forall ((F tptp.fun_Ho483360497iple_a) (A_13 tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_f2009966983iple_a (tptp.finite2092228073iple_a F) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) tptp.bot_bo214064617a_bool)) A_13)) (forall ((F tptp.fun_int_fun_int_int) (A_13 tptp.int)) (= (tptp.hAPP_f1594865479ol_int (tptp.finite_fold1_int F) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) tptp.bot_bot_fun_int_bool)) A_13)) (forall ((A_13 tptp.nat) (G tptp.fun_fun_nat_bool_nat) (F tptp.fun_nat_fun_nat_nat)) (=> (= G (tptp.finite_fold1_nat F)) (= (tptp.hAPP_f22106695ol_nat G (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) tptp.bot_bot_fun_nat_bool)) A_13))) (forall ((A_13 tptp.hoare_2076525193iple_a) (G tptp.fun_fu253747899iple_a) (F tptp.fun_Ho483360497iple_a)) (=> (= G (tptp.finite2092228073iple_a F)) (= (tptp.hAPP_f2009966983iple_a G (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) tptp.bot_bo214064617a_bool)) A_13))) (forall ((A_13 tptp.int) (G tptp.fun_fun_int_bool_int) (F tptp.fun_int_fun_int_int)) (=> (= G (tptp.finite_fold1_int F)) (= (tptp.hAPP_f1594865479ol_int G (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) tptp.bot_bot_fun_int_bool)) A_13))) (forall ((Ca tptp.nat) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.image_1778392390_a_nat (tptp.hAPP_n1236213193_a_nat tptp.cOMBK_1654814733iple_a Ca) A))) (let ((_let_2 (= A tptp.bot_bo214064617a_bool))) (and (=> _let_2 (= _let_1 tptp.bot_bot_fun_nat_bool)) (=> (not _let_2) (= _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Ca) tptp.bot_bot_fun_nat_bool))))))) (forall ((Ca tptp.nat) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.image_int_nat (tptp.hAPP_nat_fun_int_nat tptp.cOMBK_nat_int Ca) A))) (let ((_let_2 (= A tptp.bot_bot_fun_int_bool))) (and (=> _let_2 (= _let_1 tptp.bot_bot_fun_nat_bool)) (=> (not _let_2) (= _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Ca) tptp.bot_bot_fun_nat_bool))))))) (forall ((Ca tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.image_1416816325iple_a (tptp.hAPP_H1417936777iple_a tptp.cOMBK_788297294iple_a Ca) A))) (let ((_let_2 (= A tptp.bot_bo214064617a_bool))) (and (=> _let_2 (= _let_1 tptp.bot_bo214064617a_bool)) (=> (not _let_2) (= _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a Ca) tptp.bot_bo214064617a_bool))))))) (forall ((Ca tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.image_int_int (tptp.hAPP_int_fun_int_int tptp.cOMBK_int_int Ca) A))) (let ((_let_2 (= A tptp.bot_bot_fun_int_bool))) (and (=> _let_2 (= _let_1 tptp.bot_bot_fun_int_bool)) (=> (not _let_2) (= _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int Ca) tptp.bot_bot_fun_int_bool))))))) (forall ((Ca tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.image_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.cOMBK_nat_nat Ca) A))) (let ((_let_2 (= A tptp.bot_bot_fun_nat_bool))) (and (=> _let_2 (= _let_1 tptp.bot_bot_fun_nat_bool)) (=> (not _let_2) (= _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Ca) tptp.bot_bot_fun_nat_bool))))))) (forall ((Ca tptp.int) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.image_nat_int (tptp.hAPP_int_fun_nat_int tptp.cOMBK_int_nat Ca) A))) (let ((_let_2 (= A tptp.bot_bot_fun_nat_bool))) (and (=> _let_2 (= _let_1 tptp.bot_bot_fun_int_bool)) (=> (not _let_2) (= _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int Ca) tptp.bot_bot_fun_int_bool))))))) (forall ((A tptp.fun_Ho882550911a_bool) (Ba tptp.hoare_2076525193iple_a) (F tptp.fun_Ho1518252029iple_a) (X_1 tptp.hoare_2076525193iple_a)) (=> (= Ba (tptp.hAPP_H1789220885iple_a F X_1)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a Ba) (tptp.image_1416816325iple_a F A)))))) (forall ((A tptp.fun_nat_bool) (Ba tptp.hoare_2076525193iple_a) (F tptp.fun_na1240513468iple_a) (X_1 tptp.nat)) (=> (= Ba (tptp.hAPP_n887873492iple_a F X_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a Ba) (tptp.image_344477316iple_a F A)))))) (forall ((A tptp.fun_int_bool) (Ba tptp.hoare_2076525193iple_a) (F tptp.fun_in1219646560iple_a) (X_1 tptp.int)) (=> (= Ba (tptp.hAPP_i867006584iple_a F X_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a Ba) (tptp.image_323610408iple_a F A)))))) (forall ((A tptp.fun_Ho882550911a_bool) (Ba tptp.nat) (F tptp.fun_Ho864122878_a_nat) (X_1 tptp.hoare_2076525193iple_a)) (=> (= Ba (tptp.hAPP_H174304918_a_nat F X_1)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Ba) (tptp.image_1778392390_a_nat F A)))))) (forall ((A tptp.fun_int_bool) (Ba tptp.int) (F tptp.fun_int_int) (X_1 tptp.int)) (=> (= Ba (tptp.hAPP_int_int F X_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Ba) (tptp.image_int_int F A)))))) (forall ((A tptp.fun_Ho882550911a_bool) (Ba tptp.int) (F tptp.fun_Ho1026035802_a_int) (X_1 tptp.hoare_2076525193iple_a)) (=> (= Ba (tptp.hAPP_H811578610_a_int F X_1)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Ba) (tptp.image_268182434_a_int F A)))))) (forall ((A tptp.fun_nat_bool) (Ba tptp.nat) (F tptp.fun_nat_nat) (X_1 tptp.nat)) (=> (= Ba (tptp.hAPP_nat_nat F X_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Ba) (tptp.image_nat_nat F A)))))) (forall ((A tptp.fun_nat_bool) (Ba tptp.int) (F tptp.fun_nat_int) (X_1 tptp.nat)) (=> (= Ba (tptp.hAPP_nat_int F X_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Ba) (tptp.image_nat_int F A)))))) (forall ((F tptp.fun_int_fun_int_int) (A tptp.fun_int_bool)) (= (tptp.hAPP_f1594865479ol_int (tptp.finite_fold1_int F) A) (tptp.hAPP_f1594865479ol_int tptp.the_int (tptp.finite_fold1Set_int F A)))) (forall ((F tptp.fun_Ho483360497iple_a) (A tptp.fun_Ho882550911a_bool)) (= (tptp.hAPP_f2009966983iple_a (tptp.finite2092228073iple_a F) A) (tptp.hAPP_f2009966983iple_a tptp.the_Ho1456473914iple_a (tptp.finite100168025iple_a F A)))) (forall ((F tptp.fun_nat_fun_nat_nat) (A tptp.fun_nat_bool)) (= (tptp.hAPP_f22106695ol_nat (tptp.finite_fold1_nat F) A) (tptp.hAPP_f22106695ol_nat tptp.the_nat (tptp.finite_fold1Set_nat F A)))) (forall ((Vname_1 tptp.vname) (Fun_1 tptp.fun_state_nat) (Vname tptp.vname) (Fun tptp.fun_state_nat)) (= (= (tptp.ass Vname_1 Fun_1) (tptp.ass Vname Fun)) (and (= Vname_1 Vname) (= Fun_1 Fun)))) (forall ((Ba tptp.hoare_2076525193iple_a) (F tptp.fun_Ho1518252029iple_a) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A)) (=> (= Ba (tptp.hAPP_H1789220885iple_a F X_1)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a Ba) (tptp.image_1416816325iple_a F A)))))) (forall ((Ba tptp.hoare_2076525193iple_a) (F tptp.fun_na1240513468iple_a) (X_1 tptp.nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (=> (= Ba (tptp.hAPP_n887873492iple_a F X_1)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a Ba) (tptp.image_344477316iple_a F A)))))) (forall ((Ba tptp.hoare_2076525193iple_a) (F tptp.fun_in1219646560iple_a) (X_1 tptp.int) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (=> (= Ba (tptp.hAPP_i867006584iple_a F X_1)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a Ba) (tptp.image_323610408iple_a F A)))))) (forall ((Ba tptp.nat) (F tptp.fun_Ho864122878_a_nat) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A)) (=> (= Ba (tptp.hAPP_H174304918_a_nat F X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Ba) (tptp.image_1778392390_a_nat F A)))))) (forall ((Ba tptp.int) (F tptp.fun_int_int) (X_1 tptp.int) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (=> (= Ba (tptp.hAPP_int_int F X_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Ba) (tptp.image_int_int F A)))))) (forall ((Ba tptp.int) (F tptp.fun_Ho1026035802_a_int) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A)) (=> (= Ba (tptp.hAPP_H811578610_a_int F X_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Ba) (tptp.image_268182434_a_int F A)))))) (forall ((Ba tptp.nat) (F tptp.fun_nat_nat) (X_1 tptp.nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (=> (= Ba (tptp.hAPP_nat_nat F X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Ba) (tptp.image_nat_nat F A)))))) (forall ((Ba tptp.int) (F tptp.fun_nat_int) (X_1 tptp.nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (=> (= Ba (tptp.hAPP_nat_int F X_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Ba) (tptp.image_nat_int F A)))))) (forall ((F tptp.fun_Ho1518252029iple_a) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a (tptp.hAPP_H1789220885iple_a F X_1)) (tptp.image_1416816325iple_a F A))))) (forall ((F tptp.fun_na1240513468iple_a) (X_1 tptp.nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a (tptp.hAPP_n887873492iple_a F X_1)) (tptp.image_344477316iple_a F A))))) (forall ((F tptp.fun_in1219646560iple_a) (X_1 tptp.int) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a (tptp.hAPP_i867006584iple_a F X_1)) (tptp.image_323610408iple_a F A))))) (forall ((F tptp.fun_Ho864122878_a_nat) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_H174304918_a_nat F X_1)) (tptp.image_1778392390_a_nat F A))))) (forall ((F tptp.fun_int_int) (X_1 tptp.int) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_int_int F X_1)) (tptp.image_int_int F A))))) (forall ((F tptp.fun_Ho1026035802_a_int) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_H811578610_a_int F X_1)) (tptp.image_268182434_a_int F A))))) (forall ((F tptp.fun_nat_nat) (X_1 tptp.nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_nat_nat F X_1)) (tptp.image_nat_nat F A))))) (forall ((F tptp.fun_nat_int) (X_1 tptp.nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_nat_int F X_1)) (tptp.image_nat_int F A))))) (forall ((Z_1 tptp.hoare_2076525193iple_a) (F tptp.fun_Ho1518252029iple_a) (A tptp.fun_Ho882550911a_bool)) (= (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a Z_1) (tptp.image_1416816325iple_a F A))) (exists ((X_2 tptp.hoare_2076525193iple_a)) (and (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_2) A)) (= Z_1 (tptp.hAPP_H1789220885iple_a F X_2)))))) (forall ((Z_1 tptp.int) (F tptp.fun_int_int) (A tptp.fun_int_bool)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Z_1) (tptp.image_int_int F A))) (exists ((X_2 tptp.int)) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) A)) (= Z_1 (tptp.hAPP_int_int F X_2)))))) (forall ((Z_1 tptp.nat) (F tptp.fun_nat_nat) (A tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Z_1) (tptp.image_nat_nat F A))) (exists ((X_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (= Z_1 (tptp.hAPP_nat_nat F X_2)))))) (forall ((Z_1 tptp.int) (F tptp.fun_nat_int) (A tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Z_1) (tptp.image_nat_int F A))) (exists ((X_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (= Z_1 (tptp.hAPP_nat_int F X_2)))))) (forall ((F tptp.fun_nat_int) (G tptp.fun_int_nat) (A tptp.fun_int_bool)) (= (tptp.image_nat_int F (tptp.image_int_nat G A)) (tptp.image_int_int (tptp.hAPP_f147134065nt_int (tptp.hAPP_f1673907925nt_int tptp.cOMBB_nat_int_int F) G) A))) (forall ((F tptp.fun_int_int) (G tptp.fun_nat_int) (A tptp.fun_nat_bool)) (= (tptp.image_int_int F (tptp.image_nat_int G A)) (tptp.image_nat_int (tptp.hAPP_f1139079189at_int (tptp.hAPP_f1431025877at_int tptp.cOMBB_int_int_nat F) G) A))) (forall ((Y_23 tptp.fun_int_bool)) (= (tptp.image_int_int tptp.cOMBI_int Y_23) Y_23)) (forall ((Y_23 tptp.fun_Ho882550911a_bool)) (= (tptp.image_1416816325iple_a tptp.cOMBI_1928055558iple_a Y_23) Y_23)) (forall ((Y_23 tptp.fun_nat_bool)) (= (tptp.image_nat_nat tptp.cOMBI_nat Y_23) Y_23)) (forall ((Vname_1 tptp.vname) (Fun_1 tptp.fun_state_nat) (Com1 tptp.com) (Com2 tptp.com)) (not (= (tptp.ass Vname_1 Fun_1) (tptp.semi Com1 Com2)))) (forall ((Com1 tptp.com) (Com2 tptp.com) (Vname_1 tptp.vname) (Fun_1 tptp.fun_state_nat)) (not (= (tptp.semi Com1 Com2) (tptp.ass Vname_1 Fun_1)))) (forall ((Vname tptp.vname) (Fun tptp.fun_state_nat)) (not (= tptp.skip (tptp.ass Vname Fun)))) (forall ((X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (= (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A)) (tptp.hBOOL (tptp.hAPP_H454055633a_bool A X_1)))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (tptp.hBOOL (tptp.hAPP_nat_bool A X_1)))) (forall ((X_1 tptp.int) (A tptp.fun_int_bool)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (tptp.hBOOL (tptp.hAPP_int_bool A X_1)))) _let_12 (forall ((Pa tptp.fun_Ho882550911a_bool)) (= (tptp.hAPP_f642208769a_bool tptp.collec977865374iple_a Pa) Pa)) (forall ((Pa tptp.fun_nat_bool)) (= (tptp.hAPP_f800510211t_bool tptp.collect_nat Pa) Pa)) (forall ((Vname tptp.vname) (Fun tptp.fun_state_nat)) (not (= (tptp.ass Vname Fun) tptp.skip))) (forall ((F tptp.fun_Ho1518252029iple_a) (A tptp.fun_Ho882550911a_bool)) (= (= (tptp.image_1416816325iple_a F A) tptp.bot_bo214064617a_bool) (= A tptp.bot_bo214064617a_bool))) (forall ((F tptp.fun_int_int) (A tptp.fun_int_bool)) (= (= (tptp.image_int_int F A) tptp.bot_bot_fun_int_bool) (= A tptp.bot_bot_fun_int_bool))) (forall ((F tptp.fun_nat_nat) (A tptp.fun_nat_bool)) (= (= (tptp.image_nat_nat F A) tptp.bot_bot_fun_nat_bool) (= A tptp.bot_bot_fun_nat_bool))) (forall ((F tptp.fun_nat_int) (A tptp.fun_nat_bool)) (= (= (tptp.image_nat_int F A) tptp.bot_bot_fun_int_bool) (= A tptp.bot_bot_fun_nat_bool))) (forall ((F tptp.fun_Ho1518252029iple_a)) (= (tptp.image_1416816325iple_a F tptp.bot_bo214064617a_bool) tptp.bot_bo214064617a_bool)) (forall ((F tptp.fun_int_int)) (= (tptp.image_int_int F tptp.bot_bot_fun_int_bool) tptp.bot_bot_fun_int_bool)) (forall ((F tptp.fun_nat_nat)) (= (tptp.image_nat_nat F tptp.bot_bot_fun_nat_bool) tptp.bot_bot_fun_nat_bool)) (forall ((F tptp.fun_nat_int)) (= (tptp.image_nat_int F tptp.bot_bot_fun_nat_bool) tptp.bot_bot_fun_int_bool)) (forall ((F tptp.fun_Ho1518252029iple_a) (A tptp.fun_Ho882550911a_bool)) (= (= tptp.bot_bo214064617a_bool (tptp.image_1416816325iple_a F A)) (= A tptp.bot_bo214064617a_bool))) (forall ((F tptp.fun_int_int) (A tptp.fun_int_bool)) (= (= tptp.bot_bot_fun_int_bool (tptp.image_int_int F A)) (= A tptp.bot_bot_fun_int_bool))) (forall ((F tptp.fun_nat_nat) (A tptp.fun_nat_bool)) (= (= tptp.bot_bot_fun_nat_bool (tptp.image_nat_nat F A)) (= A tptp.bot_bot_fun_nat_bool))) (forall ((F tptp.fun_nat_int) (A tptp.fun_nat_bool)) (= (= tptp.bot_bot_fun_int_bool (tptp.image_nat_int F A)) (= A tptp.bot_bot_fun_nat_bool))) (forall ((F tptp.fun_int_nat) (X_1 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.image_int_nat F A))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat (tptp.hAPP_int_nat F X_1)) _let_1) _let_1)))) (forall ((F tptp.fun_Ho1518252029iple_a) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.image_1416816325iple_a F A))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A)) (= (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a (tptp.hAPP_H1789220885iple_a F X_1)) _let_1) _let_1)))) (forall ((F tptp.fun_int_int) (X_1 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.image_int_int F A))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int (tptp.hAPP_int_int F X_1)) _let_1) _let_1)))) (forall ((F tptp.fun_Ho1026035802_a_int) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.image_268182434_a_int F A))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A)) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int (tptp.hAPP_H811578610_a_int F X_1)) _let_1) _let_1)))) (forall ((F tptp.fun_nat_nat) (X_1 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.image_nat_nat F A))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat (tptp.hAPP_nat_nat F X_1)) _let_1) _let_1)))) (forall ((F tptp.fun_nat_int) (X_1 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.image_nat_int F A))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int (tptp.hAPP_nat_int F X_1)) _let_1) _let_1)))) (forall ((F tptp.fun_Ho864122878_a_nat) (A_13 tptp.hoare_2076525193iple_a) (B tptp.fun_Ho882550911a_bool)) (= (tptp.image_1778392390_a_nat F (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) B)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat (tptp.hAPP_H174304918_a_nat F A_13)) (tptp.image_1778392390_a_nat F B)))) (forall ((F tptp.fun_int_nat) (A_13 tptp.int) (B tptp.fun_int_bool)) (= (tptp.image_int_nat F (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) B)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat (tptp.hAPP_int_nat F A_13)) (tptp.image_int_nat F B)))) (forall ((F tptp.fun_Ho1518252029iple_a) (A_13 tptp.hoare_2076525193iple_a) (B tptp.fun_Ho882550911a_bool)) (= (tptp.image_1416816325iple_a F (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) B)) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a (tptp.hAPP_H1789220885iple_a F A_13)) (tptp.image_1416816325iple_a F B)))) (forall ((F tptp.fun_na1240513468iple_a) (A_13 tptp.nat) (B tptp.fun_nat_bool)) (= (tptp.image_344477316iple_a F (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) B)) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a (tptp.hAPP_n887873492iple_a F A_13)) (tptp.image_344477316iple_a F B)))) (forall ((F tptp.fun_int_int) (A_13 tptp.int) (B tptp.fun_int_bool)) (= (tptp.image_int_int F (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) B)) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int (tptp.hAPP_int_int F A_13)) (tptp.image_int_int F B)))) (forall ((F tptp.fun_nat_nat) (A_13 tptp.nat) (B tptp.fun_nat_bool)) (= (tptp.image_nat_nat F (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) B)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat (tptp.hAPP_nat_nat F A_13)) (tptp.image_nat_nat F B)))) (forall ((F tptp.fun_nat_int) (A_13 tptp.nat) (B tptp.fun_nat_bool)) (= (tptp.image_nat_int F (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) B)) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int (tptp.hAPP_nat_int F A_13)) (tptp.image_nat_int F B)))) (forall ((F tptp.fun_Ho483360497iple_a) (A tptp.fun_Ho882550911a_bool) (X_1 tptp.hoare_2076525193iple_a)) (=> (tptp.hBOOL (tptp.hAPP_H454055633a_bool (tptp.finite100168025iple_a F A) X_1)) (not (= A tptp.bot_bo214064617a_bool)))) (forall ((F tptp.fun_int_fun_int_int) (A tptp.fun_int_bool) (X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.finite_fold1Set_int F A) X_1)) (not (= A tptp.bot_bot_fun_int_bool)))) (forall ((F tptp.fun_nat_fun_nat_nat) (A tptp.fun_nat_bool) (X_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.finite_fold1Set_nat F A) X_1)) (not (= A tptp.bot_bot_fun_nat_bool)))) (forall ((F tptp.fun_Ho483360497iple_a) (X_1 tptp.hoare_2076525193iple_a)) (not (tptp.hBOOL (tptp.hAPP_H454055633a_bool (tptp.finite100168025iple_a F tptp.bot_bo214064617a_bool) X_1)))) (forall ((F tptp.fun_int_fun_int_int) (X_1 tptp.int)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.finite_fold1Set_int F tptp.bot_bot_fun_int_bool) X_1)))) (forall ((F tptp.fun_nat_fun_nat_nat) (X_1 tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.finite_fold1Set_nat F tptp.bot_bot_fun_nat_bool) X_1)))) (forall ((Ca tptp.nat) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A)) (= (tptp.image_1778392390_a_nat (tptp.hAPP_n1236213193_a_nat tptp.cOMBK_1654814733iple_a Ca) A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Ca) tptp.bot_bot_fun_nat_bool)))) (forall ((Ca tptp.nat) (X_1 tptp.int) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (= (tptp.image_int_nat (tptp.hAPP_nat_fun_int_nat tptp.cOMBK_nat_int Ca) A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Ca) tptp.bot_bot_fun_nat_bool)))) (forall ((Ca tptp.hoare_2076525193iple_a) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A)) (= (tptp.image_1416816325iple_a (tptp.hAPP_H1417936777iple_a tptp.cOMBK_788297294iple_a Ca) A) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a Ca) tptp.bot_bo214064617a_bool)))) (forall ((Ca tptp.int) (X_1 tptp.int) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (= (tptp.image_int_int (tptp.hAPP_int_fun_int_int tptp.cOMBK_int_int Ca) A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int Ca) tptp.bot_bot_fun_int_bool)))) (forall ((Ca tptp.int) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A)) (= (tptp.image_268182434_a_int (tptp.hAPP_i1058170057_a_int tptp.cOMBK_1633947825iple_a Ca) A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int Ca) tptp.bot_bot_fun_int_bool)))) (forall ((Ca tptp.nat) (X_1 tptp.nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (= (tptp.image_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.cOMBK_nat_nat Ca) A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Ca) tptp.bot_bot_fun_nat_bool)))) (forall ((Ca tptp.int) (X_1 tptp.nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (= (tptp.image_nat_int (tptp.hAPP_int_fun_nat_int tptp.cOMBK_int_nat Ca) A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int Ca) tptp.bot_bot_fun_int_bool)))) (forall ((Ba tptp.hoare_2076525193iple_a) (F tptp.fun_Ho1518252029iple_a) (A tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a Ba) (tptp.image_1416816325iple_a F A))) (not (forall ((X_2 tptp.hoare_2076525193iple_a)) (=> (= Ba (tptp.hAPP_H1789220885iple_a F X_2)) (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_2) A)))))))) (forall ((Ba tptp.nat) (F tptp.fun_Ho864122878_a_nat) (A tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Ba) (tptp.image_1778392390_a_nat F A))) (not (forall ((X_2 tptp.hoare_2076525193iple_a)) (=> (= Ba (tptp.hAPP_H174304918_a_nat F X_2)) (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_2) A)))))))) (forall ((Ba tptp.int) (F tptp.fun_Ho1026035802_a_int) (A tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Ba) (tptp.image_268182434_a_int F A))) (not (forall ((X_2 tptp.hoare_2076525193iple_a)) (=> (= Ba (tptp.hAPP_H811578610_a_int F X_2)) (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_2) A)))))))) (forall ((Ba tptp.hoare_2076525193iple_a) (F tptp.fun_na1240513468iple_a) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a Ba) (tptp.image_344477316iple_a F A))) (not (forall ((X_2 tptp.nat)) (=> (= Ba (tptp.hAPP_n887873492iple_a F X_2)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)))))))) (forall ((Ba tptp.int) (F tptp.fun_int_int) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Ba) (tptp.image_int_int F A))) (not (forall ((X_2 tptp.int)) (=> (= Ba (tptp.hAPP_int_int F X_2)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) A)))))))) (forall ((Ba tptp.hoare_2076525193iple_a) (F tptp.fun_in1219646560iple_a) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a Ba) (tptp.image_323610408iple_a F A))) (not (forall ((X_2 tptp.int)) (=> (= Ba (tptp.hAPP_i867006584iple_a F X_2)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) A)))))))) (forall ((Ba tptp.nat) (F tptp.fun_nat_nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Ba) (tptp.image_nat_nat F A))) (not (forall ((X_2 tptp.nat)) (=> (= Ba (tptp.hAPP_nat_nat F X_2)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)))))))) (forall ((Ba tptp.int) (F tptp.fun_nat_int) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Ba) (tptp.image_nat_int F A))) (not (forall ((X_2 tptp.nat)) (=> (= Ba (tptp.hAPP_nat_int F X_2)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)))))))) (forall ((X_1 tptp.int)) (= (tptp.hAPP_f1594865479ol_int tptp.the_int (tptp.hAPP_i1948725293t_bool tptp.fequal_int X_1)) X_1)) (forall ((X_1 tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_f2009966983iple_a tptp.the_Ho1456473914iple_a (tptp.hAPP_H2077279219a_bool tptp.fequal1589671816iple_a X_1)) X_1)) (forall ((X_1 tptp.nat)) (= (tptp.hAPP_f22106695ol_nat tptp.the_nat (tptp.hAPP_n1699378549t_bool tptp.fequal_nat X_1)) X_1)) (forall ((A_13 tptp.int)) (= (tptp.hAPP_f1594865479ol_int tptp.the_int (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool tptp.fequal_int) A_13)) A_13)) (forall ((A_13 tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_f2009966983iple_a tptp.the_Ho1456473914iple_a (tptp.hAPP_H2077279219a_bool (tptp.hAPP_f877684549a_bool tptp.cOMBC_1047656090a_bool tptp.fequal1589671816iple_a) A_13)) A_13)) (forall ((A_13 tptp.nat)) (= (tptp.hAPP_f22106695ol_nat tptp.the_nat (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.fequal_nat) A_13)) A_13)) (forall ((X_1 tptp.int) (Y_1 tptp.int) (Pa tptp.bool)) (let ((_let_1 (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool tptp.fequal_int))) (let ((_let_2 (tptp.hAPP_f1594865479ol_int tptp.the_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f627970963t_bool tptp.cOMBB_bool_bool_int (tptp.hAPP_b589554111l_bool tptp.fimplies Pa)) (tptp.hAPP_i1948725293t_bool _let_1 X_1)))) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f627970963t_bool tptp.cOMBB_bool_bool_int (tptp.hAPP_b589554111l_bool tptp.fimplies (tptp.hAPP_bool_bool tptp.fNot Pa))) (tptp.hAPP_i1948725293t_bool _let_1 Y_1)))))) (let ((_let_3 (tptp.hBOOL Pa))) (and (=> _let_3 (= X_1 _let_2)) (=> (not _let_3) (= Y_1 _let_2))))))) (forall ((X_1 tptp.hoare_2076525193iple_a) (Y_1 tptp.hoare_2076525193iple_a) (Pa tptp.bool)) (let ((_let_1 (tptp.hAPP_f877684549a_bool tptp.cOMBC_1047656090a_bool tptp.fequal1589671816iple_a))) (let ((_let_2 (tptp.hAPP_f2009966983iple_a tptp.the_Ho1456473914iple_a (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1004093413a_bool tptp.cOMBS_1108095524l_bool (tptp.hAPP_f268025233l_bool (tptp.hAPP_f1261090107l_bool tptp.cOMBB_345279363iple_a tptp.fconj) (tptp.hAPP_f642208769a_bool (tptp.hAPP_f629438041a_bool tptp.cOMBB_361863589iple_a (tptp.hAPP_b589554111l_bool tptp.fimplies Pa)) (tptp.hAPP_H2077279219a_bool _let_1 X_1)))) (tptp.hAPP_f642208769a_bool (tptp.hAPP_f629438041a_bool tptp.cOMBB_361863589iple_a (tptp.hAPP_b589554111l_bool tptp.fimplies (tptp.hAPP_bool_bool tptp.fNot Pa))) (tptp.hAPP_H2077279219a_bool _let_1 Y_1)))))) (let ((_let_3 (tptp.hBOOL Pa))) (and (=> _let_3 (= X_1 _let_2)) (=> (not _let_3) (= Y_1 _let_2))))))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat) (Pa tptp.bool)) (let ((_let_1 (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.fequal_nat))) (let ((_let_2 (tptp.hAPP_f22106695ol_nat tptp.the_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fconj) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f894608603t_bool tptp.cOMBB_bool_bool_nat (tptp.hAPP_b589554111l_bool tptp.fimplies Pa)) (tptp.hAPP_n1699378549t_bool _let_1 X_1)))) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f894608603t_bool tptp.cOMBB_bool_bool_nat (tptp.hAPP_b589554111l_bool tptp.fimplies (tptp.hAPP_bool_bool tptp.fNot Pa))) (tptp.hAPP_n1699378549t_bool _let_1 Y_1)))))) (let ((_let_3 (tptp.hBOOL Pa))) (and (=> _let_3 (= X_1 _let_2)) (=> (not _let_3) (= Y_1 _let_2))))))) (forall ((F tptp.fun_Ho1518252029iple_a) (G tptp.fun_Ho1518252029iple_a) (M_3 tptp.fun_Ho882550911a_bool) (N_3 tptp.fun_Ho882550911a_bool)) (=> (= M_3 N_3) (=> (forall ((X_2 tptp.hoare_2076525193iple_a)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_2) N_3)) (= (tptp.hAPP_H1789220885iple_a F X_2) (tptp.hAPP_H1789220885iple_a G X_2)))) (= (tptp.image_1416816325iple_a F M_3) (tptp.image_1416816325iple_a G N_3))))) (forall ((F tptp.fun_int_int) (G tptp.fun_int_int) (M_3 tptp.fun_int_bool) (N_3 tptp.fun_int_bool)) (=> (= M_3 N_3) (=> (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) N_3)) (= (tptp.hAPP_int_int F X_2) (tptp.hAPP_int_int G X_2)))) (= (tptp.image_int_int F M_3) (tptp.image_int_int G N_3))))) (forall ((F tptp.fun_nat_nat) (G tptp.fun_nat_nat) (M_3 tptp.fun_nat_bool) (N_3 tptp.fun_nat_bool)) (=> (= M_3 N_3) (=> (forall ((X_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) N_3)) (= (tptp.hAPP_nat_nat F X_2) (tptp.hAPP_nat_nat G X_2)))) (= (tptp.image_nat_nat F M_3) (tptp.image_nat_nat G N_3))))) (forall ((F tptp.fun_nat_int) (G tptp.fun_nat_int) (M_3 tptp.fun_nat_bool) (N_3 tptp.fun_nat_bool)) (=> (= M_3 N_3) (=> (forall ((X_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) N_3)) (= (tptp.hAPP_nat_int F X_2) (tptp.hAPP_nat_int G X_2)))) (= (tptp.image_nat_int F M_3) (tptp.image_nat_int G N_3))))) (forall ((F tptp.fun_nat_fun_nat_nat) (A_13 tptp.nat) (A tptp.fun_nat_bool) (X_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool (tptp.finite929467206at_nat F) A_13) A) X_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_13) A))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.finite_fold1Set_nat F (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) A)) X_1))))) (forall ((F tptp.fun_Ho483360497iple_a) (A_13 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (X_1 tptp.hoare_2076525193iple_a)) (=> (tptp.hBOOL (tptp.hAPP_H454055633a_bool (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool (tptp.finite974267142iple_a F) A_13) A) X_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a A_13) A))) (tptp.hBOOL (tptp.hAPP_H454055633a_bool (tptp.finite100168025iple_a F (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) A)) X_1))))) (forall ((F tptp.fun_int_fun_int_int) (A_13 tptp.int) (A tptp.fun_int_bool) (X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool (tptp.finite772772422nt_int F) A_13) A) X_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_13) A))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.finite_fold1Set_int F (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) A)) X_1))))) (forall ((Pa tptp.fun_int_bool) (A_13 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa A_13)) (=> (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa X_2)) (= X_2 A_13))) (= (tptp.hAPP_f1594865479ol_int tptp.the_int Pa) A_13)))) (forall ((Pa tptp.fun_Ho882550911a_bool) (A_13 tptp.hoare_2076525193iple_a)) (=> (tptp.hBOOL (tptp.hAPP_H454055633a_bool Pa A_13)) (=> (forall ((X_2 tptp.hoare_2076525193iple_a)) (=> (tptp.hBOOL (tptp.hAPP_H454055633a_bool Pa X_2)) (= X_2 A_13))) (= (tptp.hAPP_f2009966983iple_a tptp.the_Ho1456473914iple_a Pa) A_13)))) (forall ((Pa tptp.fun_nat_bool) (A_13 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa A_13)) (=> (forall ((X_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa X_2)) (= X_2 A_13))) (= (tptp.hAPP_f22106695ol_nat tptp.the_nat Pa) A_13)))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool) (F tptp.fun_nat_fun_nat_nat) (F_1 tptp.fun_fun_nat_bool_nat)) (=> (tptp.hBOOL (tptp.finite988810631ne_nat F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A))) (=> (not (= A tptp.bot_bot_fun_nat_bool)) (= (tptp.hAPP_f22106695ol_nat F_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F X_1) (tptp.hAPP_f22106695ol_nat F_1 A)))))))) (forall ((X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (F tptp.fun_Ho483360497iple_a) (F_1 tptp.fun_fu253747899iple_a)) (=> (tptp.hBOOL (tptp.finite232328454iple_a F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (=> (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A))) (=> (not (= A tptp.bot_bo214064617a_bool)) (= (tptp.hAPP_f2009966983iple_a F_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1) A)) (tptp.hAPP_H1789220885iple_a (tptp.hAPP_H1417936777iple_a F X_1) (tptp.hAPP_f2009966983iple_a F_1 A)))))))) (forall ((X_1 tptp.int) (A tptp.fun_int_bool) (F tptp.fun_int_fun_int_int) (F_1 tptp.fun_fun_int_bool_int)) (=> (tptp.hBOOL (tptp.finite1626084323ne_int F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A))) (=> (not (= A tptp.bot_bot_fun_int_bool)) (= (tptp.hAPP_f1594865479ol_int F_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int F X_1) (tptp.hAPP_f1594865479ol_int F_1 A)))))))) (forall ((A tptp.fun_Ho882550911a_bool) (F tptp.fun_Ho483360497iple_a) (F_1 tptp.fun_fu253747899iple_a)) (=> (tptp.hBOOL (tptp.finite232328454iple_a F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (= (tptp.hAPP_f2009966983iple_a F_1 A) (tptp.hAPP_f2009966983iple_a (tptp.finite2092228073iple_a F) A))))) (forall ((A tptp.fun_nat_bool) (F tptp.fun_nat_fun_nat_nat) (F_1 tptp.fun_fun_nat_bool_nat)) (=> (tptp.hBOOL (tptp.finite988810631ne_nat F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_f22106695ol_nat F_1 A) (tptp.hAPP_f22106695ol_nat (tptp.finite_fold1_nat F) A))))) (forall ((A tptp.fun_int_bool) (F tptp.fun_int_fun_int_int) (F_1 tptp.fun_fun_int_bool_int)) (=> (tptp.hBOOL (tptp.finite1626084323ne_int F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (= (tptp.hAPP_f1594865479ol_int F_1 A) (tptp.hAPP_f1594865479ol_int (tptp.finite_fold1_int F) A))))) (forall ((A tptp.fun_nat_bool) (F tptp.fun_nat_fun_nat_nat) (F_1 tptp.fun_fun_nat_bool_nat)) (=> (tptp.hBOOL (tptp.finite988810631ne_nat F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (= A tptp.bot_bot_fun_nat_bool)) (=> (forall ((X_2 tptp.nat) (Y_21 tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F X_2) Y_21)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_2) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Y_21) tptp.bot_bot_fun_nat_bool))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_f22106695ol_nat F_1 A)) A))))))) (forall ((A tptp.fun_Ho882550911a_bool) (F tptp.fun_Ho483360497iple_a) (F_1 tptp.fun_fu253747899iple_a)) (=> (tptp.hBOOL (tptp.finite232328454iple_a F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (=> (not (= A tptp.bot_bo214064617a_bool)) (=> (forall ((X_2 tptp.hoare_2076525193iple_a) (Y_21 tptp.hoare_2076525193iple_a)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a (tptp.hAPP_H1789220885iple_a (tptp.hAPP_H1417936777iple_a F X_2) Y_21)) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_2) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a Y_21) tptp.bot_bo214064617a_bool))))) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a (tptp.hAPP_f2009966983iple_a F_1 A)) A))))))) (forall ((A tptp.fun_int_bool) (F tptp.fun_int_fun_int_int) (F_1 tptp.fun_fun_int_bool_int)) (=> (tptp.hBOOL (tptp.finite1626084323ne_int F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (not (= A tptp.bot_bot_fun_int_bool)) (=> (forall ((X_2 tptp.int) (Y_21 tptp.int)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int F X_2) Y_21)) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_2) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int Y_21) tptp.bot_bot_fun_int_bool))))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_f1594865479ol_int F_1 A)) A))))))) (forall ((Q_1 tptp.fun_Ho882550911a_bool) (Pa tptp.fun_Ho882550911a_bool)) (=> (or (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a (tptp.hAPP_f642208769a_bool tptp.collec977865374iple_a Pa))) (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a (tptp.hAPP_f642208769a_bool tptp.collec977865374iple_a Q_1)))) (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a (tptp.hAPP_f642208769a_bool tptp.collec977865374iple_a (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1004093413a_bool tptp.cOMBS_1108095524l_bool (tptp.hAPP_f268025233l_bool (tptp.hAPP_f1261090107l_bool tptp.cOMBB_345279363iple_a tptp.fconj) Pa)) Q_1)))))) (forall ((Q_1 tptp.fun_int_bool) (Pa tptp.fun_int_bool)) (=> (or (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.hAPP_f1805168059t_bool tptp.collect_int Pa))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.hAPP_f1805168059t_bool tptp.collect_int Q_1)))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.hAPP_f1805168059t_bool tptp.collect_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) Pa)) Q_1)))))) (forall ((Q_1 tptp.fun_nat_bool) (Pa tptp.fun_nat_bool)) (=> (or (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool tptp.collect_nat Pa))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool tptp.collect_nat Q_1)))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fconj) Pa)) Q_1)))))) (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a tptp.bot_bo214064617a_bool)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat tptp.bot_bot_fun_nat_bool)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int tptp.bot_bot_fun_int_bool)) (forall ((A_13 tptp.nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) A))))) (forall ((A_13 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) A))))) (forall ((A_13 tptp.int) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) A))))) (forall ((H tptp.fun_Ho1518252029iple_a) (F_1 tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a F_1)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a (tptp.image_1416816325iple_a H F_1))))) (forall ((H tptp.fun_na1240513468iple_a) (F_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F_1)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a (tptp.image_344477316iple_a H F_1))))) (forall ((H tptp.fun_in1219646560iple_a) (F_1 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int F_1)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a (tptp.image_323610408iple_a H F_1))))) (forall ((H tptp.fun_Ho864122878_a_nat) (F_1 tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a F_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.image_1778392390_a_nat H F_1))))) (forall ((H tptp.fun_int_int) (F_1 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int F_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.image_int_int H F_1))))) (forall ((H tptp.fun_Ho1026035802_a_int) (F_1 tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a F_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.image_268182434_a_int H F_1))))) (forall ((H tptp.fun_nat_nat) (F_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.image_nat_nat H F_1))))) (forall ((H tptp.fun_nat_int) (F_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.image_nat_int H F_1))))) (forall ((Pa tptp.fun_Ho882550911a_bool) (Q_1 tptp.fun_Ho882550911a_bool)) (= (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a (tptp.hAPP_f642208769a_bool tptp.collec977865374iple_a (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1004093413a_bool tptp.cOMBS_1108095524l_bool (tptp.hAPP_f268025233l_bool (tptp.hAPP_f1261090107l_bool tptp.cOMBB_345279363iple_a tptp.fdisj) Pa)) Q_1)))) (and (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a (tptp.hAPP_f642208769a_bool tptp.collec977865374iple_a Pa))) (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a (tptp.hAPP_f642208769a_bool tptp.collec977865374iple_a Q_1)))))) (forall ((Pa tptp.fun_int_bool) (Q_1 tptp.fun_int_bool)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.hAPP_f1805168059t_bool tptp.collect_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fdisj) Pa)) Q_1)))) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.hAPP_f1805168059t_bool tptp.collect_int Pa))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.hAPP_f1805168059t_bool tptp.collect_int Q_1)))))) (forall ((Pa tptp.fun_nat_bool) (Q_1 tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fdisj) Pa)) Q_1)))) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool tptp.collect_nat Pa))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool tptp.collect_nat Q_1)))))) (forall ((A_13 tptp.nat) (A tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) A))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)))) (forall ((A_13 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (= (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) A))) (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)))) (forall ((A_13 tptp.int) (A tptp.fun_int_bool)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) A))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)))) (forall ((F tptp.fun_Ho483360497iple_a) (Z_1 tptp.hoare_2076525193iple_a)) (tptp.hBOOL (tptp.hAPP_H454055633a_bool (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool (tptp.finite974267142iple_a F) Z_1) tptp.bot_bo214064617a_bool) Z_1))) (forall ((F tptp.fun_int_fun_int_int) (Z_1 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool (tptp.finite772772422nt_int F) Z_1) tptp.bot_bot_fun_int_bool) Z_1))) (forall ((F tptp.fun_nat_fun_nat_nat) (Z_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool (tptp.finite929467206at_nat F) Z_1) tptp.bot_bot_fun_nat_bool) Z_1))) (forall ((F tptp.fun_Ho483360497iple_a) (Z_1 tptp.hoare_2076525193iple_a) (X_1 tptp.hoare_2076525193iple_a)) (=> (tptp.hBOOL (tptp.hAPP_H454055633a_bool (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool (tptp.finite974267142iple_a F) Z_1) tptp.bot_bo214064617a_bool) X_1)) (= X_1 Z_1))) (forall ((F tptp.fun_int_fun_int_int) (Z_1 tptp.int) (X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool (tptp.finite772772422nt_int F) Z_1) tptp.bot_bot_fun_int_bool) X_1)) (= X_1 Z_1))) (forall ((F tptp.fun_nat_fun_nat_nat) (Z_1 tptp.nat) (X_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool (tptp.finite929467206at_nat F) Z_1) tptp.bot_bot_fun_nat_bool) X_1)) (= X_1 Z_1))) (forall ((F tptp.fun_nat_fun_nat_nat) (Z_1 tptp.nat) (Y_1 tptp.nat) (X_1 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool (tptp.finite929467206at_nat F) Z_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool _let_1 A) Y_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F X_1) Y_1))))))) (forall ((F tptp.fun_Ho483360497iple_a) (Z_1 tptp.hoare_2076525193iple_a) (Y_1 tptp.hoare_2076525193iple_a) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_H1940471919a_bool (tptp.finite974267142iple_a F) Z_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A))) (=> (tptp.hBOOL (tptp.hAPP_H454055633a_bool (tptp.hAPP_f642208769a_bool _let_1 A) Y_1)) (tptp.hBOOL (tptp.hAPP_H454055633a_bool (tptp.hAPP_f642208769a_bool _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1) A)) (tptp.hAPP_H1789220885iple_a (tptp.hAPP_H1417936777iple_a F X_1) Y_1))))))) (forall ((F tptp.fun_int_fun_int_int) (Z_1 tptp.int) (Y_1 tptp.int) (X_1 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool (tptp.finite772772422nt_int F) Z_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool _let_1 A) Y_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int F X_1) Y_1))))))) (forall ((F tptp.fun_nat_fun_nat_nat) (A_13 tptp.nat) (X_28 tptp.fun_nat_bool) (X_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.finite_fold1Set_nat F (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) X_28)) X_1)) (not (forall ((A_12 tptp.nat) (A_43 tptp.fun_nat_bool)) (=> (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) X_28) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_12) A_43)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool (tptp.finite929467206at_nat F) A_12) A_43) X_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_12) A_43)))))))) (forall ((F tptp.fun_Ho483360497iple_a) (A_13 tptp.hoare_2076525193iple_a) (X_28 tptp.fun_Ho882550911a_bool) (X_1 tptp.hoare_2076525193iple_a)) (=> (tptp.hBOOL (tptp.hAPP_H454055633a_bool (tptp.finite100168025iple_a F (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) X_28)) X_1)) (not (forall ((A_12 tptp.hoare_2076525193iple_a) (A_43 tptp.fun_Ho882550911a_bool)) (=> (= (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) X_28) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_12) A_43)) (=> (tptp.hBOOL (tptp.hAPP_H454055633a_bool (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool (tptp.finite974267142iple_a F) A_12) A_43) X_1)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a A_12) A_43)))))))) (forall ((F tptp.fun_int_fun_int_int) (A_13 tptp.int) (X_28 tptp.fun_int_bool) (X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.finite_fold1Set_int F (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) X_28)) X_1)) (not (forall ((A_12 tptp.int) (A_43 tptp.fun_int_bool)) (=> (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) X_28) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_12) A_43)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool (tptp.finite772772422nt_int F) A_12) A_43) X_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_12) A_43)))))))) (forall ((F tptp.fun_Ho483360497iple_a) (A tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (=> (not (= A tptp.bot_bo214064617a_bool)) (exists ((X1 tptp.hoare_2076525193iple_a)) (tptp.hBOOL (tptp.hAPP_H454055633a_bool (tptp.finite100168025iple_a F A) X1)))))) (forall ((F tptp.fun_nat_fun_nat_nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (= A tptp.bot_bot_fun_nat_bool)) (exists ((X1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.finite_fold1Set_nat F A) X1)))))) (forall ((F tptp.fun_int_fun_int_int) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (not (= A tptp.bot_bot_fun_int_bool)) (exists ((X1 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.finite_fold1Set_int F A) X1)))))) (forall ((A_13 tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A_13)) (or (= A_13 tptp.bot_bot_fun_nat_bool) (exists ((A_43 tptp.fun_nat_bool) (A_12 tptp.nat)) (and (= A_13 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_12) A_43)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A_43))))))) (forall ((A_13 tptp.fun_Ho882550911a_bool)) (= (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A_13)) (or (= A_13 tptp.bot_bo214064617a_bool) (exists ((A_43 tptp.fun_Ho882550911a_bool) (A_12 tptp.hoare_2076525193iple_a)) (and (= A_13 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_12) A_43)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A_43))))))) (forall ((A_13 tptp.fun_int_bool)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A_13)) (or (= A_13 tptp.bot_bot_fun_int_bool) (exists ((A_43 tptp.fun_int_bool) (A_12 tptp.int)) (and (= A_13 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_12) A_43)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A_43))))))) (forall ((Pa tptp.fun_fu425979586l_bool) (F_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa tptp.bot_bot_fun_nat_bool)) (=> (forall ((X_2 tptp.nat) (F_2 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F_2)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_2) F_2))))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa F_1)))))) (forall ((Pa tptp.fun_fu2026518849l_bool) (F_1 tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a F_1)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool Pa tptp.bot_bo214064617a_bool)) (=> (forall ((X_2 tptp.hoare_2076525193iple_a) (F_2 tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a F_2)) (=> (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool Pa (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_2) F_2))))))) (tptp.hBOOL (tptp.hAPP_f500854239l_bool Pa F_1)))))) (forall ((Pa tptp.fun_fu819804446l_bool) (F_1 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int F_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa tptp.bot_bot_fun_int_bool)) (=> (forall ((X_2 tptp.int) (F_2 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int F_2)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_2) F_2))))))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa F_1)))))) (forall ((F tptp.fun_Ho1518252029iple_a) (A tptp.fun_Ho882550911a_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a (tptp.image_1416816325iple_a F A))) (exists ((X_2 tptp.hoare_2076525193iple_a)) (and (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a (tptp.hAPP_f642208769a_bool tptp.collec977865374iple_a (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1004093413a_bool tptp.cOMBS_1108095524l_bool (tptp.hAPP_f268025233l_bool (tptp.hAPP_f1261090107l_bool tptp.cOMBB_345279363iple_a tptp.fconj) (tptp.hAPP_f642208769a_bool (tptp.hAPP_f325481667a_bool tptp.cOMBC_1529670358l_bool tptp.member276146780iple_a) A))) (tptp.hAPP_H2077279219a_bool (tptp.hAPP_f877684549a_bool tptp.cOMBC_1047656090a_bool (tptp.hAPP_f1075886601a_bool (tptp.hAPP_f256103387a_bool tptp.cOMBB_135702095iple_a tptp.fequal1589671816iple_a) F)) (tptp.hAPP_H1789220885iple_a F X_2)))))))))))) (forall ((F tptp.fun_Ho864122878_a_nat) (A tptp.fun_Ho882550911a_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.image_1778392390_a_nat F A))) (exists ((X_2 tptp.hoare_2076525193iple_a)) (and (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a (tptp.hAPP_f642208769a_bool tptp.collec977865374iple_a (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1004093413a_bool tptp.cOMBS_1108095524l_bool (tptp.hAPP_f268025233l_bool (tptp.hAPP_f1261090107l_bool tptp.cOMBB_345279363iple_a tptp.fconj) (tptp.hAPP_f642208769a_bool (tptp.hAPP_f325481667a_bool tptp.cOMBC_1529670358l_bool tptp.member276146780iple_a) A))) (tptp.hAPP_n1335981428a_bool (tptp.hAPP_f1040149703a_bool tptp.cOMBC_240829083t_bool (tptp.hAPP_f570970635t_bool (tptp.hAPP_f2096737119t_bool tptp.cOMBB_2017898829iple_a tptp.fequal_nat) F)) (tptp.hAPP_H174304918_a_nat F X_2)))))))))))) (forall ((F tptp.fun_int_nat) (A tptp.fun_int_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.image_int_nat F A))) (exists ((X_2 tptp.int)) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.hAPP_f1805168059t_bool tptp.collect_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f202917053t_bool tptp.cOMBC_94739984l_bool tptp.member_int) A))) (tptp.hAPP_n1082236369t_bool (tptp.hAPP_f175561985t_bool tptp.cOMBC_int_nat_bool (tptp.hAPP_f876579787t_bool (tptp.hAPP_f2026117279t_bool tptp.cOMBB_1437810218ol_int tptp.fequal_nat) F)) (tptp.hAPP_int_nat F X_2)))))))))))) (forall ((F tptp.fun_Ho1026035802_a_int) (A tptp.fun_Ho882550911a_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.image_268182434_a_int F A))) (exists ((X_2 tptp.hoare_2076525193iple_a)) (and (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a (tptp.hAPP_f642208769a_bool tptp.collec977865374iple_a (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1004093413a_bool tptp.cOMBS_1108095524l_bool (tptp.hAPP_f268025233l_bool (tptp.hAPP_f1261090107l_bool tptp.cOMBB_345279363iple_a tptp.fconj) (tptp.hAPP_f642208769a_bool (tptp.hAPP_f325481667a_bool tptp.cOMBC_1529670358l_bool tptp.member276146780iple_a) A))) (tptp.hAPP_i28602320a_bool (tptp.hAPP_f1732083583a_bool tptp.cOMBC_1771170551t_bool (tptp.hAPP_f841024195t_bool (tptp.hAPP_f1444703951t_bool tptp.cOMBB_2132063381iple_a tptp.fequal_int) F)) (tptp.hAPP_H811578610_a_int F X_2)))))))))))) (forall ((F tptp.fun_na1240513468iple_a) (A tptp.fun_nat_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a (tptp.image_344477316iple_a F A))) (exists ((X_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fconj) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat) A))) (tptp.hAPP_H904886772t_bool (tptp.hAPP_f1460432071t_bool tptp.cOMBC_2097822937a_bool (tptp.hAPP_f1324734153a_bool (tptp.hAPP_f946563611a_bool tptp.cOMBB_315605200ol_nat tptp.fequal1589671816iple_a) F)) (tptp.hAPP_n887873492iple_a F X_2)))))))))))) (forall ((F tptp.fun_int_int) (A tptp.fun_int_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.image_int_int F A))) (exists ((X_2 tptp.int)) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.hAPP_f1805168059t_bool tptp.collect_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f202917053t_bool tptp.cOMBC_94739984l_bool tptp.member_int) A))) (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool (tptp.hAPP_f1791153283t_bool (tptp.hAPP_f1399575567t_bool tptp.cOMBB_118231410ol_int tptp.fequal_int) F)) (tptp.hAPP_int_int F X_2)))))))))))) (forall ((F tptp.fun_in1219646560iple_a) (A tptp.fun_int_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a (tptp.image_323610408iple_a F A))) (exists ((X_2 tptp.int)) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.hAPP_f1805168059t_bool tptp.collect_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f202917053t_bool tptp.cOMBC_94739984l_bool tptp.member_int) A))) (tptp.hAPP_H287744592t_bool (tptp.hAPP_f510295935t_bool tptp.cOMBC_1135948669a_bool (tptp.hAPP_f1362463689a_bool (tptp.hAPP_f438022427a_bool tptp.cOMBB_952878892ol_int tptp.fequal1589671816iple_a) F)) (tptp.hAPP_i867006584iple_a F X_2)))))))))))) (forall ((F tptp.fun_nat_nat) (A tptp.fun_nat_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.image_nat_nat F A))) (exists ((X_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fconj) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat) A))) (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool (tptp.hAPP_f618557131t_bool (tptp.hAPP_f1505651103t_bool tptp.cOMBB_800536526ol_nat tptp.fequal_nat) F)) (tptp.hAPP_nat_nat F X_2)))))))))))) (forall ((F tptp.fun_nat_int) (A tptp.fun_nat_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.image_nat_int F A))) (exists ((X_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fconj) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat) A))) (tptp.hAPP_i418383825t_bool (tptp.hAPP_f482008321t_bool tptp.cOMBC_nat_int_bool (tptp.hAPP_f1533130627t_bool (tptp.hAPP_f879109391t_bool tptp.cOMBB_1628441366ol_nat tptp.fequal_int) F)) (tptp.hAPP_nat_int F X_2)))))))))))) (forall ((F tptp.fun_Ho483360497iple_a) (Z_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (exists ((X1 tptp.hoare_2076525193iple_a)) (tptp.hBOOL (tptp.hAPP_H454055633a_bool (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool (tptp.finite974267142iple_a F) Z_1) A) X1))))) (forall ((F tptp.fun_nat_fun_nat_nat) (Z_1 tptp.nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (exists ((X1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool (tptp.finite929467206at_nat F) Z_1) A) X1))))) (forall ((F tptp.fun_int_fun_int_int) (Z_1 tptp.int) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (exists ((X1 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool (tptp.finite772772422nt_int F) Z_1) A) X1))))) (forall ((F tptp.fun_nat_fun_nat_nat) (A1 tptp.fun_nat_bool) (A2 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.finite_fold1Set_nat F A1) A2)) (exists ((A_12 tptp.nat) (A_43 tptp.fun_nat_bool) (X_2 tptp.nat)) (and (= A1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_12) A_43)) (= A2 X_2) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool (tptp.finite929467206at_nat F) A_12) A_43) X_2)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_12) A_43))))))) (forall ((F tptp.fun_Ho483360497iple_a) (A1 tptp.fun_Ho882550911a_bool) (A2 tptp.hoare_2076525193iple_a)) (= (tptp.hBOOL (tptp.hAPP_H454055633a_bool (tptp.finite100168025iple_a F A1) A2)) (exists ((A_12 tptp.hoare_2076525193iple_a) (A_43 tptp.fun_Ho882550911a_bool) (X_2 tptp.hoare_2076525193iple_a)) (and (= A1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_12) A_43)) (= A2 X_2) (tptp.hBOOL (tptp.hAPP_H454055633a_bool (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool (tptp.finite974267142iple_a F) A_12) A_43) X_2)) (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a A_12) A_43))))))) (forall ((F tptp.fun_int_fun_int_int) (A1 tptp.fun_int_bool) (A2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.finite_fold1Set_int F A1) A2)) (exists ((A_12 tptp.int) (A_43 tptp.fun_int_bool) (X_2 tptp.int)) (and (= A1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_12) A_43)) (= A2 X_2) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool (tptp.finite772772422nt_int F) A_12) A_43) X_2)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_12) A_43))))))) (forall ((Pa tptp.fun_int_bool) (A_13 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa A_13)) (=> (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa X_2)) (= X_2 A_13))) (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_f1594865479ol_int tptp.the_int Pa)))))) (forall ((Pa tptp.fun_Ho882550911a_bool) (A_13 tptp.hoare_2076525193iple_a)) (=> (tptp.hBOOL (tptp.hAPP_H454055633a_bool Pa A_13)) (=> (forall ((X_2 tptp.hoare_2076525193iple_a)) (=> (tptp.hBOOL (tptp.hAPP_H454055633a_bool Pa X_2)) (= X_2 A_13))) (tptp.hBOOL (tptp.hAPP_H454055633a_bool Pa (tptp.hAPP_f2009966983iple_a tptp.the_Ho1456473914iple_a Pa)))))) (forall ((Pa tptp.fun_nat_bool) (A_13 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa A_13)) (=> (forall ((X_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa X_2)) (= X_2 A_13))) (tptp.hBOOL (tptp.hAPP_nat_bool Pa (tptp.hAPP_f22106695ol_nat tptp.the_nat Pa)))))) (forall ((A_13 tptp.int) (Pa tptp.fun_int_bool)) (=> (exists ((X_2 tptp.int)) (and (tptp.hBOOL (tptp.hAPP_int_bool Pa X_2)) (forall ((Y_21 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa Y_21)) (= Y_21 X_2))))) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa A_13)) (= (tptp.hAPP_f1594865479ol_int tptp.the_int Pa) A_13)))) (forall ((A_13 tptp.hoare_2076525193iple_a) (Pa tptp.fun_Ho882550911a_bool)) (=> (exists ((X_2 tptp.hoare_2076525193iple_a)) (and (tptp.hBOOL (tptp.hAPP_H454055633a_bool Pa X_2)) (forall ((Y_21 tptp.hoare_2076525193iple_a)) (=> (tptp.hBOOL (tptp.hAPP_H454055633a_bool Pa Y_21)) (= Y_21 X_2))))) (=> (tptp.hBOOL (tptp.hAPP_H454055633a_bool Pa A_13)) (= (tptp.hAPP_f2009966983iple_a tptp.the_Ho1456473914iple_a Pa) A_13)))) (forall ((A_13 tptp.nat) (Pa tptp.fun_nat_bool)) (=> (exists ((X_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool Pa X_2)) (forall ((Y_21 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa Y_21)) (= Y_21 X_2))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa A_13)) (= (tptp.hAPP_f22106695ol_nat tptp.the_nat Pa) A_13)))) (forall ((Pa tptp.fun_int_bool)) (=> (exists ((X_2 tptp.int)) (and (tptp.hBOOL (tptp.hAPP_int_bool Pa X_2)) (forall ((Y_21 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa Y_21)) (= Y_21 X_2))))) (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_f1594865479ol_int tptp.the_int Pa))))) (forall ((Pa tptp.fun_Ho882550911a_bool)) (=> (exists ((X_2 tptp.hoare_2076525193iple_a)) (and (tptp.hBOOL (tptp.hAPP_H454055633a_bool Pa X_2)) (forall ((Y_21 tptp.hoare_2076525193iple_a)) (=> (tptp.hBOOL (tptp.hAPP_H454055633a_bool Pa Y_21)) (= Y_21 X_2))))) (tptp.hBOOL (tptp.hAPP_H454055633a_bool Pa (tptp.hAPP_f2009966983iple_a tptp.the_Ho1456473914iple_a Pa))))) (forall ((Pa tptp.fun_nat_bool)) (=> (exists ((X_2 tptp.nat)) (and (tptp.hBOOL (tptp.hAPP_nat_bool Pa X_2)) (forall ((Y_21 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa Y_21)) (= Y_21 X_2))))) (tptp.hBOOL (tptp.hAPP_nat_bool Pa (tptp.hAPP_f22106695ol_nat tptp.the_nat Pa))))) (forall ((F tptp.fun_nat_fun_nat_nat) (Z_1 tptp.nat) (A1 tptp.fun_nat_bool) (A2 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool (tptp.finite929467206at_nat F) Z_1) A1) A2)) (or (and (= A1 tptp.bot_bot_fun_nat_bool) (= A2 Z_1)) (exists ((X_2 tptp.nat) (A_43 tptp.fun_nat_bool) (Y_21 tptp.nat)) (and (= A1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_2) A_43)) (= A2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F X_2) Y_21)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A_43))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool (tptp.finite929467206at_nat F) Z_1) A_43) Y_21))))))) (forall ((F tptp.fun_Ho483360497iple_a) (Z_1 tptp.hoare_2076525193iple_a) (A1 tptp.fun_Ho882550911a_bool) (A2 tptp.hoare_2076525193iple_a)) (= (tptp.hBOOL (tptp.hAPP_H454055633a_bool (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool (tptp.finite974267142iple_a F) Z_1) A1) A2)) (or (and (= A1 tptp.bot_bo214064617a_bool) (= A2 Z_1)) (exists ((X_2 tptp.hoare_2076525193iple_a) (A_43 tptp.fun_Ho882550911a_bool) (Y_21 tptp.hoare_2076525193iple_a)) (and (= A1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_2) A_43)) (= A2 (tptp.hAPP_H1789220885iple_a (tptp.hAPP_H1417936777iple_a F X_2) Y_21)) (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_2) A_43))) (tptp.hBOOL (tptp.hAPP_H454055633a_bool (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool (tptp.finite974267142iple_a F) Z_1) A_43) Y_21))))))) (forall ((F tptp.fun_int_fun_int_int) (Z_1 tptp.int) (A1 tptp.fun_int_bool) (A2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool (tptp.finite772772422nt_int F) Z_1) A1) A2)) (or (and (= A1 tptp.bot_bot_fun_int_bool) (= A2 Z_1)) (exists ((X_2 tptp.int) (A_43 tptp.fun_int_bool) (Y_21 tptp.int)) (and (= A1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_2) A_43)) (= A2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int F X_2) Y_21)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) A_43))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool (tptp.finite772772422nt_int F) Z_1) A_43) Y_21))))))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool) (F tptp.fun_nat_fun_nat_nat) (F_1 tptp.fun_fun_nat_bool_nat)) (=> (tptp.hBOOL (tptp.finite795500164em_nat F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (= A tptp.bot_bot_fun_nat_bool)) (= (tptp.hAPP_f22106695ol_nat F_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F X_1) (tptp.hAPP_f22106695ol_nat F_1 A))))))) (forall ((X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (F tptp.fun_Ho483360497iple_a) (F_1 tptp.fun_fu253747899iple_a)) (=> (tptp.hBOOL (tptp.finite1659845635iple_a F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (=> (not (= A tptp.bot_bo214064617a_bool)) (= (tptp.hAPP_f2009966983iple_a F_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1) A)) (tptp.hAPP_H1789220885iple_a (tptp.hAPP_H1417936777iple_a F X_1) (tptp.hAPP_f2009966983iple_a F_1 A))))))) (forall ((X_1 tptp.int) (A tptp.fun_int_bool) (F tptp.fun_int_fun_int_int) (F_1 tptp.fun_fun_int_bool_int)) (=> (tptp.hBOOL (tptp.finite1432773856em_int F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (not (= A tptp.bot_bot_fun_int_bool)) (= (tptp.hAPP_f1594865479ol_int F_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int F X_1) (tptp.hAPP_f1594865479ol_int F_1 A))))))) (forall ((Pa tptp.fun_fu425979586l_bool) (F_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F_1)) (=> (not (= F_1 tptp.bot_bot_fun_nat_bool)) (=> (forall ((X_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_2) tptp.bot_bot_fun_nat_bool)))) (=> (forall ((X_2 tptp.nat) (F_2 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F_2)) (=> (not (= F_2 tptp.bot_bot_fun_nat_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_2) F_2)))))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa F_1))))))) (forall ((Pa tptp.fun_fu2026518849l_bool) (F_1 tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a F_1)) (=> (not (= F_1 tptp.bot_bo214064617a_bool)) (=> (forall ((X_2 tptp.hoare_2076525193iple_a)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool Pa (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_2) tptp.bot_bo214064617a_bool)))) (=> (forall ((X_2 tptp.hoare_2076525193iple_a) (F_2 tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a F_2)) (=> (not (= F_2 tptp.bot_bo214064617a_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool Pa (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_2) F_2)))))))) (tptp.hBOOL (tptp.hAPP_f500854239l_bool Pa F_1))))))) (forall ((Pa tptp.fun_fu819804446l_bool) (F_1 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int F_1)) (=> (not (= F_1 tptp.bot_bot_fun_int_bool)) (=> (forall ((X_2 tptp.int)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_2) tptp.bot_bot_fun_int_bool)))) (=> (forall ((X_2 tptp.int) (F_2 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int F_2)) (=> (not (= F_2 tptp.bot_bot_fun_int_bool)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) F_2))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_2) F_2)))))))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa F_1))))))) (forall ((A tptp.fun_Ho882550911a_bool) (F tptp.fun_Ho483360497iple_a) (F_1 tptp.fun_fu253747899iple_a)) (=> (tptp.hBOOL (tptp.big_se82156639iple_a F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (= (tptp.hAPP_f2009966983iple_a F_1 A) (tptp.hAPP_f2009966983iple_a (tptp.finite2092228073iple_a F) A))))) (forall ((A tptp.fun_nat_bool) (F tptp.fun_nat_fun_nat_nat) (F_1 tptp.fun_fun_nat_bool_nat)) (=> (tptp.hBOOL (tptp.big_se275732192ig_nat F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_f22106695ol_nat F_1 A) (tptp.hAPP_f22106695ol_nat (tptp.finite_fold1_nat F) A))))) (forall ((A tptp.fun_int_bool) (F tptp.fun_int_fun_int_int) (F_1 tptp.fun_fun_int_bool_int)) (=> (tptp.hBOOL (tptp.big_se913005884ig_int F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (= (tptp.hAPP_f1594865479ol_int F_1 A) (tptp.hAPP_f1594865479ol_int (tptp.finite_fold1_int F) A))))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool) (F tptp.fun_nat_fun_nat_nat) (F_1 tptp.fun_fun_nat_bool_nat)) (let ((_let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) tptp.bot_bot_fun_nat_bool)))) (let ((_let_2 (tptp.hAPP_f22106695ol_nat F_1 A))) (let ((_let_3 (= _let_1 tptp.bot_bot_fun_nat_bool))) (=> (tptp.hBOOL (tptp.finite988810631ne_nat F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (and (=> _let_3 (= _let_2 X_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F X_1) (tptp.hAPP_f22106695ol_nat F_1 _let_1)))))))))))) (forall ((X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (F tptp.fun_Ho483360497iple_a) (F_1 tptp.fun_fu253747899iple_a)) (let ((_let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1) tptp.bot_bo214064617a_bool)))) (let ((_let_2 (tptp.hAPP_f2009966983iple_a F_1 A))) (let ((_let_3 (= _let_1 tptp.bot_bo214064617a_bool))) (=> (tptp.hBOOL (tptp.finite232328454iple_a F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A)) (and (=> _let_3 (= _let_2 X_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_H1789220885iple_a (tptp.hAPP_H1417936777iple_a F X_1) (tptp.hAPP_f2009966983iple_a F_1 _let_1)))))))))))) (forall ((X_1 tptp.int) (A tptp.fun_int_bool) (F tptp.fun_int_fun_int_int) (F_1 tptp.fun_fun_int_bool_int)) (let ((_let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) tptp.bot_bot_fun_int_bool)))) (let ((_let_2 (tptp.hAPP_f1594865479ol_int F_1 A))) (let ((_let_3 (= _let_1 tptp.bot_bot_fun_int_bool))) (=> (tptp.hBOOL (tptp.finite1626084323ne_int F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (and (=> _let_3 (= _let_2 X_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int F X_1) (tptp.hAPP_f1594865479ol_int F_1 _let_1)))))))))))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool) (F tptp.fun_nat_fun_nat_nat) (F_1 tptp.fun_fun_nat_bool_nat)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1))) (let ((_let_2 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool _let_1 tptp.bot_bot_fun_nat_bool)))) (let ((_let_3 (tptp.hAPP_f22106695ol_nat F_1 (tptp.hAPP_f800510211t_bool _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bot_fun_nat_bool))) (=> (tptp.hBOOL (tptp.finite988810631ne_nat F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (and (=> _let_4 (= _let_3 X_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F X_1) (tptp.hAPP_f22106695ol_nat F_1 _let_2)))))))))))) (forall ((X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (F tptp.fun_Ho483360497iple_a) (F_1 tptp.fun_fu253747899iple_a)) (let ((_let_1 (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1))) (let ((_let_2 (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) (tptp.hAPP_f642208769a_bool _let_1 tptp.bot_bo214064617a_bool)))) (let ((_let_3 (tptp.hAPP_f2009966983iple_a F_1 (tptp.hAPP_f642208769a_bool _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bo214064617a_bool))) (=> (tptp.hBOOL (tptp.finite232328454iple_a F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (and (=> _let_4 (= _let_3 X_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_H1789220885iple_a (tptp.hAPP_H1417936777iple_a F X_1) (tptp.hAPP_f2009966983iple_a F_1 _let_2)))))))))))) (forall ((X_1 tptp.int) (A tptp.fun_int_bool) (F tptp.fun_int_fun_int_int) (F_1 tptp.fun_fun_int_bool_int)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1))) (let ((_let_2 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool _let_1 tptp.bot_bot_fun_int_bool)))) (let ((_let_3 (tptp.hAPP_f1594865479ol_int F_1 (tptp.hAPP_f1805168059t_bool _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bot_fun_int_bool))) (=> (tptp.hBOOL (tptp.finite1626084323ne_int F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (and (=> _let_4 (= _let_3 X_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int F X_1) (tptp.hAPP_f1594865479ol_int F_1 _let_2)))))))))))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.finite_fold1_nat tptp.times_times_nat))) (=> (not (= A tptp.bot_bot_fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A))) (= (tptp.hAPP_f22106695ol_nat _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat X_1) (tptp.hAPP_f22106695ol_nat _let_1 A)))))))) (forall ((X_1 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.finite_fold1_int tptp.times_times_int))) (=> (not (= A tptp.bot_bot_fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A))) (= (tptp.hAPP_f1594865479ol_int _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X_1) (tptp.hAPP_f1594865479ol_int _let_1 A)))))))) (forall ((B tptp.fun_Ho882550911a_bool) (Ca tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a Ca))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 B))) (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) B))))))) (forall ((B tptp.fun_nat_bool) (Ca tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat Ca))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B))))))) (forall ((B tptp.fun_int_bool) (Ca tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int Ca))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B))))))) (forall ((Ca tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (B tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a Ca))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) B))) (not (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 B))))))) (forall ((Ca tptp.nat) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat Ca))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B))) (not (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B))))))) (forall ((Ca tptp.int) (A tptp.fun_int_bool) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int Ca))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B))) (not (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B))))))) (forall ((B tptp.fun_Ho882550911a_bool) (A tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) B))))) (forall ((B tptp.fun_nat_bool) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B))))) (forall ((B tptp.fun_int_bool) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B))))) (forall ((X_1 tptp.int) (F tptp.fun_int_fun_int_int) (F_1 tptp.fun_fun_int_bool_int)) (=> (tptp.hBOOL (tptp.finite1432773856em_int F F_1)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int F X_1) X_1) X_1))) (forall ((X_1 tptp.hoare_2076525193iple_a) (F tptp.fun_Ho483360497iple_a) (F_1 tptp.fun_fu253747899iple_a)) (=> (tptp.hBOOL (tptp.finite1659845635iple_a F F_1)) (= (tptp.hAPP_H1789220885iple_a (tptp.hAPP_H1417936777iple_a F X_1) X_1) X_1))) (forall ((X_1 tptp.nat) (F tptp.fun_nat_fun_nat_nat) (F_1 tptp.fun_fun_nat_bool_nat)) (=> (tptp.hBOOL (tptp.finite795500164em_nat F F_1)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F X_1) X_1) X_1))) (forall ((A tptp.fun_Ho882550911a_bool) (B tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_f325481667a_bool tptp.cOMBC_1529670358l_bool tptp.member276146780iple_a))) (= (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) B) (tptp.hAPP_f642208769a_bool tptp.collec977865374iple_a (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1004093413a_bool tptp.cOMBS_1108095524l_bool (tptp.hAPP_f268025233l_bool (tptp.hAPP_f1261090107l_bool tptp.cOMBB_345279363iple_a tptp.fconj) (tptp.hAPP_f642208769a_bool _let_1 A))) (tptp.hAPP_f642208769a_bool (tptp.hAPP_f629438041a_bool tptp.cOMBB_361863589iple_a tptp.fNot) (tptp.hAPP_f642208769a_bool _let_1 B))))))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat))) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B) (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fconj) (tptp.hAPP_f800510211t_bool _let_1 A))) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f894608603t_bool tptp.cOMBB_bool_bool_nat tptp.fNot) (tptp.hAPP_f800510211t_bool _let_1 B))))))) (forall ((A tptp.fun_int_bool) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f202917053t_bool tptp.cOMBC_94739984l_bool tptp.member_int))) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B) (tptp.hAPP_f1805168059t_bool tptp.collect_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_f1805168059t_bool _let_1 A))) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f627970963t_bool tptp.cOMBB_bool_bool_int tptp.fNot) (tptp.hAPP_f1805168059t_bool _let_1 B))))))) (forall ((Ca tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (B tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a Ca))) (= (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) B))) (and (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 A)) (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 B))))))) (forall ((Ca tptp.nat) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat Ca))) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B))) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B))))))) (forall ((Ca tptp.int) (A tptp.fun_int_bool) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int Ca))) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B))) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B))))))) (forall ((A tptp.fun_int_bool) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B))) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool _let_1) B) _let_1))) (forall ((A tptp.fun_Ho882550911a_bool) (B tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) B))) (= (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool _let_1) B) _let_1))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B))) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool _let_1) B) _let_1))) (forall ((Ca tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (B tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a Ca))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) B))) (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 A))))) (forall ((Ca tptp.nat) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat Ca))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A))))) (forall ((Ca tptp.int) (A tptp.fun_int_bool) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int Ca))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A))))) (forall ((Ca tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (B tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a Ca))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) B))) (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 B)))))) (forall ((Ca tptp.nat) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat Ca))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B))) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B)))))) (forall ((Ca tptp.int) (A tptp.fun_int_bool) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int Ca))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B))) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B)))))) (forall ((A tptp.fun_Ho882550911a_bool)) (= (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool tptp.bot_bo214064617a_bool) A) tptp.bot_bo214064617a_bool)) (forall ((A tptp.fun_int_bool)) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool tptp.bot_bot_fun_int_bool) A) tptp.bot_bot_fun_int_bool)) (forall ((A tptp.fun_nat_bool)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool tptp.bot_bot_fun_nat_bool) A) tptp.bot_bot_fun_nat_bool)) (forall ((A tptp.fun_Ho882550911a_bool)) (= (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) tptp.bot_bo214064617a_bool) A)) (forall ((A tptp.fun_int_bool)) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) tptp.bot_bot_fun_int_bool) A)) (forall ((A tptp.fun_nat_bool)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) tptp.bot_bot_fun_nat_bool) A)) (forall ((A tptp.fun_Ho882550911a_bool)) (= (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) A) tptp.bot_bo214064617a_bool)) (forall ((A tptp.fun_int_bool)) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) A) tptp.bot_bot_fun_int_bool)) (forall ((A tptp.fun_nat_bool)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) A) tptp.bot_bot_fun_nat_bool)) (forall ((A tptp.fun_Ho882550911a_bool) (B tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a B)) (= (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) B))) (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A))))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A))))) (forall ((A tptp.fun_int_bool) (B tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int B)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A))))) (forall ((A tptp.fun_nat_bool) (X_1 tptp.nat) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B))) (let ((_let_2 (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1))) (let ((_let_3 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool (tptp.hAPP_f800510211t_bool _let_2 A)) B))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) B)))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_f800510211t_bool _let_2 _let_1))))))))) (forall ((A tptp.fun_Ho882550911a_bool) (X_1 tptp.hoare_2076525193iple_a) (B tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) B))) (let ((_let_2 (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1))) (let ((_let_3 (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool (tptp.hAPP_f642208769a_bool _let_2 A)) B))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) B)))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_f642208769a_bool _let_2 _let_1))))))))) (forall ((A tptp.fun_int_bool) (X_1 tptp.int) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B))) (let ((_let_2 (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1))) (let ((_let_3 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool (tptp.hAPP_f1805168059t_bool _let_2 A)) B))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) B)))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP_f1805168059t_bool _let_2 _let_1))))))))) (forall ((A tptp.fun_nat_bool) (X_1 tptp.nat) (B tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) B)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) B) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B)))) (forall ((A tptp.fun_Ho882550911a_bool) (X_1 tptp.hoare_2076525193iple_a) (B tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) B)) (= (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1) A)) B) (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) B)))) (forall ((A tptp.fun_int_bool) (X_1 tptp.int) (B tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) B)) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) A)) B) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B)))) (forall ((A_13 tptp.nat) (Ba tptp.nat) (A tptp.fun_nat_bool) (X_1 tptp.nat)) (let ((_let_1 (tptp.finite929467206at_nat tptp.times_times_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool _let_1 Ba) A) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_13) A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Ba) A))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool _let_1 A_13) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Ba) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) tptp.bot_bot_fun_nat_bool)))) X_1))))))) (forall ((A_13 tptp.int) (Ba tptp.int) (A tptp.fun_int_bool) (X_1 tptp.int)) (let ((_let_1 (tptp.finite772772422nt_int tptp.times_times_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool _let_1 Ba) A) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_13) A)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Ba) A))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool _let_1 A_13) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int Ba) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) tptp.bot_bot_fun_int_bool)))) X_1))))))) (forall ((A tptp.fun_nat_bool) (A_13 tptp.nat) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13))) (let ((_let_2 (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A))) (= (tptp.hAPP_f800510211t_bool _let_2 (tptp.hAPP_f800510211t_bool _let_1 B)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool (tptp.hAPP_f800510211t_bool _let_2 B)) (tptp.hAPP_f800510211t_bool _let_1 tptp.bot_bot_fun_nat_bool)))))) (forall ((A tptp.fun_Ho882550911a_bool) (A_13 tptp.hoare_2076525193iple_a) (B tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13))) (let ((_let_2 (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A))) (= (tptp.hAPP_f642208769a_bool _let_2 (tptp.hAPP_f642208769a_bool _let_1 B)) (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool (tptp.hAPP_f642208769a_bool _let_2 B)) (tptp.hAPP_f642208769a_bool _let_1 tptp.bot_bo214064617a_bool)))))) (forall ((A tptp.fun_int_bool) (A_13 tptp.int) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13))) (let ((_let_2 (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A))) (= (tptp.hAPP_f1805168059t_bool _let_2 (tptp.hAPP_f1805168059t_bool _let_1 B)) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool (tptp.hAPP_f1805168059t_bool _let_2 B)) (tptp.hAPP_f1805168059t_bool _let_1 tptp.bot_bot_fun_int_bool)))))) (forall ((A tptp.fun_nat_bool) (A_13 tptp.nat) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13))) (let ((_let_2 (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A))) (= (tptp.hAPP_f800510211t_bool _let_2 (tptp.hAPP_f800510211t_bool _let_1 B)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool (tptp.hAPP_f800510211t_bool _let_2 (tptp.hAPP_f800510211t_bool _let_1 tptp.bot_bot_fun_nat_bool))) B))))) (forall ((A tptp.fun_Ho882550911a_bool) (A_13 tptp.hoare_2076525193iple_a) (B tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13))) (let ((_let_2 (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A))) (= (tptp.hAPP_f642208769a_bool _let_2 (tptp.hAPP_f642208769a_bool _let_1 B)) (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool (tptp.hAPP_f642208769a_bool _let_2 (tptp.hAPP_f642208769a_bool _let_1 tptp.bot_bo214064617a_bool))) B))))) (forall ((A tptp.fun_int_bool) (A_13 tptp.int) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13))) (let ((_let_2 (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A))) (= (tptp.hAPP_f1805168059t_bool _let_2 (tptp.hAPP_f1805168059t_bool _let_1 B)) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool (tptp.hAPP_f1805168059t_bool _let_2 (tptp.hAPP_f1805168059t_bool _let_1 tptp.bot_bot_fun_int_bool))) B))))) (forall ((A_13 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13))) (= (tptp.hAPP_f800510211t_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool _let_1 tptp.bot_bot_fun_nat_bool))) (tptp.hAPP_f800510211t_bool _let_1 A)))) (forall ((A_13 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13))) (= (tptp.hAPP_f642208769a_bool _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) (tptp.hAPP_f642208769a_bool _let_1 tptp.bot_bo214064617a_bool))) (tptp.hAPP_f642208769a_bool _let_1 A)))) (forall ((A_13 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13))) (= (tptp.hAPP_f1805168059t_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool _let_1 tptp.bot_bot_fun_int_bool))) (tptp.hAPP_f1805168059t_bool _let_1 A)))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A))) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool (tptp.hAPP_f800510211t_bool _let_1 A)) (tptp.hAPP_f800510211t_bool _let_1 tptp.bot_bot_fun_nat_bool)) A)))) (forall ((X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A))) (= (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool (tptp.hAPP_f642208769a_bool _let_1 A)) (tptp.hAPP_f642208769a_bool _let_1 tptp.bot_bo214064617a_bool)) A)))) (forall ((X_1 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1))) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A))) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool (tptp.hAPP_f1805168059t_bool _let_1 A)) (tptp.hAPP_f1805168059t_bool _let_1 tptp.bot_bot_fun_int_bool)) A)))) (forall ((A_13 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_13) A)) (= (tptp.hAPP_f800510211t_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool _let_1 tptp.bot_bot_fun_nat_bool))) A)))) (forall ((A_13 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a A_13) A)) (= (tptp.hAPP_f642208769a_bool _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) (tptp.hAPP_f642208769a_bool _let_1 tptp.bot_bo214064617a_bool))) A)))) (forall ((A_13 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_13) A)) (= (tptp.hAPP_f1805168059t_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool _let_1 tptp.bot_bot_fun_int_bool))) A)))) (forall ((A tptp.fun_nat_bool) (A_13 tptp.nat) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A))) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) B)))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool _let_1 B)))))) (forall ((A tptp.fun_Ho882550911a_bool) (A_13 tptp.hoare_2076525193iple_a) (B tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A))) (= (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a (tptp.hAPP_f642208769a_bool _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) B)))) (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a (tptp.hAPP_f642208769a_bool _let_1 B)))))) (forall ((A tptp.fun_int_bool) (A_13 tptp.int) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A))) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.hAPP_f1805168059t_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) B)))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.hAPP_f1805168059t_bool _let_1 B)))))) (forall ((Z_1 tptp.nat) (Ba tptp.nat) (A tptp.fun_nat_bool) (Y_1 tptp.nat)) (let ((_let_1 (tptp.finite929467206at_nat tptp.times_times_nat))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool _let_1 Ba) A) Y_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat Ba) A))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool _let_1 Z_1) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Ba) A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Z_1) Y_1))))))) (forall ((Z_1 tptp.int) (Ba tptp.int) (A tptp.fun_int_bool) (Y_1 tptp.int)) (let ((_let_1 (tptp.finite772772422nt_int tptp.times_times_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool _let_1 Ba) A) Y_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int Ba) A))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool _let_1 Z_1) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int Ba) A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Z_1) Y_1))))))) (forall ((X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (F tptp.fun_Ho483360497iple_a) (F_1 tptp.fun_fu253747899iple_a)) (let ((_let_1 (tptp.hAPP_f2009966983iple_a F_1 A))) (=> (tptp.hBOOL (tptp.finite1659845635iple_a F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A)) (= (tptp.hAPP_H1789220885iple_a (tptp.hAPP_H1417936777iple_a F X_1) _let_1) _let_1)))))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool) (F tptp.fun_nat_fun_nat_nat) (F_1 tptp.fun_fun_nat_bool_nat)) (let ((_let_1 (tptp.hAPP_f22106695ol_nat F_1 A))) (=> (tptp.hBOOL (tptp.finite795500164em_nat F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F X_1) _let_1) _let_1)))))) (forall ((X_1 tptp.int) (A tptp.fun_int_bool) (F tptp.fun_int_fun_int_int) (F_1 tptp.fun_fun_int_bool_int)) (let ((_let_1 (tptp.hAPP_f1594865479ol_int F_1 A))) (=> (tptp.hBOOL (tptp.finite1432773856em_int F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int F X_1) _let_1) _let_1)))))) (forall ((A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (= A tptp.bot_bot_fun_nat_bool)) (=> (forall ((X_2 tptp.nat) (Y_21 tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat X_2) Y_21)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_2) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Y_21) tptp.bot_bot_fun_nat_bool))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_f22106695ol_nat (tptp.finite_fold1_nat tptp.times_times_nat) A)) A)))))) (forall ((A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (not (= A tptp.bot_bot_fun_int_bool)) (=> (forall ((X_2 tptp.int) (Y_21 tptp.int)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X_2) Y_21)) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_2) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int Y_21) tptp.bot_bot_fun_int_bool))))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_f1594865479ol_int (tptp.finite_fold1_int tptp.times_times_int) A)) A)))))) (forall ((N_3 tptp.fun_Ho882550911a_bool) (H tptp.fun_Ho1518252029iple_a) (F tptp.fun_Ho483360497iple_a) (F_1 tptp.fun_fu253747899iple_a)) (=> (tptp.hBOOL (tptp.finite1659845635iple_a F F_1)) (=> (forall ((X_2 tptp.hoare_2076525193iple_a) (Y_21 tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H1789220885iple_a H (tptp.hAPP_H1789220885iple_a (tptp.hAPP_H1417936777iple_a F X_2) Y_21)) (tptp.hAPP_H1789220885iple_a (tptp.hAPP_H1417936777iple_a F (tptp.hAPP_H1789220885iple_a H X_2)) (tptp.hAPP_H1789220885iple_a H Y_21)))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a N_3)) (=> (not (= N_3 tptp.bot_bo214064617a_bool)) (= (tptp.hAPP_H1789220885iple_a H (tptp.hAPP_f2009966983iple_a F_1 N_3)) (tptp.hAPP_f2009966983iple_a F_1 (tptp.image_1416816325iple_a H N_3)))))))) (forall ((N_3 tptp.fun_int_bool) (H tptp.fun_int_int) (F tptp.fun_int_fun_int_int) (F_1 tptp.fun_fun_int_bool_int)) (=> (tptp.hBOOL (tptp.finite1432773856em_int F F_1)) (=> (forall ((X_2 tptp.int) (Y_21 tptp.int)) (= (tptp.hAPP_int_int H (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int F X_2) Y_21)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int F (tptp.hAPP_int_int H X_2)) (tptp.hAPP_int_int H Y_21)))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int N_3)) (=> (not (= N_3 tptp.bot_bot_fun_int_bool)) (= (tptp.hAPP_int_int H (tptp.hAPP_f1594865479ol_int F_1 N_3)) (tptp.hAPP_f1594865479ol_int F_1 (tptp.image_int_int H N_3)))))))) (forall ((N_3 tptp.fun_nat_bool) (H tptp.fun_nat_nat) (F tptp.fun_nat_fun_nat_nat) (F_1 tptp.fun_fun_nat_bool_nat)) (=> (tptp.hBOOL (tptp.finite795500164em_nat F F_1)) (=> (forall ((X_2 tptp.nat) (Y_21 tptp.nat)) (= (tptp.hAPP_nat_nat H (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F X_2) Y_21)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F (tptp.hAPP_nat_nat H X_2)) (tptp.hAPP_nat_nat H Y_21)))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat N_3)) (=> (not (= N_3 tptp.bot_bot_fun_nat_bool)) (= (tptp.hAPP_nat_nat H (tptp.hAPP_f22106695ol_nat F_1 N_3)) (tptp.hAPP_f22106695ol_nat F_1 (tptp.image_nat_nat H N_3)))))))) (forall ((Pa tptp.fun_fu425979586l_bool) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa A)) (=> (forall ((A_12 tptp.nat) (A_43 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A_43)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_12) A_43)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa A_43)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A_43) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_12) tptp.bot_bot_fun_nat_bool)))))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa tptp.bot_bot_fun_nat_bool)))))) (forall ((Pa tptp.fun_fu2026518849l_bool) (A tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool Pa A)) (=> (forall ((A_12 tptp.hoare_2076525193iple_a) (A_43 tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A_43)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a A_12) A_43)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool Pa A_43)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool Pa (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A_43) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_12) tptp.bot_bo214064617a_bool)))))))) (tptp.hBOOL (tptp.hAPP_f500854239l_bool Pa tptp.bot_bo214064617a_bool)))))) (forall ((Pa tptp.fun_fu819804446l_bool) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa A)) (=> (forall ((A_12 tptp.int) (A_43 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A_43)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_12) A_43)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa A_43)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A_43) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_12) tptp.bot_bot_fun_int_bool)))))))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa tptp.bot_bot_fun_int_bool)))))) (forall ((A tptp.fun_int_bool) (B tptp.fun_int_bool) (X_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B) X_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.minus_minus_bool (tptp.hAPP_int_bool A X_1)) (tptp.hAPP_int_bool B X_1))))) (forall ((A tptp.fun_Ho882550911a_bool) (B tptp.fun_Ho882550911a_bool) (X_1 tptp.hoare_2076525193iple_a)) (= (tptp.hBOOL (tptp.hAPP_H454055633a_bool (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) B) X_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.minus_minus_bool (tptp.hAPP_H454055633a_bool A X_1)) (tptp.hAPP_H454055633a_bool B X_1))))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool) (X_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B) X_1)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.minus_minus_bool (tptp.hAPP_nat_bool A X_1)) (tptp.hAPP_nat_bool B X_1))))) (forall ((A tptp.fun_int_bool) (B tptp.fun_int_bool) (X_2 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B) X_2)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.minus_minus_bool (tptp.hAPP_int_bool A X_2)) (tptp.hAPP_int_bool B X_2))))) (forall ((A tptp.fun_Ho882550911a_bool) (B tptp.fun_Ho882550911a_bool) (X_2 tptp.hoare_2076525193iple_a)) (= (tptp.hBOOL (tptp.hAPP_H454055633a_bool (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) B) X_2)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.minus_minus_bool (tptp.hAPP_H454055633a_bool A X_2)) (tptp.hAPP_H454055633a_bool B X_2))))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool) (X_2 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B) X_2)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.minus_minus_bool (tptp.hAPP_nat_bool A X_2)) (tptp.hAPP_nat_bool B X_2))))) (tptp.hBOOL (tptp.finite1956789438t_bool (tptp.hAPP_f10625010t_bool (tptp.hAPP_f1115950719t_bool tptp.cOMBB_1654519265ol_nat (tptp.hAPP_f1311642927t_bool tptp.cOMBC_646315179t_bool tptp.minus_2067140911t_bool)) (tptp.hAPP_f1570313510t_bool (tptp.hAPP_f688831301t_bool tptp.cOMBC_178881787t_bool tptp.insert_nat) tptp.bot_bot_fun_nat_bool)))) (tptp.hBOOL (tptp.finite1306023740a_bool (tptp.hAPP_f102426163a_bool (tptp.hAPP_f300022271a_bool tptp.cOMBB_2036667361iple_a (tptp.hAPP_f86610733a_bool tptp.cOMBC_2005334440a_bool tptp.minus_1649626414a_bool)) (tptp.hAPP_f219434403a_bool (tptp.hAPP_f1824299331a_bool tptp.cOMBC_175592824a_bool tptp.insert1582918915iple_a) tptp.bot_bo214064617a_bool)))) (tptp.hBOOL (tptp.finite58652534t_bool (tptp.hAPP_f1468280982t_bool (tptp.hAPP_f1596157055t_bool tptp.cOMBB_765314529ol_int (tptp.hAPP_f194616807t_bool tptp.cOMBC_922884543t_bool tptp.minus_1449998731t_bool)) (tptp.hAPP_f1048215610t_bool (tptp.hAPP_f472159229t_bool tptp.cOMBC_1683390479t_bool tptp.insert_int) tptp.bot_bot_fun_int_bool)))) (forall ((X_1 tptp.int) (Z_1 tptp.fun_int_bool) (F tptp.fun_in719570932t_bool)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool F X_1))) (let ((_let_2 (tptp.hAPP_f1805168059t_bool _let_1 Z_1))) (=> (tptp.hBOOL (tptp.finite58652534t_bool F)) (= (tptp.hAPP_f1805168059t_bool _let_1 _let_2) _let_2))))) (forall ((X_1 tptp.hoare_2076525193iple_a) (Z_1 tptp.fun_Ho882550911a_bool) (F tptp.fun_Ho112928087a_bool)) (let ((_let_1 (tptp.hAPP_H1940471919a_bool F X_1))) (let ((_let_2 (tptp.hAPP_f642208769a_bool _let_1 Z_1))) (=> (tptp.hBOOL (tptp.finite1306023740a_bool F)) (= (tptp.hAPP_f642208769a_bool _let_1 _let_2) _let_2))))) (forall ((X_1 tptp.nat) (Z_1 tptp.fun_nat_bool) (F tptp.fun_na35521688t_bool)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool F X_1))) (let ((_let_2 (tptp.hAPP_f800510211t_bool _let_1 Z_1))) (=> (tptp.hBOOL (tptp.finite1956789438t_bool F)) (= (tptp.hAPP_f800510211t_bool _let_1 _let_2) _let_2))))) (tptp.hBOOL (tptp.finite1956789438t_bool tptp.insert_nat)) (tptp.hBOOL (tptp.finite1306023740a_bool tptp.insert1582918915iple_a)) (tptp.hBOOL (tptp.finite58652534t_bool tptp.insert_int)) (forall ((A_13 tptp.nat) (Z_1 tptp.nat) (A tptp.fun_nat_bool) (Y_1 tptp.nat) (F tptp.fun_nat_fun_nat_nat)) (=> (tptp.hBOOL (tptp.finite2130160977at_nat F)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool (tptp.finite929467206at_nat F) Z_1) A) Y_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_13) A)) (exists ((Y_22 tptp.nat)) (and (= Y_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F A_13) Y_22)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool (tptp.finite929467206at_nat F) Z_1) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) tptp.bot_bot_fun_nat_bool))) Y_22)))))))) (forall ((A_13 tptp.hoare_2076525193iple_a) (Z_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (Y_1 tptp.hoare_2076525193iple_a) (F tptp.fun_Ho483360497iple_a)) (=> (tptp.hBOOL (tptp.finite164030737iple_a F)) (=> (tptp.hBOOL (tptp.hAPP_H454055633a_bool (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool (tptp.finite974267142iple_a F) Z_1) A) Y_1)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a A_13) A)) (exists ((Y_22 tptp.hoare_2076525193iple_a)) (and (= Y_1 (tptp.hAPP_H1789220885iple_a (tptp.hAPP_H1417936777iple_a F A_13) Y_22)) (tptp.hBOOL (tptp.hAPP_H454055633a_bool (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool (tptp.finite974267142iple_a F) Z_1) (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) tptp.bot_bo214064617a_bool))) Y_22)))))))) (forall ((A_13 tptp.int) (Z_1 tptp.int) (A tptp.fun_int_bool) (Y_1 tptp.int) (F tptp.fun_int_fun_int_int)) (=> (tptp.hBOOL (tptp.finite1973466193nt_int F)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool (tptp.finite772772422nt_int F) Z_1) A) Y_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_13) A)) (exists ((Y_22 tptp.int)) (and (= Y_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int F A_13) Y_22)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool (tptp.finite772772422nt_int F) Z_1) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) tptp.bot_bot_fun_int_bool))) Y_22)))))))) (forall ((F tptp.fun_nat_int) (A_13 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f1599440987ol_int tptp.big_co1024481617at_int F))) (let ((_let_2 (tptp.hAPP_f659380387ol_int _let_1 A))) (let ((_let_3 (tptp.hAPP_f659380387ol_int _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) tptp.bot_bot_fun_nat_bool))))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_13) A)))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (and (=> _let_4 (= _let_3 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int _let_2) (tptp.hAPP_nat_int F A_13)))) (=> (not _let_4) (= _let_3 _let_2))))))))) (forall ((F tptp.fun_Ho1026035802_a_int) (A_13 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_f1870360797ol_int tptp.big_co1560107922_a_int F))) (let ((_let_2 (tptp.hAPP_f827914852ol_int _let_1 A))) (let ((_let_3 (tptp.hAPP_f827914852ol_int _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) tptp.bot_bo214064617a_bool))))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a A_13) A)))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (and (=> _let_4 (= _let_3 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int _let_2) (tptp.hAPP_H811578610_a_int F A_13)))) (=> (not _let_4) (= _let_3 _let_2))))))))) (forall ((F tptp.fun_int_int) (A_13 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f1926459811ol_int tptp.big_co230513141nt_int F))) (let ((_let_2 (tptp.hAPP_f1594865479ol_int _let_1 A))) (let ((_let_3 (tptp.hAPP_f1594865479ol_int _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) tptp.bot_bot_fun_int_bool))))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_13) A)))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (and (=> _let_4 (= _let_3 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int _let_2) (tptp.hAPP_int_int F A_13)))) (=> (not _let_4) (= _let_3 _let_2))))))))) (forall ((F tptp.fun_nat_int) (A_13 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f1599440987ol_int tptp.big_co1024481617at_int F))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_13) A)) (= (tptp.hAPP_f659380387ol_int _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) tptp.bot_bot_fun_nat_bool))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_f659380387ol_int _let_1 A)) (tptp.hAPP_nat_int F A_13))))))) (forall ((F tptp.fun_Ho1026035802_a_int) (A_13 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_f1870360797ol_int tptp.big_co1560107922_a_int F))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a A_13) A)) (= (tptp.hAPP_f827914852ol_int _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) tptp.bot_bo214064617a_bool))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_f827914852ol_int _let_1 A)) (tptp.hAPP_H811578610_a_int F A_13))))))) (forall ((F tptp.fun_int_int) (A_13 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f1926459811ol_int tptp.big_co230513141nt_int F))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_13) A)) (= (tptp.hAPP_f1594865479ol_int _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) tptp.bot_bot_fun_int_bool))) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_f1594865479ol_int _let_1 A)) (tptp.hAPP_int_int F A_13))))))) (forall ((G tptp.fun_nat_nat) (X_1 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1))) (let ((_let_2 (tptp.big_co1705425894at_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_f22106695ol_nat _let_2 (tptp.hAPP_f800510211t_bool _let_1 A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat G X_1)) (tptp.hAPP_f22106695ol_nat _let_2 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool _let_1 tptp.bot_bot_fun_nat_bool))))))))) (forall ((G tptp.fun_Ho864122878_a_nat) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1))) (let ((_let_2 (tptp.big_co1398215719_a_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (= (tptp.hAPP_f190641160ol_nat _let_2 (tptp.hAPP_f642208769a_bool _let_1 A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_H174304918_a_nat G X_1)) (tptp.hAPP_f190641160ol_nat _let_2 (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) (tptp.hAPP_f642208769a_bool _let_1 tptp.bot_bo214064617a_bool))))))))) (forall ((G tptp.fun_int_nat) (X_1 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1))) (let ((_let_2 (tptp.big_co911457418nt_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (= (tptp.hAPP_f957591787ol_nat _let_2 (tptp.hAPP_f1805168059t_bool _let_1 A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat G X_1)) (tptp.hAPP_f957591787ol_nat _let_2 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool _let_1 tptp.bot_bot_fun_int_bool))))))))) (forall ((G tptp.fun_nat_int) (X_1 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1))) (let ((_let_2 (tptp.big_co195215938at_int G))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_f659380387ol_int _let_2 (tptp.hAPP_f800510211t_bool _let_1 A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_nat_int G X_1)) (tptp.hAPP_f659380387ol_int _let_2 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool _let_1 tptp.bot_bot_fun_nat_bool))))))))) (forall ((G tptp.fun_Ho1026035802_a_int) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1))) (let ((_let_2 (tptp.big_co2035489411_a_int G))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (= (tptp.hAPP_f827914852ol_int _let_2 (tptp.hAPP_f642208769a_bool _let_1 A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_H811578610_a_int G X_1)) (tptp.hAPP_f827914852ol_int _let_2 (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) (tptp.hAPP_f642208769a_bool _let_1 tptp.bot_bo214064617a_bool))))))))) (forall ((G tptp.fun_int_int) (X_1 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1))) (let ((_let_2 (tptp.big_co1548731110nt_int G))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (= (tptp.hAPP_f1594865479ol_int _let_2 (tptp.hAPP_f1805168059t_bool _let_1 A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int G X_1)) (tptp.hAPP_f1594865479ol_int _let_2 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool _let_1 tptp.bot_bot_fun_int_bool))))))))) (forall ((G tptp.fun_nat_nat) (X_1 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.big_co1705425894at_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (= (tptp.hAPP_f22106695ol_nat _let_1 A) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat G X_1)) (tptp.hAPP_f22106695ol_nat _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) tptp.bot_bot_fun_nat_bool))))))))) (forall ((G tptp.fun_Ho864122878_a_nat) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.big_co1398215719_a_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A)) (= (tptp.hAPP_f190641160ol_nat _let_1 A) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_H174304918_a_nat G X_1)) (tptp.hAPP_f190641160ol_nat _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1) tptp.bot_bo214064617a_bool))))))))) (forall ((G tptp.fun_int_nat) (X_1 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.big_co911457418nt_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (= (tptp.hAPP_f957591787ol_nat _let_1 A) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_int_nat G X_1)) (tptp.hAPP_f957591787ol_nat _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) tptp.bot_bot_fun_int_bool))))))))) (forall ((G tptp.fun_nat_int) (X_1 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.big_co195215938at_int G))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (= (tptp.hAPP_f659380387ol_int _let_1 A) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_nat_int G X_1)) (tptp.hAPP_f659380387ol_int _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) tptp.bot_bot_fun_nat_bool))))))))) (forall ((G tptp.fun_Ho1026035802_a_int) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.big_co2035489411_a_int G))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A)) (= (tptp.hAPP_f827914852ol_int _let_1 A) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_H811578610_a_int G X_1)) (tptp.hAPP_f827914852ol_int _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1) tptp.bot_bo214064617a_bool))))))))) (forall ((G tptp.fun_int_int) (X_1 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.big_co1548731110nt_int G))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (= (tptp.hAPP_f1594865479ol_int _let_1 A) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int G X_1)) (tptp.hAPP_f1594865479ol_int _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) tptp.bot_bot_fun_int_bool))))))))) (forall ((B tptp.fun_nat_bool) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool B) A) (tptp.hAPP_f800510211t_bool (tptp.finite1578363458t_bool (tptp.hAPP_f10625010t_bool (tptp.hAPP_f1115950719t_bool tptp.cOMBB_1654519265ol_nat (tptp.hAPP_f1311642927t_bool tptp.cOMBC_646315179t_bool tptp.minus_2067140911t_bool)) (tptp.hAPP_f1570313510t_bool (tptp.hAPP_f688831301t_bool tptp.cOMBC_178881787t_bool tptp.insert_nat) tptp.bot_bot_fun_nat_bool)) B) A)))) (forall ((B tptp.fun_Ho882550911a_bool) (A tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (= (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool B) A) (tptp.hAPP_f642208769a_bool (tptp.finite718386368a_bool (tptp.hAPP_f102426163a_bool (tptp.hAPP_f300022271a_bool tptp.cOMBB_2036667361iple_a (tptp.hAPP_f86610733a_bool tptp.cOMBC_2005334440a_bool tptp.minus_1649626414a_bool)) (tptp.hAPP_f219434403a_bool (tptp.hAPP_f1824299331a_bool tptp.cOMBC_175592824a_bool tptp.insert1582918915iple_a) tptp.bot_bo214064617a_bool)) B) A)))) (forall ((B tptp.fun_int_bool) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool B) A) (tptp.hAPP_f1805168059t_bool (tptp.finite1827710202t_bool (tptp.hAPP_f1468280982t_bool (tptp.hAPP_f1596157055t_bool tptp.cOMBB_765314529ol_int (tptp.hAPP_f194616807t_bool tptp.cOMBC_922884543t_bool tptp.minus_1449998731t_bool)) (tptp.hAPP_f1048215610t_bool (tptp.hAPP_f472159229t_bool tptp.cOMBC_1683390479t_bool tptp.insert_int) tptp.bot_bot_fun_int_bool)) B) A)))) (forall ((X_1 tptp.hoare_2076525193iple_a) (Z_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (F tptp.fun_Ho483360497iple_a)) (let ((_let_1 (tptp.hAPP_H1417936777iple_a F X_1))) (=> (tptp.hBOOL (tptp.finite164030737iple_a F)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (= (tptp.hAPP_H1789220885iple_a _let_1 (tptp.hAPP_f2009966983iple_a (tptp.finite2089344904iple_a F Z_1) A)) (tptp.hAPP_f2009966983iple_a (tptp.finite2089344904iple_a F (tptp.hAPP_H1789220885iple_a _let_1 Z_1)) A)))))) (forall ((X_1 tptp.hoare_2076525193iple_a) (Z_1 tptp.fun_Ho882550911a_bool) (A tptp.fun_Ho882550911a_bool) (F tptp.fun_Ho112928087a_bool)) (let ((_let_1 (tptp.hAPP_H1940471919a_bool F X_1))) (=> (tptp.hBOOL (tptp.finite1617795063a_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (= (tptp.hAPP_f642208769a_bool _let_1 (tptp.hAPP_f642208769a_bool (tptp.finite718386368a_bool F Z_1) A)) (tptp.hAPP_f642208769a_bool (tptp.finite718386368a_bool F (tptp.hAPP_f642208769a_bool _let_1 Z_1)) A)))))) (forall ((X_1 tptp.nat) (Z_1 tptp.nat) (A tptp.fun_nat_bool) (F tptp.fun_nat_fun_nat_nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat F X_1))) (=> (tptp.hBOOL (tptp.finite2130160977at_nat F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_f22106695ol_nat (tptp.finite_fold_nat_nat F Z_1) A)) (tptp.hAPP_f22106695ol_nat (tptp.finite_fold_nat_nat F (tptp.hAPP_nat_nat _let_1 Z_1)) A)))))) (forall ((X_1 tptp.nat) (Z_1 tptp.fun_nat_bool) (A tptp.fun_nat_bool) (F tptp.fun_na35521688t_bool)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool F X_1))) (=> (tptp.hBOOL (tptp.finite1071749497t_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_f800510211t_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.finite1578363458t_bool F Z_1) A)) (tptp.hAPP_f800510211t_bool (tptp.finite1578363458t_bool F (tptp.hAPP_f800510211t_bool _let_1 Z_1)) A)))))) (forall ((X_1 tptp.int) (Z_1 tptp.int) (A tptp.fun_int_bool) (F tptp.fun_int_fun_int_int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int F X_1))) (=> (tptp.hBOOL (tptp.finite1973466193nt_int F)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_f1594865479ol_int (tptp.finite_fold_int_int F Z_1) A)) (tptp.hAPP_f1594865479ol_int (tptp.finite_fold_int_int F (tptp.hAPP_int_int _let_1 Z_1)) A)))))) (forall ((X_1 tptp.int) (Z_1 tptp.fun_int_bool) (A tptp.fun_int_bool) (F tptp.fun_in719570932t_bool)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool F X_1))) (=> (tptp.hBOOL (tptp.finite1321096241t_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (= (tptp.hAPP_f1805168059t_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.finite1827710202t_bool F Z_1) A)) (tptp.hAPP_f1805168059t_bool (tptp.finite1827710202t_bool F (tptp.hAPP_f1805168059t_bool _let_1 Z_1)) A)))))) (forall ((X_1 tptp.int) (Y_1 tptp.int) (Z_1 tptp.int) (F tptp.fun_int_fun_int_int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int F X_1))) (let ((_let_2 (tptp.hAPP_int_fun_int_int F Y_1))) (=> (tptp.hBOOL (tptp.finite1973466193nt_int F)) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int _let_2 Z_1)) (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int _let_1 Z_1))))))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat) (Z_1 tptp.nat) (F tptp.fun_nat_fun_nat_nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat F X_1))) (let ((_let_2 (tptp.hAPP_nat_fun_nat_nat F Y_1))) (=> (tptp.hBOOL (tptp.finite2130160977at_nat F)) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_2 Z_1)) (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat _let_1 Z_1))))))) (forall ((F tptp.fun_nat_fun_int_nat) (B tptp.fun_int_bool) (A tptp.fun_nat_bool)) (= (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat (tptp.hAPP_f1473602334at_nat (tptp.hAPP_f630508183at_nat tptp.cOMBC_1505178355ol_nat (tptp.hAPP_f299305025ol_nat (tptp.hAPP_f1632710027ol_nat tptp.cOMBB_1453893592at_nat tptp.big_co1740723097nt_nat) F)) B)) A) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat (tptp.hAPP_f787214110nt_nat (tptp.hAPP_f261731407nt_nat tptp.cOMBC_462113011ol_nat (tptp.hAPP_f1501159417ol_nat (tptp.hAPP_f1029311995ol_nat tptp.cOMBB_1562322300at_int tptp.big_co387207925at_nat) (tptp.hAPP_f446977493at_nat tptp.cOMBC_nat_int_nat F))) A)) B))) (forall ((F tptp.fun_na841142961_a_nat) (B tptp.fun_Ho882550911a_bool) (A tptp.fun_nat_bool)) (= (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat (tptp.hAPP_f479558075at_nat (tptp.hAPP_f1173305809at_nat tptp.cOMBC_129115664ol_nat (tptp.hAPP_f1356625915ol_nat (tptp.hAPP_f2033836159ol_nat tptp.cOMBB_1944586014at_nat tptp.big_co922834230_a_nat) F)) B)) A) (tptp.hAPP_f190641160ol_nat (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat (tptp.hAPP_f1047071419_a_nat (tptp.hAPP_f1217804815_a_nat tptp.cOMBC_1664565648ol_nat (tptp.hAPP_f1296292793ol_nat (tptp.hAPP_f153943611ol_nat tptp.cOMBB_636937375iple_a tptp.big_co387207925at_nat) (tptp.hAPP_f982543381at_nat tptp.cOMBC_23578254_a_nat F))) A)) B))) (forall ((F tptp.fun_int_fun_nat_nat) (B tptp.fun_nat_bool) (A tptp.fun_int_bool)) (= (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat (tptp.hAPP_f787214110nt_nat (tptp.hAPP_f261731407nt_nat tptp.cOMBC_462113011ol_nat (tptp.hAPP_f1501159417ol_nat (tptp.hAPP_f1029311995ol_nat tptp.cOMBB_1562322300at_int tptp.big_co387207925at_nat) F)) B)) A) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat (tptp.hAPP_f1473602334at_nat (tptp.hAPP_f630508183at_nat tptp.cOMBC_1505178355ol_nat (tptp.hAPP_f299305025ol_nat (tptp.hAPP_f1632710027ol_nat tptp.cOMBB_1453893592at_nat tptp.big_co1740723097nt_nat) (tptp.hAPP_f879494613nt_nat tptp.cOMBC_int_nat_nat F))) A)) B))) (forall ((F tptp.fun_Ho1036508337at_nat) (B tptp.fun_nat_bool) (A tptp.fun_Ho882550911a_bool)) (= (tptp.hAPP_f190641160ol_nat (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat (tptp.hAPP_f1047071419_a_nat (tptp.hAPP_f1217804815_a_nat tptp.cOMBC_1664565648ol_nat (tptp.hAPP_f1296292793ol_nat (tptp.hAPP_f153943611ol_nat tptp.cOMBB_636937375iple_a tptp.big_co387207925at_nat) F)) B)) A) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat (tptp.hAPP_f479558075at_nat (tptp.hAPP_f1173305809at_nat tptp.cOMBC_129115664ol_nat (tptp.hAPP_f1356625915ol_nat (tptp.hAPP_f2033836159ol_nat tptp.cOMBB_1944586014at_nat tptp.big_co922834230_a_nat) (tptp.hAPP_f668391445_a_nat tptp.cOMBC_1942990924at_nat F))) A)) B))) (forall ((Z_1 tptp.int) (A tptp.fun_int_bool) (Y_1 tptp.int) (F tptp.fun_int_fun_int_int)) (=> (tptp.hBOOL (tptp.finite1973466193nt_int F)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool (tptp.finite772772422nt_int F) Z_1) A) Y_1)) (= (tptp.hAPP_f1594865479ol_int (tptp.finite_fold_int_int F Z_1) A) Y_1)))) (forall ((Z_1 tptp.nat) (A tptp.fun_nat_bool) (Y_1 tptp.nat) (F tptp.fun_nat_fun_nat_nat)) (=> (tptp.hBOOL (tptp.finite2130160977at_nat F)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool (tptp.finite929467206at_nat F) Z_1) A) Y_1)) (= (tptp.hAPP_f22106695ol_nat (tptp.finite_fold_nat_nat F Z_1) A) Y_1)))) (forall ((Z_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (Y_1 tptp.hoare_2076525193iple_a) (F tptp.fun_Ho483360497iple_a)) (=> (tptp.hBOOL (tptp.finite164030737iple_a F)) (=> (tptp.hBOOL (tptp.hAPP_H454055633a_bool (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool (tptp.finite974267142iple_a F) Z_1) A) Y_1)) (= (tptp.hAPP_f2009966983iple_a (tptp.finite2089344904iple_a F Z_1) A) Y_1)))) (forall ((Z_1 tptp.fun_int_bool) (A tptp.fun_int_bool) (Y_1 tptp.fun_int_bool) (F tptp.fun_in719570932t_bool)) (=> (tptp.hBOOL (tptp.finite1321096241t_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool (tptp.hAPP_f1634429330l_bool (tptp.finite1008073724t_bool F) Z_1) A) Y_1)) (= (tptp.hAPP_f1805168059t_bool (tptp.finite1827710202t_bool F Z_1) A) Y_1)))) (forall ((Z_1 tptp.fun_Ho882550911a_bool) (A tptp.fun_Ho882550911a_bool) (Y_1 tptp.fun_Ho882550911a_bool) (F tptp.fun_Ho112928087a_bool)) (=> (tptp.hBOOL (tptp.finite1617795063a_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool (tptp.hAPP_f845487733l_bool (tptp.finite655745986a_bool F) Z_1) A) Y_1)) (= (tptp.hAPP_f642208769a_bool (tptp.finite718386368a_bool F Z_1) A) Y_1)))) (forall ((Z_1 tptp.fun_nat_bool) (A tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool) (F tptp.fun_na35521688t_bool)) (=> (tptp.hBOOL (tptp.finite1071749497t_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool (tptp.hAPP_f1266913334l_bool (tptp.finite758726980t_bool F) Z_1) A) Y_1)) (= (tptp.hAPP_f800510211t_bool (tptp.finite1578363458t_bool F Z_1) A) Y_1)))) (forall ((F tptp.fun_Ho483360497iple_a) (Z_1 tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_f2009966983iple_a (tptp.finite2089344904iple_a F Z_1) tptp.bot_bo214064617a_bool) Z_1)) (forall ((F tptp.fun_Ho112928087a_bool) (Z_1 tptp.fun_Ho882550911a_bool)) (= (tptp.hAPP_f642208769a_bool (tptp.finite718386368a_bool F Z_1) tptp.bot_bo214064617a_bool) Z_1)) (forall ((F tptp.fun_int_fun_int_int) (Z_1 tptp.int)) (= (tptp.hAPP_f1594865479ol_int (tptp.finite_fold_int_int F Z_1) tptp.bot_bot_fun_int_bool) Z_1)) (forall ((F tptp.fun_in719570932t_bool) (Z_1 tptp.fun_int_bool)) (= (tptp.hAPP_f1805168059t_bool (tptp.finite1827710202t_bool F Z_1) tptp.bot_bot_fun_int_bool) Z_1)) (forall ((F tptp.fun_nat_fun_nat_nat) (Z_1 tptp.nat)) (= (tptp.hAPP_f22106695ol_nat (tptp.finite_fold_nat_nat F Z_1) tptp.bot_bot_fun_nat_bool) Z_1)) (forall ((F tptp.fun_na35521688t_bool) (Z_1 tptp.fun_nat_bool)) (= (tptp.hAPP_f800510211t_bool (tptp.finite1578363458t_bool F Z_1) tptp.bot_bot_fun_nat_bool) Z_1)) (forall ((Z_1 tptp.nat) (X_1 tptp.nat) (A tptp.fun_nat_bool) (F tptp.fun_nat_fun_nat_nat)) (=> (tptp.hBOOL (tptp.finite2130160977at_nat F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A))) (= (tptp.hAPP_f22106695ol_nat (tptp.finite_fold_nat_nat F Z_1) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_f22106695ol_nat (tptp.finite_fold_nat_nat F (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F X_1) Z_1)) A)))))) (forall ((Z_1 tptp.fun_nat_bool) (X_1 tptp.nat) (A tptp.fun_nat_bool) (F tptp.fun_na35521688t_bool)) (=> (tptp.hBOOL (tptp.finite1071749497t_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A))) (= (tptp.hAPP_f800510211t_bool (tptp.finite1578363458t_bool F Z_1) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_f800510211t_bool (tptp.finite1578363458t_bool F (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool F X_1) Z_1)) A)))))) (forall ((Z_1 tptp.hoare_2076525193iple_a) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (F tptp.fun_Ho483360497iple_a)) (=> (tptp.hBOOL (tptp.finite164030737iple_a F)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (=> (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A))) (= (tptp.hAPP_f2009966983iple_a (tptp.finite2089344904iple_a F Z_1) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1) A)) (tptp.hAPP_f2009966983iple_a (tptp.finite2089344904iple_a F (tptp.hAPP_H1789220885iple_a (tptp.hAPP_H1417936777iple_a F X_1) Z_1)) A)))))) (forall ((Z_1 tptp.fun_Ho882550911a_bool) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (F tptp.fun_Ho112928087a_bool)) (=> (tptp.hBOOL (tptp.finite1617795063a_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (=> (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A))) (= (tptp.hAPP_f642208769a_bool (tptp.finite718386368a_bool F Z_1) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1) A)) (tptp.hAPP_f642208769a_bool (tptp.finite718386368a_bool F (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool F X_1) Z_1)) A)))))) (forall ((Z_1 tptp.int) (X_1 tptp.int) (A tptp.fun_int_bool) (F tptp.fun_int_fun_int_int)) (=> (tptp.hBOOL (tptp.finite1973466193nt_int F)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A))) (= (tptp.hAPP_f1594865479ol_int (tptp.finite_fold_int_int F Z_1) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) A)) (tptp.hAPP_f1594865479ol_int (tptp.finite_fold_int_int F (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int F X_1) Z_1)) A)))))) (forall ((Z_1 tptp.fun_int_bool) (X_1 tptp.int) (A tptp.fun_int_bool) (F tptp.fun_in719570932t_bool)) (=> (tptp.hBOOL (tptp.finite1321096241t_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A))) (= (tptp.hAPP_f1805168059t_bool (tptp.finite1827710202t_bool F Z_1) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) A)) (tptp.hAPP_f1805168059t_bool (tptp.finite1827710202t_bool F (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool F X_1) Z_1)) A)))))) (forall ((Z_1 tptp.nat) (X_1 tptp.nat) (A tptp.fun_nat_bool) (F tptp.fun_nat_fun_nat_nat)) (let ((_let_1 (tptp.finite_fold_nat_nat F Z_1))) (=> (tptp.hBOOL (tptp.finite2130160977at_nat F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A))) (= (tptp.hAPP_f22106695ol_nat _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F X_1) (tptp.hAPP_f22106695ol_nat _let_1 A)))))))) (forall ((Z_1 tptp.fun_nat_bool) (X_1 tptp.nat) (A tptp.fun_nat_bool) (F tptp.fun_na35521688t_bool)) (let ((_let_1 (tptp.finite1578363458t_bool F Z_1))) (=> (tptp.hBOOL (tptp.finite1071749497t_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A))) (= (tptp.hAPP_f800510211t_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool F X_1) (tptp.hAPP_f800510211t_bool _let_1 A)))))))) (forall ((Z_1 tptp.hoare_2076525193iple_a) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (F tptp.fun_Ho483360497iple_a)) (let ((_let_1 (tptp.finite2089344904iple_a F Z_1))) (=> (tptp.hBOOL (tptp.finite164030737iple_a F)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (=> (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A))) (= (tptp.hAPP_f2009966983iple_a _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1) A)) (tptp.hAPP_H1789220885iple_a (tptp.hAPP_H1417936777iple_a F X_1) (tptp.hAPP_f2009966983iple_a _let_1 A)))))))) (forall ((Z_1 tptp.fun_Ho882550911a_bool) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (F tptp.fun_Ho112928087a_bool)) (let ((_let_1 (tptp.finite718386368a_bool F Z_1))) (=> (tptp.hBOOL (tptp.finite1617795063a_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (=> (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A))) (= (tptp.hAPP_f642208769a_bool _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1) A)) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool F X_1) (tptp.hAPP_f642208769a_bool _let_1 A)))))))) (forall ((Z_1 tptp.int) (X_1 tptp.int) (A tptp.fun_int_bool) (F tptp.fun_int_fun_int_int)) (let ((_let_1 (tptp.finite_fold_int_int F Z_1))) (=> (tptp.hBOOL (tptp.finite1973466193nt_int F)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A))) (= (tptp.hAPP_f1594865479ol_int _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int F X_1) (tptp.hAPP_f1594865479ol_int _let_1 A)))))))) (forall ((Z_1 tptp.fun_int_bool) (X_1 tptp.int) (A tptp.fun_int_bool) (F tptp.fun_in719570932t_bool)) (let ((_let_1 (tptp.finite1827710202t_bool F Z_1))) (=> (tptp.hBOOL (tptp.finite1321096241t_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A))) (= (tptp.hAPP_f1805168059t_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) A)) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool F X_1) (tptp.hAPP_f1805168059t_bool _let_1 A)))))))) (forall ((Z_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (F tptp.fun_Ho483360497iple_a)) (=> (tptp.hBOOL (tptp.finite164030737iple_a F)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (tptp.hBOOL (tptp.hAPP_H454055633a_bool (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool (tptp.finite974267142iple_a F) Z_1) A) (tptp.hAPP_f2009966983iple_a (tptp.finite2089344904iple_a F Z_1) A)))))) (forall ((Z_1 tptp.fun_Ho882550911a_bool) (A tptp.fun_Ho882550911a_bool) (F tptp.fun_Ho112928087a_bool)) (=> (tptp.hBOOL (tptp.finite1617795063a_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool (tptp.hAPP_f845487733l_bool (tptp.finite655745986a_bool F) Z_1) A) (tptp.hAPP_f642208769a_bool (tptp.finite718386368a_bool F Z_1) A)))))) (forall ((Z_1 tptp.nat) (A tptp.fun_nat_bool) (F tptp.fun_nat_fun_nat_nat)) (=> (tptp.hBOOL (tptp.finite2130160977at_nat F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool (tptp.finite929467206at_nat F) Z_1) A) (tptp.hAPP_f22106695ol_nat (tptp.finite_fold_nat_nat F Z_1) A)))))) (forall ((Z_1 tptp.fun_nat_bool) (A tptp.fun_nat_bool) (F tptp.fun_na35521688t_bool)) (=> (tptp.hBOOL (tptp.finite1071749497t_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool (tptp.hAPP_f1266913334l_bool (tptp.finite758726980t_bool F) Z_1) A) (tptp.hAPP_f800510211t_bool (tptp.finite1578363458t_bool F Z_1) A)))))) (forall ((Z_1 tptp.int) (A tptp.fun_int_bool) (F tptp.fun_int_fun_int_int)) (=> (tptp.hBOOL (tptp.finite1973466193nt_int F)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool (tptp.finite772772422nt_int F) Z_1) A) (tptp.hAPP_f1594865479ol_int (tptp.finite_fold_int_int F Z_1) A)))))) (forall ((Z_1 tptp.fun_int_bool) (A tptp.fun_int_bool) (F tptp.fun_in719570932t_bool)) (=> (tptp.hBOOL (tptp.finite1321096241t_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool (tptp.hAPP_f1634429330l_bool (tptp.finite1008073724t_bool F) Z_1) A) (tptp.hAPP_f1805168059t_bool (tptp.finite1827710202t_bool F Z_1) A)))))) (forall ((F tptp.fun_nat_nat) (A tptp.fun_nat_bool) (G tptp.fun_int_nat) (B tptp.fun_int_bool)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat F) A)) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat G) B)) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat (tptp.hAPP_f1473602334at_nat (tptp.hAPP_f630508183at_nat tptp.cOMBC_1505178355ol_nat (tptp.hAPP_f299305025ol_nat (tptp.hAPP_f1632710027ol_nat tptp.cOMBB_1453893592at_nat tptp.big_co1740723097nt_nat) (tptp.hAPP_f237327688nt_nat (tptp.hAPP_f1633513941nt_nat tptp.cOMBC_1218031117nt_nat (tptp.hAPP_f2080483477nt_nat (tptp.hAPP_f1701814485nt_nat tptp.cOMBB_737513486at_nat tptp.cOMBB_nat_nat_int) (tptp.hAPP_f1639111240at_nat (tptp.hAPP_f1731313045at_nat tptp.cOMBB_963856155at_nat tptp.times_times_nat) F))) G))) B)) A))) (forall ((F tptp.fun_nat_nat) (A tptp.fun_nat_bool) (G tptp.fun_Ho864122878_a_nat) (B tptp.fun_Ho882550911a_bool)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat F) A)) (tptp.hAPP_f190641160ol_nat (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat G) B)) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat (tptp.hAPP_f479558075at_nat (tptp.hAPP_f1173305809at_nat tptp.cOMBC_129115664ol_nat (tptp.hAPP_f1356625915ol_nat (tptp.hAPP_f2033836159ol_nat tptp.cOMBB_1944586014at_nat tptp.big_co922834230_a_nat) (tptp.hAPP_f536288520_a_nat (tptp.hAPP_f928984021_a_nat tptp.cOMBC_130242509_a_nat (tptp.hAPP_f935848405_a_nat (tptp.hAPP_f450378965_a_nat tptp.cOMBB_1353751246at_nat tptp.cOMBB_1877004557iple_a) (tptp.hAPP_f1639111240at_nat (tptp.hAPP_f1731313045at_nat tptp.cOMBB_963856155at_nat tptp.times_times_nat) F))) G))) B)) A))) (forall ((F tptp.fun_int_nat) (A tptp.fun_int_bool) (G tptp.fun_nat_nat) (B tptp.fun_nat_bool)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat F) A)) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat G) B)) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat (tptp.hAPP_f787214110nt_nat (tptp.hAPP_f261731407nt_nat tptp.cOMBC_462113011ol_nat (tptp.hAPP_f1501159417ol_nat (tptp.hAPP_f1029311995ol_nat tptp.cOMBB_1562322300at_int tptp.big_co387207925at_nat) (tptp.hAPP_f1169617132at_nat (tptp.hAPP_f701299925at_nat tptp.cOMBC_1294079849at_nat (tptp.hAPP_f1033905301at_nat (tptp.hAPP_f1315855317at_nat tptp.cOMBB_891709290at_int tptp.cOMBB_nat_nat_nat) (tptp.hAPP_f1463450952at_nat (tptp.hAPP_f1087393429at_nat tptp.cOMBB_1601129847at_int tptp.times_times_nat) F))) G))) B)) A))) (forall ((F tptp.fun_Ho864122878_a_nat) (A tptp.fun_Ho882550911a_bool) (G tptp.fun_nat_nat) (B tptp.fun_nat_bool)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_f190641160ol_nat (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat F) A)) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat G) B)) (tptp.hAPP_f190641160ol_nat (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat (tptp.hAPP_f1047071419_a_nat (tptp.hAPP_f1217804815_a_nat tptp.cOMBC_1664565648ol_nat (tptp.hAPP_f1296292793ol_nat (tptp.hAPP_f153943611ol_nat tptp.cOMBB_636937375iple_a tptp.big_co387207925at_nat) (tptp.hAPP_f1016910345at_nat (tptp.hAPP_f1112019605at_nat tptp.cOMBC_340603916at_nat (tptp.hAPP_f564893909at_nat (tptp.hAPP_f250842005at_nat tptp.cOMBB_151870093iple_a tptp.cOMBB_nat_nat_nat) (tptp.hAPP_f731653896at_nat (tptp.hAPP_f648261589at_nat tptp.cOMBB_1416330906iple_a tptp.times_times_nat) F))) G))) B)) A))) (forall ((F tptp.fun_nat_nat) (A tptp.fun_nat_bool) (R_2 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat F) A)) R_2) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat (tptp.hAPP_f1639111240at_nat (tptp.hAPP_f1731313045at_nat tptp.cOMBB_963856155at_nat tptp.times_times_nat) F)) R_2)) A))) (forall ((F tptp.fun_int_nat) (A tptp.fun_int_bool) (R_2 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat F) A)) R_2) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat (tptp.hAPP_nat_fun_int_nat (tptp.hAPP_f879494613nt_nat tptp.cOMBC_int_nat_nat (tptp.hAPP_f1463450952at_nat (tptp.hAPP_f1087393429at_nat tptp.cOMBB_1601129847at_int tptp.times_times_nat) F)) R_2)) A))) (forall ((F tptp.fun_Ho864122878_a_nat) (A tptp.fun_Ho882550911a_bool) (R_2 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_f190641160ol_nat (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat F) A)) R_2) (tptp.hAPP_f190641160ol_nat (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat (tptp.hAPP_n1236213193_a_nat (tptp.hAPP_f668391445_a_nat tptp.cOMBC_1942990924at_nat (tptp.hAPP_f731653896at_nat (tptp.hAPP_f648261589at_nat tptp.cOMBB_1416330906iple_a tptp.times_times_nat) F)) R_2)) A))) (forall ((R_2 tptp.nat) (F tptp.fun_nat_nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat R_2))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat F) A)) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat (tptp.hAPP_f1914919701at_nat (tptp.hAPP_f1585078997at_nat tptp.cOMBB_nat_nat_nat _let_1) F)) A)))) (forall ((R_2 tptp.nat) (F tptp.fun_int_nat) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat R_2))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat F) A)) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat (tptp.hAPP_f2132704789nt_nat (tptp.hAPP_f901215189nt_nat tptp.cOMBB_nat_nat_int _let_1) F)) A)))) (forall ((R_2 tptp.nat) (F tptp.fun_Ho864122878_a_nat) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat R_2))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_f190641160ol_nat (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat F) A)) (tptp.hAPP_f190641160ol_nat (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat (tptp.hAPP_f2075363285_a_nat (tptp.hAPP_f375421205_a_nat tptp.cOMBB_1877004557iple_a _let_1) F)) A)))) (tptp.hBOOL (tptp.finite2130160977at_nat tptp.times_times_nat)) (tptp.hBOOL (tptp.finite1973466193nt_int tptp.times_times_int)) (forall ((Y_1 tptp.int) (Z_1 tptp.int) (A tptp.fun_int_bool) (X_1 tptp.int) (F tptp.fun_int_fun_int_int)) (let ((_let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool (tptp.finite772772422nt_int F) Z_1) A))) (=> (tptp.hBOOL (tptp.finite1973466193nt_int F)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_1)) (= Y_1 X_1)))))) (forall ((Y_1 tptp.nat) (Z_1 tptp.nat) (A tptp.fun_nat_bool) (X_1 tptp.nat) (F tptp.fun_nat_fun_nat_nat)) (let ((_let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool (tptp.finite929467206at_nat F) Z_1) A))) (=> (tptp.hBOOL (tptp.finite2130160977at_nat F)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_1)) (= Y_1 X_1)))))) (forall ((Y_1 tptp.hoare_2076525193iple_a) (Z_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (X_1 tptp.hoare_2076525193iple_a) (F tptp.fun_Ho483360497iple_a)) (let ((_let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool (tptp.finite974267142iple_a F) Z_1) A))) (=> (tptp.hBOOL (tptp.finite164030737iple_a F)) (=> (tptp.hBOOL (tptp.hAPP_H454055633a_bool _let_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP_H454055633a_bool _let_1 Y_1)) (= Y_1 X_1)))))) (forall ((G tptp.fun_Ho864122878_a_nat) (H tptp.fun_Ho864122878_a_nat) (A tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (= (tptp.hAPP_f190641160ol_nat (tptp.big_co1398215719_a_nat (tptp.hAPP_f2075363285_a_nat (tptp.hAPP_f1659339553_a_nat tptp.cOMBS_885136444at_nat (tptp.hAPP_f731653896at_nat (tptp.hAPP_f648261589at_nat tptp.cOMBB_1416330906iple_a tptp.times_times_nat) G)) H)) A) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_f190641160ol_nat (tptp.big_co1398215719_a_nat G) A)) (tptp.hAPP_f190641160ol_nat (tptp.big_co1398215719_a_nat H) A))))) (forall ((G tptp.fun_Ho1026035802_a_int) (H tptp.fun_Ho1026035802_a_int) (A tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (= (tptp.hAPP_f827914852ol_int (tptp.big_co2035489411_a_int (tptp.hAPP_f1382137045_a_int (tptp.hAPP_f1031139617_a_int tptp.cOMBS_728441660nt_int (tptp.hAPP_f534508204nt_int (tptp.hAPP_f1566620885nt_int tptp.cOMBB_364359670iple_a tptp.times_times_int) G)) H)) A) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_f827914852ol_int (tptp.big_co2035489411_a_int G) A)) (tptp.hAPP_f827914852ol_int (tptp.big_co2035489411_a_int H) A))))) (forall ((Z_1 tptp.nat) (X_1 tptp.nat) (A tptp.fun_nat_bool) (F tptp.fun_nat_fun_nat_nat)) (let ((_let_1 (tptp.finite_fold_nat_nat F Z_1))) (=> (tptp.hBOOL (tptp.finite2130160977at_nat F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (= (tptp.hAPP_f22106695ol_nat _let_1 A) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F X_1) (tptp.hAPP_f22106695ol_nat _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) tptp.bot_bot_fun_nat_bool)))))))))) (forall ((Z_1 tptp.fun_nat_bool) (X_1 tptp.nat) (A tptp.fun_nat_bool) (F tptp.fun_na35521688t_bool)) (let ((_let_1 (tptp.finite1578363458t_bool F Z_1))) (=> (tptp.hBOOL (tptp.finite1071749497t_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (= (tptp.hAPP_f800510211t_bool _let_1 A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool F X_1) (tptp.hAPP_f800510211t_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) tptp.bot_bot_fun_nat_bool)))))))))) (forall ((Z_1 tptp.hoare_2076525193iple_a) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (F tptp.fun_Ho483360497iple_a)) (let ((_let_1 (tptp.finite2089344904iple_a F Z_1))) (=> (tptp.hBOOL (tptp.finite164030737iple_a F)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A)) (= (tptp.hAPP_f2009966983iple_a _let_1 A) (tptp.hAPP_H1789220885iple_a (tptp.hAPP_H1417936777iple_a F X_1) (tptp.hAPP_f2009966983iple_a _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1) tptp.bot_bo214064617a_bool)))))))))) (forall ((Z_1 tptp.fun_Ho882550911a_bool) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (F tptp.fun_Ho112928087a_bool)) (let ((_let_1 (tptp.finite718386368a_bool F Z_1))) (=> (tptp.hBOOL (tptp.finite1617795063a_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A)) (= (tptp.hAPP_f642208769a_bool _let_1 A) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool F X_1) (tptp.hAPP_f642208769a_bool _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1) tptp.bot_bo214064617a_bool)))))))))) (forall ((Z_1 tptp.int) (X_1 tptp.int) (A tptp.fun_int_bool) (F tptp.fun_int_fun_int_int)) (let ((_let_1 (tptp.finite_fold_int_int F Z_1))) (=> (tptp.hBOOL (tptp.finite1973466193nt_int F)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (= (tptp.hAPP_f1594865479ol_int _let_1 A) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int F X_1) (tptp.hAPP_f1594865479ol_int _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) tptp.bot_bot_fun_int_bool)))))))))) (forall ((Z_1 tptp.fun_int_bool) (X_1 tptp.int) (A tptp.fun_int_bool) (F tptp.fun_in719570932t_bool)) (let ((_let_1 (tptp.finite1827710202t_bool F Z_1))) (=> (tptp.hBOOL (tptp.finite1321096241t_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (= (tptp.hAPP_f1805168059t_bool _let_1 A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool F X_1) (tptp.hAPP_f1805168059t_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) tptp.bot_bot_fun_int_bool)))))))))) (forall ((Z_1 tptp.nat) (X_1 tptp.nat) (A tptp.fun_nat_bool) (F tptp.fun_nat_fun_nat_nat)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1))) (let ((_let_2 (tptp.finite_fold_nat_nat F Z_1))) (=> (tptp.hBOOL (tptp.finite2130160977at_nat F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_f22106695ol_nat _let_2 (tptp.hAPP_f800510211t_bool _let_1 A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F X_1) (tptp.hAPP_f22106695ol_nat _let_2 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool _let_1 tptp.bot_bot_fun_nat_bool)))))))))) (forall ((Z_1 tptp.fun_nat_bool) (X_1 tptp.nat) (A tptp.fun_nat_bool) (F tptp.fun_na35521688t_bool)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1))) (let ((_let_2 (tptp.finite1578363458t_bool F Z_1))) (=> (tptp.hBOOL (tptp.finite1071749497t_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_f800510211t_bool _let_2 (tptp.hAPP_f800510211t_bool _let_1 A)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool F X_1) (tptp.hAPP_f800510211t_bool _let_2 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool _let_1 tptp.bot_bot_fun_nat_bool)))))))))) (forall ((Z_1 tptp.hoare_2076525193iple_a) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (F tptp.fun_Ho483360497iple_a)) (let ((_let_1 (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1))) (let ((_let_2 (tptp.finite2089344904iple_a F Z_1))) (=> (tptp.hBOOL (tptp.finite164030737iple_a F)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (= (tptp.hAPP_f2009966983iple_a _let_2 (tptp.hAPP_f642208769a_bool _let_1 A)) (tptp.hAPP_H1789220885iple_a (tptp.hAPP_H1417936777iple_a F X_1) (tptp.hAPP_f2009966983iple_a _let_2 (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) (tptp.hAPP_f642208769a_bool _let_1 tptp.bot_bo214064617a_bool)))))))))) (forall ((Z_1 tptp.fun_Ho882550911a_bool) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (F tptp.fun_Ho112928087a_bool)) (let ((_let_1 (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1))) (let ((_let_2 (tptp.finite718386368a_bool F Z_1))) (=> (tptp.hBOOL (tptp.finite1617795063a_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (= (tptp.hAPP_f642208769a_bool _let_2 (tptp.hAPP_f642208769a_bool _let_1 A)) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool F X_1) (tptp.hAPP_f642208769a_bool _let_2 (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) (tptp.hAPP_f642208769a_bool _let_1 tptp.bot_bo214064617a_bool)))))))))) (forall ((Z_1 tptp.int) (X_1 tptp.int) (A tptp.fun_int_bool) (F tptp.fun_int_fun_int_int)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1))) (let ((_let_2 (tptp.finite_fold_int_int F Z_1))) (=> (tptp.hBOOL (tptp.finite1973466193nt_int F)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (= (tptp.hAPP_f1594865479ol_int _let_2 (tptp.hAPP_f1805168059t_bool _let_1 A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int F X_1) (tptp.hAPP_f1594865479ol_int _let_2 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool _let_1 tptp.bot_bot_fun_int_bool)))))))))) (forall ((Z_1 tptp.fun_int_bool) (X_1 tptp.int) (A tptp.fun_int_bool) (F tptp.fun_in719570932t_bool)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1))) (let ((_let_2 (tptp.finite1827710202t_bool F Z_1))) (=> (tptp.hBOOL (tptp.finite1321096241t_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (= (tptp.hAPP_f1805168059t_bool _let_2 (tptp.hAPP_f1805168059t_bool _let_1 A)) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool F X_1) (tptp.hAPP_f1805168059t_bool _let_2 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool _let_1 tptp.bot_bot_fun_int_bool)))))))))) (forall ((F tptp.fun_nat_nat) (A_13 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.big_co1705425894at_nat F))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_13) A))) (= (tptp.hAPP_f22106695ol_nat _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat F A_13)) (tptp.hAPP_f22106695ol_nat _let_1 A))))))) (forall ((F tptp.fun_Ho864122878_a_nat) (A_13 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.big_co1398215719_a_nat F))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (=> (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a A_13) A))) (= (tptp.hAPP_f190641160ol_nat _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_H174304918_a_nat F A_13)) (tptp.hAPP_f190641160ol_nat _let_1 A))))))) (forall ((F tptp.fun_nat_int) (A_13 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.big_co195215938at_int F))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_13) A))) (= (tptp.hAPP_f659380387ol_int _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_nat_int F A_13)) (tptp.hAPP_f659380387ol_int _let_1 A))))))) (forall ((F tptp.fun_Ho1026035802_a_int) (A_13 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.big_co2035489411_a_int F))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (=> (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a A_13) A))) (= (tptp.hAPP_f827914852ol_int _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_H811578610_a_int F A_13)) (tptp.hAPP_f827914852ol_int _let_1 A))))))) (forall ((G tptp.fun_nat_nat) (X_1 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.big_co1705425894at_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A))) (= (tptp.hAPP_f22106695ol_nat _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat G X_1)) (tptp.hAPP_f22106695ol_nat _let_1 A))))))) (forall ((G tptp.fun_Ho864122878_a_nat) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.big_co1398215719_a_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (=> (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A))) (= (tptp.hAPP_f190641160ol_nat _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1) A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_H174304918_a_nat G X_1)) (tptp.hAPP_f190641160ol_nat _let_1 A))))))) (forall ((G tptp.fun_nat_int) (X_1 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.big_co195215938at_int G))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A))) (= (tptp.hAPP_f659380387ol_int _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_nat_int G X_1)) (tptp.hAPP_f659380387ol_int _let_1 A))))))) (forall ((G tptp.fun_Ho1026035802_a_int) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.big_co2035489411_a_int G))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (=> (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A))) (= (tptp.hAPP_f827914852ol_int _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1) A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_H811578610_a_int G X_1)) (tptp.hAPP_f827914852ol_int _let_1 A))))))) (forall ((F tptp.fun_nat_nat) (A_13 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat F))) (let ((_let_2 (tptp.hAPP_f22106695ol_nat _let_1 A))) (let ((_let_3 (tptp.hAPP_f22106695ol_nat _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) tptp.bot_bot_fun_nat_bool))))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_13) A)))) (and (=> _let_4 (= _let_3 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat _let_2) (tptp.hAPP_nat_nat F A_13)))) (=> (not _let_4) (= _let_3 _let_2)))))))) (forall ((F tptp.fun_Ho864122878_a_nat) (A_13 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat F))) (let ((_let_2 (tptp.hAPP_f190641160ol_nat _let_1 A))) (let ((_let_3 (tptp.hAPP_f190641160ol_nat _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) tptp.bot_bo214064617a_bool))))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a A_13) A)))) (and (=> _let_4 (= _let_3 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat _let_2) (tptp.hAPP_H174304918_a_nat F A_13)))) (=> (not _let_4) (= _let_3 _let_2)))))))) (forall ((F tptp.fun_int_nat) (A_13 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat F))) (let ((_let_2 (tptp.hAPP_f957591787ol_nat _let_1 A))) (let ((_let_3 (tptp.hAPP_f957591787ol_nat _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) tptp.bot_bot_fun_int_bool))))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_13) A)))) (and (=> _let_4 (= _let_3 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat _let_2) (tptp.hAPP_int_nat F A_13)))) (=> (not _let_4) (= _let_3 _let_2)))))))) (forall ((F tptp.fun_int_fun_int_int) (Z_1 tptp.int) (A tptp.fun_int_bool)) (= (tptp.hAPP_f1594865479ol_int (tptp.finite_fold_int_int F Z_1) A) (tptp.hAPP_f1594865479ol_int tptp.the_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool (tptp.finite772772422nt_int F) Z_1) A)))) (forall ((F tptp.fun_nat_fun_nat_nat) (Z_1 tptp.nat) (A tptp.fun_nat_bool)) (= (tptp.hAPP_f22106695ol_nat (tptp.finite_fold_nat_nat F Z_1) A) (tptp.hAPP_f22106695ol_nat tptp.the_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool (tptp.finite929467206at_nat F) Z_1) A)))) (forall ((F tptp.fun_Ho483360497iple_a) (Z_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (= (tptp.hAPP_f2009966983iple_a (tptp.finite2089344904iple_a F Z_1) A) (tptp.hAPP_f2009966983iple_a tptp.the_Ho1456473914iple_a (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool (tptp.finite974267142iple_a F) Z_1) A)))) (forall ((F tptp.fun_in719570932t_bool) (Z_1 tptp.fun_int_bool) (A tptp.fun_int_bool)) (= (tptp.hAPP_f1805168059t_bool (tptp.finite1827710202t_bool F Z_1) A) (tptp.hAPP_f631471077t_bool tptp.the_fun_int_bool (tptp.hAPP_f284875647l_bool (tptp.hAPP_f1634429330l_bool (tptp.finite1008073724t_bool F) Z_1) A)))) (forall ((F tptp.fun_Ho112928087a_bool) (Z_1 tptp.fun_Ho882550911a_bool) (A tptp.fun_Ho882550911a_bool)) (= (tptp.hAPP_f642208769a_bool (tptp.finite718386368a_bool F Z_1) A) (tptp.hAPP_f1758315691a_bool tptp.the_fu972267150a_bool (tptp.hAPP_f256727871l_bool (tptp.hAPP_f845487733l_bool (tptp.finite655745986a_bool F) Z_1) A)))) (forall ((F tptp.fun_na35521688t_bool) (Z_1 tptp.fun_nat_bool) (A tptp.fun_nat_bool)) (= (tptp.hAPP_f800510211t_bool (tptp.finite1578363458t_bool F Z_1) A) (tptp.hAPP_f582319405t_bool tptp.the_fun_nat_bool (tptp.hAPP_f103356543l_bool (tptp.hAPP_f1266913334l_bool (tptp.finite758726980t_bool F) Z_1) A)))) (forall ((Z_1 tptp.nat) (X_1 tptp.nat) (A tptp.fun_nat_bool) (F tptp.fun_nat_fun_nat_nat)) (=> (tptp.hBOOL (tptp.finite1860950092at_nat F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_f22106695ol_nat (tptp.finite_fold_nat_nat F Z_1) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_f22106695ol_nat (tptp.finite_fold_nat_nat F (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F X_1) Z_1)) A))))) (forall ((Z_1 tptp.fun_nat_bool) (X_1 tptp.nat) (A tptp.fun_nat_bool) (F tptp.fun_na35521688t_bool)) (=> (tptp.hBOOL (tptp.finite1956789438t_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_f800510211t_bool (tptp.finite1578363458t_bool F Z_1) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_f800510211t_bool (tptp.finite1578363458t_bool F (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool F X_1) Z_1)) A))))) (forall ((Z_1 tptp.hoare_2076525193iple_a) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (F tptp.fun_Ho483360497iple_a)) (=> (tptp.hBOOL (tptp.finite1532229644iple_a F)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (= (tptp.hAPP_f2009966983iple_a (tptp.finite2089344904iple_a F Z_1) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1) A)) (tptp.hAPP_f2009966983iple_a (tptp.finite2089344904iple_a F (tptp.hAPP_H1789220885iple_a (tptp.hAPP_H1417936777iple_a F X_1) Z_1)) A))))) (forall ((Z_1 tptp.fun_Ho882550911a_bool) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (F tptp.fun_Ho112928087a_bool)) (=> (tptp.hBOOL (tptp.finite1306023740a_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (= (tptp.hAPP_f642208769a_bool (tptp.finite718386368a_bool F Z_1) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1) A)) (tptp.hAPP_f642208769a_bool (tptp.finite718386368a_bool F (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool F X_1) Z_1)) A))))) (forall ((Z_1 tptp.int) (X_1 tptp.int) (A tptp.fun_int_bool) (F tptp.fun_int_fun_int_int)) (=> (tptp.hBOOL (tptp.finite1704255308nt_int F)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (= (tptp.hAPP_f1594865479ol_int (tptp.finite_fold_int_int F Z_1) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) A)) (tptp.hAPP_f1594865479ol_int (tptp.finite_fold_int_int F (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int F X_1) Z_1)) A))))) (forall ((Z_1 tptp.fun_int_bool) (X_1 tptp.int) (A tptp.fun_int_bool) (F tptp.fun_in719570932t_bool)) (=> (tptp.hBOOL (tptp.finite58652534t_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (= (tptp.hAPP_f1805168059t_bool (tptp.finite1827710202t_bool F Z_1) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) A)) (tptp.hAPP_f1805168059t_bool (tptp.finite1827710202t_bool F (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool F X_1) Z_1)) A))))) (forall ((Z_1 tptp.nat) (X_1 tptp.nat) (A tptp.fun_nat_bool) (F tptp.fun_nat_fun_nat_nat)) (let ((_let_1 (tptp.finite_fold_nat_nat F Z_1))) (=> (tptp.hBOOL (tptp.finite1860950092at_nat F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_f22106695ol_nat _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F X_1) (tptp.hAPP_f22106695ol_nat _let_1 A))))))) (forall ((Z_1 tptp.fun_nat_bool) (X_1 tptp.nat) (A tptp.fun_nat_bool) (F tptp.fun_na35521688t_bool)) (let ((_let_1 (tptp.finite1578363458t_bool F Z_1))) (=> (tptp.hBOOL (tptp.finite1956789438t_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_f800510211t_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool F X_1) (tptp.hAPP_f800510211t_bool _let_1 A))))))) (forall ((Z_1 tptp.hoare_2076525193iple_a) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (F tptp.fun_Ho483360497iple_a)) (let ((_let_1 (tptp.finite2089344904iple_a F Z_1))) (=> (tptp.hBOOL (tptp.finite1532229644iple_a F)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (= (tptp.hAPP_f2009966983iple_a _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1) A)) (tptp.hAPP_H1789220885iple_a (tptp.hAPP_H1417936777iple_a F X_1) (tptp.hAPP_f2009966983iple_a _let_1 A))))))) (forall ((Z_1 tptp.fun_Ho882550911a_bool) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (F tptp.fun_Ho112928087a_bool)) (let ((_let_1 (tptp.finite718386368a_bool F Z_1))) (=> (tptp.hBOOL (tptp.finite1306023740a_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (= (tptp.hAPP_f642208769a_bool _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1) A)) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool F X_1) (tptp.hAPP_f642208769a_bool _let_1 A))))))) (forall ((Z_1 tptp.int) (X_1 tptp.int) (A tptp.fun_int_bool) (F tptp.fun_int_fun_int_int)) (let ((_let_1 (tptp.finite_fold_int_int F Z_1))) (=> (tptp.hBOOL (tptp.finite1704255308nt_int F)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (= (tptp.hAPP_f1594865479ol_int _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int F X_1) (tptp.hAPP_f1594865479ol_int _let_1 A))))))) (forall ((Z_1 tptp.fun_int_bool) (X_1 tptp.int) (A tptp.fun_int_bool) (F tptp.fun_in719570932t_bool)) (let ((_let_1 (tptp.finite1827710202t_bool F Z_1))) (=> (tptp.hBOOL (tptp.finite58652534t_bool F)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (= (tptp.hAPP_f1805168059t_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) A)) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool F X_1) (tptp.hAPP_f1805168059t_bool _let_1 A))))))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool) (F tptp.fun_nat_fun_nat_nat) (F_1 tptp.fun_fun_nat_bool_nat)) (=> (tptp.hBOOL (tptp.finite988810631ne_nat F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A))) (= (tptp.hAPP_f22106695ol_nat F_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_f22106695ol_nat (tptp.finite_fold_nat_nat F X_1) A)))))) (forall ((X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (F tptp.fun_Ho483360497iple_a) (F_1 tptp.fun_fu253747899iple_a)) (=> (tptp.hBOOL (tptp.finite232328454iple_a F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (=> (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A))) (= (tptp.hAPP_f2009966983iple_a F_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1) A)) (tptp.hAPP_f2009966983iple_a (tptp.finite2089344904iple_a F X_1) A)))))) (forall ((X_1 tptp.int) (A tptp.fun_int_bool) (F tptp.fun_int_fun_int_int) (F_1 tptp.fun_fun_int_bool_int)) (=> (tptp.hBOOL (tptp.finite1626084323ne_int F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A))) (= (tptp.hAPP_f1594865479ol_int F_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) A)) (tptp.hAPP_f1594865479ol_int (tptp.finite_fold_int_int F X_1) A)))))) (forall ((A_13 tptp.nat) (A tptp.fun_nat_bool) (F tptp.fun_nat_fun_nat_nat) (F_1 tptp.fun_fun_nat_bool_nat)) (=> (tptp.hBOOL (tptp.finite795500164em_nat F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_f22106695ol_nat F_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) A)) (tptp.hAPP_f22106695ol_nat (tptp.finite_fold_nat_nat F A_13) A))))) (forall ((A_13 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (F tptp.fun_Ho483360497iple_a) (F_1 tptp.fun_fu253747899iple_a)) (=> (tptp.hBOOL (tptp.finite1659845635iple_a F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (= (tptp.hAPP_f2009966983iple_a F_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) A)) (tptp.hAPP_f2009966983iple_a (tptp.finite2089344904iple_a F A_13) A))))) (forall ((A_13 tptp.int) (A tptp.fun_int_bool) (F tptp.fun_int_fun_int_int) (F_1 tptp.fun_fun_int_bool_int)) (=> (tptp.hBOOL (tptp.finite1432773856em_int F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (= (tptp.hAPP_f1594865479ol_int F_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) A)) (tptp.hAPP_f1594865479ol_int (tptp.finite_fold_int_int F A_13) A))))) (forall ((A_13 tptp.nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_13) A))) (= (tptp.hAPP_f22106695ol_nat (tptp.finite_fold1_nat tptp.times_times_nat) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) A)) (tptp.hAPP_f22106695ol_nat (tptp.finite_fold_nat_nat tptp.times_times_nat A_13) A))))) (forall ((A_13 tptp.int) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_13) A))) (= (tptp.hAPP_f1594865479ol_int (tptp.finite_fold1_int tptp.times_times_int) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) A)) (tptp.hAPP_f1594865479ol_int (tptp.finite_fold_int_int tptp.times_times_int A_13) A))))) (forall ((Z_1 tptp.nat) (X_1 tptp.nat) (A tptp.fun_nat_bool) (V tptp.nat) (F tptp.fun_nat_fun_nat_nat)) (=> (tptp.hBOOL (tptp.finite2130160977at_nat F)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool (tptp.finite929467206at_nat F) Z_1) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) V)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A))) (not (forall ((Y_21 tptp.nat)) (=> (= V (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F X_1) Y_21)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool (tptp.finite929467206at_nat F) Z_1) A) Y_21)))))))))) (forall ((Z_1 tptp.hoare_2076525193iple_a) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (V tptp.hoare_2076525193iple_a) (F tptp.fun_Ho483360497iple_a)) (=> (tptp.hBOOL (tptp.finite164030737iple_a F)) (=> (tptp.hBOOL (tptp.hAPP_H454055633a_bool (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool (tptp.finite974267142iple_a F) Z_1) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1) A)) V)) (=> (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A))) (not (forall ((Y_21 tptp.hoare_2076525193iple_a)) (=> (= V (tptp.hAPP_H1789220885iple_a (tptp.hAPP_H1417936777iple_a F X_1) Y_21)) (not (tptp.hBOOL (tptp.hAPP_H454055633a_bool (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool (tptp.finite974267142iple_a F) Z_1) A) Y_21)))))))))) (forall ((Z_1 tptp.int) (X_1 tptp.int) (A tptp.fun_int_bool) (V tptp.int) (F tptp.fun_int_fun_int_int)) (=> (tptp.hBOOL (tptp.finite1973466193nt_int F)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool (tptp.finite772772422nt_int F) Z_1) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) A)) V)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A))) (not (forall ((Y_21 tptp.int)) (=> (= V (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int F X_1) Y_21)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool (tptp.finite772772422nt_int F) Z_1) A) Y_21)))))))))) (forall ((G tptp.fun_Ho864122878_a_nat) (F tptp.fun_Ho864122878_a_nat) (S_1 tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a S_1)) (= (tptp.hAPP_f190641160ol_nat _let_1 S_1) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat (tptp.hAPP_f420120536at_nat (tptp.hAPP_f228445643at_nat tptp.cOMBB_605112827at_nat _let_1) (tptp.hAPP_f1869543111a_bool (tptp.hAPP_f1882853211a_bool tptp.cOMBB_1211601634ol_nat tptp.collec977865374iple_a) (tptp.hAPP_f1869543111a_bool (tptp.hAPP_f1882853211a_bool tptp.cOMBB_1211601634ol_nat (tptp.hAPP_f1004093413a_bool tptp.cOMBS_1108095524l_bool (tptp.hAPP_f268025233l_bool (tptp.hAPP_f1261090107l_bool tptp.cOMBB_345279363iple_a tptp.fconj) (tptp.hAPP_f642208769a_bool (tptp.hAPP_f325481667a_bool tptp.cOMBC_1529670358l_bool tptp.member276146780iple_a) S_1)))) (tptp.hAPP_f1040149703a_bool tptp.cOMBC_240829083t_bool (tptp.hAPP_f570970635t_bool (tptp.hAPP_f2096737119t_bool tptp.cOMBB_2017898829iple_a tptp.fequal_nat) F)))))) (tptp.image_1778392390_a_nat F S_1)))))) (forall ((G tptp.fun_int_nat) (F tptp.fun_int_nat) (S_1 tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int S_1)) (= (tptp.hAPP_f957591787ol_nat _let_1 S_1) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat (tptp.hAPP_f389300155at_nat (tptp.hAPP_f109563153at_nat tptp.cOMBB_1381347800at_nat _let_1) (tptp.hAPP_f2022049025t_bool (tptp.hAPP_f1986088027t_bool tptp.cOMBB_2101530536ol_nat tptp.collect_int) (tptp.hAPP_f2022049025t_bool (tptp.hAPP_f1986088027t_bool tptp.cOMBB_2101530536ol_nat (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f202917053t_bool tptp.cOMBC_94739984l_bool tptp.member_int) S_1)))) (tptp.hAPP_f175561985t_bool tptp.cOMBC_int_nat_bool (tptp.hAPP_f876579787t_bool (tptp.hAPP_f2026117279t_bool tptp.cOMBB_1437810218ol_int tptp.fequal_nat) F)))))) (tptp.image_int_nat F S_1)))))) (forall ((G tptp.fun_nat_nat) (F tptp.fun_na1240513468iple_a) (S_1 tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat S_1)) (= (tptp.hAPP_f22106695ol_nat _let_1 S_1) (tptp.hAPP_f190641160ol_nat (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat (tptp.hAPP_f1753252377_a_nat (tptp.hAPP_f456064075_a_nat tptp.cOMBB_1733887227iple_a _let_1) (tptp.hAPP_f631038663t_bool (tptp.hAPP_f69420889t_bool tptp.cOMBB_1063904223iple_a tptp.collect_nat) (tptp.hAPP_f631038663t_bool (tptp.hAPP_f69420889t_bool tptp.cOMBB_1063904223iple_a (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fconj) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat) S_1)))) (tptp.hAPP_f1460432071t_bool tptp.cOMBC_2097822937a_bool (tptp.hAPP_f1324734153a_bool (tptp.hAPP_f946563611a_bool tptp.cOMBB_315605200ol_nat tptp.fequal1589671816iple_a) F)))))) (tptp.image_344477316iple_a F S_1)))))) (forall ((G tptp.fun_int_nat) (F tptp.fun_int_int) (S_1 tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int S_1)) (= (tptp.hAPP_f957591787ol_nat _let_1 S_1) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat (tptp.hAPP_f1134349059nt_nat (tptp.hAPP_f2100446809nt_nat tptp.cOMBB_2018621492at_int _let_1) (tptp.hAPP_f428220345t_bool (tptp.hAPP_f654702867t_bool tptp.cOMBB_591320580ol_int tptp.collect_int) (tptp.hAPP_f428220345t_bool (tptp.hAPP_f654702867t_bool tptp.cOMBB_591320580ol_int (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f202917053t_bool tptp.cOMBC_94739984l_bool tptp.member_int) S_1)))) (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool (tptp.hAPP_f1791153283t_bool (tptp.hAPP_f1399575567t_bool tptp.cOMBB_118231410ol_int tptp.fequal_int) F)))))) (tptp.image_int_int F S_1)))))) (forall ((G tptp.fun_int_nat) (F tptp.fun_in1219646560iple_a) (S_1 tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int S_1)) (= (tptp.hAPP_f957591787ol_nat _let_1 S_1) (tptp.hAPP_f190641160ol_nat (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat (tptp.hAPP_f10452157_a_nat (tptp.hAPP_f296893331_a_nat tptp.cOMBB_1983399767iple_a _let_1) (tptp.hAPP_f741913983t_bool (tptp.hAPP_f1871962969t_bool tptp.cOMBB_349652263iple_a tptp.collect_int) (tptp.hAPP_f741913983t_bool (tptp.hAPP_f1871962969t_bool tptp.cOMBB_349652263iple_a (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f202917053t_bool tptp.cOMBC_94739984l_bool tptp.member_int) S_1)))) (tptp.hAPP_f510295935t_bool tptp.cOMBC_1135948669a_bool (tptp.hAPP_f1362463689a_bool (tptp.hAPP_f438022427a_bool tptp.cOMBB_952878892ol_int tptp.fequal1589671816iple_a) F)))))) (tptp.image_323610408iple_a F S_1)))))) (forall ((G tptp.fun_nat_nat) (F tptp.fun_nat_int) (S_1 tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat S_1)) (= (tptp.hAPP_f22106695ol_nat _let_1 S_1) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat (tptp.hAPP_f1161717855nt_nat (tptp.hAPP_f1964560145nt_nat tptp.cOMBB_1125113304at_int _let_1) (tptp.hAPP_f783004929t_bool (tptp.hAPP_f1410409747t_bool tptp.cOMBB_1746576572ol_int tptp.collect_nat) (tptp.hAPP_f783004929t_bool (tptp.hAPP_f1410409747t_bool tptp.cOMBB_1746576572ol_int (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fconj) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat) S_1)))) (tptp.hAPP_f482008321t_bool tptp.cOMBC_nat_int_bool (tptp.hAPP_f1533130627t_bool (tptp.hAPP_f879109391t_bool tptp.cOMBB_1628441366ol_nat tptp.fequal_int) F)))))) (tptp.image_nat_int F S_1)))))) (forall ((G tptp.fun_Ho864122878_a_nat) (H tptp.fun_Ho864122878_a_nat) (A tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (=> (forall ((X_2 tptp.hoare_2076525193iple_a)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_2) A)) (= (tptp.hAPP_H174304918_a_nat G X_2) (tptp.hAPP_H174304918_a_nat H X_2)))) (= (tptp.hAPP_f190641160ol_nat (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat G) A) (tptp.hAPP_f190641160ol_nat (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat H) A))))) (forall ((G tptp.fun_nat_nat) (H tptp.fun_nat_nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (forall ((X_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (= (tptp.hAPP_nat_nat G X_2) (tptp.hAPP_nat_nat H X_2)))) (= (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat G) A) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat H) A))))) (forall ((G tptp.fun_int_nat) (H tptp.fun_int_nat) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) A)) (= (tptp.hAPP_int_nat G X_2) (tptp.hAPP_int_nat H X_2)))) (= (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat G) A) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat H) A))))) (forall ((F tptp.fun_int_fun_nat_nat) (R_1 tptp.fun_int_fun_nat_bool) (T_1 tptp.fun_nat_bool) (S_1 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int S_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat T_1)) (= (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat (tptp.hAPP_f1161717855nt_nat (tptp.hAPP_f369809936nt_nat tptp.cOMBS_1063588099ol_nat (tptp.hAPP_f1501159417ol_nat (tptp.hAPP_f1029311995ol_nat tptp.cOMBB_1562322300at_int tptp.big_co387207925at_nat) F)) (tptp.hAPP_f783004929t_bool (tptp.hAPP_f1410409747t_bool tptp.cOMBB_1746576572ol_int tptp.collect_nat) (tptp.hAPP_f783004929t_bool (tptp.hAPP_f1410409747t_bool tptp.cOMBB_1746576572ol_int (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fconj) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat) T_1)))) R_1)))) S_1) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat (tptp.hAPP_f389300155at_nat (tptp.hAPP_f1750007732at_nat tptp.cOMBS_2106653443ol_nat (tptp.hAPP_f299305025ol_nat (tptp.hAPP_f1632710027ol_nat tptp.cOMBB_1453893592at_nat tptp.big_co1740723097nt_nat) (tptp.hAPP_f879494613nt_nat tptp.cOMBC_int_nat_nat F))) (tptp.hAPP_f2022049025t_bool (tptp.hAPP_f1986088027t_bool tptp.cOMBB_2101530536ol_nat tptp.collect_int) (tptp.hAPP_f2022049025t_bool (tptp.hAPP_f1986088027t_bool tptp.cOMBB_2101530536ol_nat (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f202917053t_bool tptp.cOMBC_94739984l_bool tptp.member_int) S_1)))) (tptp.hAPP_f175561985t_bool tptp.cOMBC_int_nat_bool R_1))))) T_1))))) (forall ((F tptp.fun_Ho1036508337at_nat) (R_1 tptp.fun_Ho1349715618t_bool) (T_1 tptp.fun_nat_bool) (S_1 tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a S_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat T_1)) (= (tptp.hAPP_f190641160ol_nat (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat (tptp.hAPP_f1753252377_a_nat (tptp.hAPP_f991915629_a_nat tptp.cOMBS_902588832ol_nat (tptp.hAPP_f1296292793ol_nat (tptp.hAPP_f153943611ol_nat tptp.cOMBB_636937375iple_a tptp.big_co387207925at_nat) F)) (tptp.hAPP_f631038663t_bool (tptp.hAPP_f69420889t_bool tptp.cOMBB_1063904223iple_a tptp.collect_nat) (tptp.hAPP_f631038663t_bool (tptp.hAPP_f69420889t_bool tptp.cOMBB_1063904223iple_a (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fconj) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat) T_1)))) R_1)))) S_1) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat (tptp.hAPP_f420120536at_nat (tptp.hAPP_f1323480046at_nat tptp.cOMBS_1514622496ol_nat (tptp.hAPP_f1356625915ol_nat (tptp.hAPP_f2033836159ol_nat tptp.cOMBB_1944586014at_nat tptp.big_co922834230_a_nat) (tptp.hAPP_f668391445_a_nat tptp.cOMBC_1942990924at_nat F))) (tptp.hAPP_f1869543111a_bool (tptp.hAPP_f1882853211a_bool tptp.cOMBB_1211601634ol_nat tptp.collec977865374iple_a) (tptp.hAPP_f1869543111a_bool (tptp.hAPP_f1882853211a_bool tptp.cOMBB_1211601634ol_nat (tptp.hAPP_f1004093413a_bool tptp.cOMBS_1108095524l_bool (tptp.hAPP_f268025233l_bool (tptp.hAPP_f1261090107l_bool tptp.cOMBB_345279363iple_a tptp.fconj) (tptp.hAPP_f642208769a_bool (tptp.hAPP_f325481667a_bool tptp.cOMBC_1529670358l_bool tptp.member276146780iple_a) S_1)))) (tptp.hAPP_f1040149703a_bool tptp.cOMBC_240829083t_bool R_1))))) T_1))))) (forall ((F tptp.fun_Ho1488374613nt_nat) (R_1 tptp.fun_Ho1608761598t_bool) (T_1 tptp.fun_int_bool) (S_1 tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a S_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int T_1)) (= (tptp.hAPP_f190641160ol_nat (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat (tptp.hAPP_f10452157_a_nat (tptp.hAPP_f209886133_a_nat tptp.cOMBS_1838073924ol_nat (tptp.hAPP_f1998933761ol_nat (tptp.hAPP_f1772247755ol_nat tptp.cOMBB_1701789015iple_a tptp.big_co1740723097nt_nat) F)) (tptp.hAPP_f741913983t_bool (tptp.hAPP_f1871962969t_bool tptp.cOMBB_349652263iple_a tptp.collect_int) (tptp.hAPP_f741913983t_bool (tptp.hAPP_f1871962969t_bool tptp.cOMBB_349652263iple_a (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f202917053t_bool tptp.cOMBC_94739984l_bool tptp.member_int) T_1)))) R_1)))) S_1) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat (tptp.hAPP_f1503898400nt_nat (tptp.hAPP_f807099282nt_nat tptp.cOMBS_443177668ol_nat (tptp.hAPP_f1914880763ol_nat (tptp.hAPP_f534494591ol_nat tptp.cOMBB_434376058at_int tptp.big_co922834230_a_nat) (tptp.hAPP_f1096027413_a_nat tptp.cOMBC_1149022448nt_nat F))) (tptp.hAPP_f1500465535a_bool (tptp.hAPP_f967504915a_bool tptp.cOMBB_1848875326ol_int tptp.collec977865374iple_a) (tptp.hAPP_f1500465535a_bool (tptp.hAPP_f967504915a_bool tptp.cOMBB_1848875326ol_int (tptp.hAPP_f1004093413a_bool tptp.cOMBS_1108095524l_bool (tptp.hAPP_f268025233l_bool (tptp.hAPP_f1261090107l_bool tptp.cOMBB_345279363iple_a tptp.fconj) (tptp.hAPP_f642208769a_bool (tptp.hAPP_f325481667a_bool tptp.cOMBC_1529670358l_bool tptp.member276146780iple_a) S_1)))) (tptp.hAPP_f1732083583a_bool tptp.cOMBC_1771170551t_bool R_1))))) T_1))))) (forall ((F tptp.fun_nat_fun_int_nat) (R_1 tptp.fun_nat_fun_int_bool) (T_1 tptp.fun_int_bool) (S_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat S_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int T_1)) (= (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat (tptp.hAPP_f389300155at_nat (tptp.hAPP_f1750007732at_nat tptp.cOMBS_2106653443ol_nat (tptp.hAPP_f299305025ol_nat (tptp.hAPP_f1632710027ol_nat tptp.cOMBB_1453893592at_nat tptp.big_co1740723097nt_nat) F)) (tptp.hAPP_f2022049025t_bool (tptp.hAPP_f1986088027t_bool tptp.cOMBB_2101530536ol_nat tptp.collect_int) (tptp.hAPP_f2022049025t_bool (tptp.hAPP_f1986088027t_bool tptp.cOMBB_2101530536ol_nat (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f202917053t_bool tptp.cOMBC_94739984l_bool tptp.member_int) T_1)))) R_1)))) S_1) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat (tptp.hAPP_f1161717855nt_nat (tptp.hAPP_f369809936nt_nat tptp.cOMBS_1063588099ol_nat (tptp.hAPP_f1501159417ol_nat (tptp.hAPP_f1029311995ol_nat tptp.cOMBB_1562322300at_int tptp.big_co387207925at_nat) (tptp.hAPP_f446977493at_nat tptp.cOMBC_nat_int_nat F))) (tptp.hAPP_f783004929t_bool (tptp.hAPP_f1410409747t_bool tptp.cOMBB_1746576572ol_int tptp.collect_nat) (tptp.hAPP_f783004929t_bool (tptp.hAPP_f1410409747t_bool tptp.cOMBB_1746576572ol_int (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fconj) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat) S_1)))) (tptp.hAPP_f482008321t_bool tptp.cOMBC_nat_int_bool R_1))))) T_1))))) (forall ((F tptp.fun_na841142961_a_nat) (R_1 tptp.fun_na1758826658a_bool) (T_1 tptp.fun_Ho882550911a_bool) (S_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat S_1)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a T_1)) (= (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat (tptp.hAPP_f420120536at_nat (tptp.hAPP_f1323480046at_nat tptp.cOMBS_1514622496ol_nat (tptp.hAPP_f1356625915ol_nat (tptp.hAPP_f2033836159ol_nat tptp.cOMBB_1944586014at_nat tptp.big_co922834230_a_nat) F)) (tptp.hAPP_f1869543111a_bool (tptp.hAPP_f1882853211a_bool tptp.cOMBB_1211601634ol_nat tptp.collec977865374iple_a) (tptp.hAPP_f1869543111a_bool (tptp.hAPP_f1882853211a_bool tptp.cOMBB_1211601634ol_nat (tptp.hAPP_f1004093413a_bool tptp.cOMBS_1108095524l_bool (tptp.hAPP_f268025233l_bool (tptp.hAPP_f1261090107l_bool tptp.cOMBB_345279363iple_a tptp.fconj) (tptp.hAPP_f642208769a_bool (tptp.hAPP_f325481667a_bool tptp.cOMBC_1529670358l_bool tptp.member276146780iple_a) T_1)))) R_1)))) S_1) (tptp.hAPP_f190641160ol_nat (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat (tptp.hAPP_f1753252377_a_nat (tptp.hAPP_f991915629_a_nat tptp.cOMBS_902588832ol_nat (tptp.hAPP_f1296292793ol_nat (tptp.hAPP_f153943611ol_nat tptp.cOMBB_636937375iple_a tptp.big_co387207925at_nat) (tptp.hAPP_f982543381at_nat tptp.cOMBC_23578254_a_nat F))) (tptp.hAPP_f631038663t_bool (tptp.hAPP_f69420889t_bool tptp.cOMBB_1063904223iple_a tptp.collect_nat) (tptp.hAPP_f631038663t_bool (tptp.hAPP_f69420889t_bool tptp.cOMBB_1063904223iple_a (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fconj) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat) S_1)))) (tptp.hAPP_f1460432071t_bool tptp.cOMBC_2097822937a_bool R_1))))) T_1))))) (forall ((F tptp.fun_int_fun_int_nat) (R_1 tptp.fun_int_fun_int_bool) (T_1 tptp.fun_int_bool) (S_1 tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f202917053t_bool tptp.cOMBC_94739984l_bool tptp.member_int))) (let ((_let_2 (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj))) (let ((_let_3 (tptp.hAPP_f654702867t_bool tptp.cOMBB_591320580ol_int tptp.collect_int))) (let ((_let_4 (tptp.hAPP_f1331458699ol_nat tptp.cOMBB_2091167284at_int tptp.big_co1740723097nt_nat))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int S_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int T_1)) (= (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat (tptp.hAPP_f1134349059nt_nat (tptp.hAPP_f446447448nt_nat tptp.cOMBS_1999073191ol_nat (tptp.hAPP_f1548925761ol_nat _let_4 F)) (tptp.hAPP_f428220345t_bool _let_3 (tptp.hAPP_f428220345t_bool (tptp.hAPP_f654702867t_bool tptp.cOMBB_591320580ol_int (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool _let_2 (tptp.hAPP_f1805168059t_bool _let_1 T_1)))) R_1)))) S_1) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat (tptp.hAPP_f1134349059nt_nat (tptp.hAPP_f446447448nt_nat tptp.cOMBS_1999073191ol_nat (tptp.hAPP_f1548925761ol_nat _let_4 (tptp.hAPP_f909851349nt_nat tptp.cOMBC_int_int_nat F))) (tptp.hAPP_f428220345t_bool _let_3 (tptp.hAPP_f428220345t_bool (tptp.hAPP_f654702867t_bool tptp.cOMBB_591320580ol_int (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool _let_2 (tptp.hAPP_f1805168059t_bool _let_1 S_1)))) (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool R_1))))) T_1))))))))) (forall ((F tptp.fun_in501186901_a_nat) (R_1 tptp.fun_in451447550a_bool) (T_1 tptp.fun_Ho882550911a_bool) (S_1 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int S_1)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a T_1)) (= (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat (tptp.hAPP_f1503898400nt_nat (tptp.hAPP_f807099282nt_nat tptp.cOMBS_443177668ol_nat (tptp.hAPP_f1914880763ol_nat (tptp.hAPP_f534494591ol_nat tptp.cOMBB_434376058at_int tptp.big_co922834230_a_nat) F)) (tptp.hAPP_f1500465535a_bool (tptp.hAPP_f967504915a_bool tptp.cOMBB_1848875326ol_int tptp.collec977865374iple_a) (tptp.hAPP_f1500465535a_bool (tptp.hAPP_f967504915a_bool tptp.cOMBB_1848875326ol_int (tptp.hAPP_f1004093413a_bool tptp.cOMBS_1108095524l_bool (tptp.hAPP_f268025233l_bool (tptp.hAPP_f1261090107l_bool tptp.cOMBB_345279363iple_a tptp.fconj) (tptp.hAPP_f642208769a_bool (tptp.hAPP_f325481667a_bool tptp.cOMBC_1529670358l_bool tptp.member276146780iple_a) T_1)))) R_1)))) S_1) (tptp.hAPP_f190641160ol_nat (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat (tptp.hAPP_f10452157_a_nat (tptp.hAPP_f209886133_a_nat tptp.cOMBS_1838073924ol_nat (tptp.hAPP_f1998933761ol_nat (tptp.hAPP_f1772247755ol_nat tptp.cOMBB_1701789015iple_a tptp.big_co1740723097nt_nat) (tptp.hAPP_f287449365nt_nat tptp.cOMBC_1499522794_a_nat F))) (tptp.hAPP_f741913983t_bool (tptp.hAPP_f1871962969t_bool tptp.cOMBB_349652263iple_a tptp.collect_int) (tptp.hAPP_f741913983t_bool (tptp.hAPP_f1871962969t_bool tptp.cOMBB_349652263iple_a (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int tptp.fconj) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f202917053t_bool tptp.cOMBC_94739984l_bool tptp.member_int) S_1)))) (tptp.hAPP_f510295935t_bool tptp.cOMBC_1135948669a_bool R_1))))) T_1))))) (forall ((G tptp.fun_nat_nat) (X_1 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (= (tptp.hAPP_f22106695ol_nat _let_1 A) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat G X_1)) (tptp.hAPP_f22106695ol_nat _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) tptp.bot_bot_fun_nat_bool))))))))) (forall ((G tptp.fun_nat_int) (X_1 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f1599440987ol_int tptp.big_co1024481617at_int G))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (= (tptp.hAPP_f659380387ol_int _let_1 A) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int G X_1)) (tptp.hAPP_f659380387ol_int _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) tptp.bot_bot_fun_nat_bool))))))))) (forall ((G tptp.fun_Ho1026035802_a_int) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_f1870360797ol_int tptp.big_co1560107922_a_int G))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A)) (= (tptp.hAPP_f827914852ol_int _let_1 A) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_H811578610_a_int G X_1)) (tptp.hAPP_f827914852ol_int _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1) tptp.bot_bo214064617a_bool))))))))) (forall ((G tptp.fun_int_int) (X_1 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f1926459811ol_int tptp.big_co230513141nt_int G))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (= (tptp.hAPP_f1594865479ol_int _let_1 A) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int G X_1)) (tptp.hAPP_f1594865479ol_int _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) tptp.bot_bot_fun_int_bool))))))))) (forall ((G tptp.fun_Ho864122878_a_nat) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A)) (= (tptp.hAPP_f190641160ol_nat _let_1 A) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_H174304918_a_nat G X_1)) (tptp.hAPP_f190641160ol_nat _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1) tptp.bot_bo214064617a_bool))))))))) (forall ((G tptp.fun_int_nat) (X_1 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (= (tptp.hAPP_f957591787ol_nat _let_1 A) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_int_nat G X_1)) (tptp.hAPP_f957591787ol_nat _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) tptp.bot_bot_fun_int_bool))))))))) (forall ((F tptp.fun_nat_nat) (A_13 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat F))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_13) A)) (= (tptp.hAPP_f22106695ol_nat _let_1 A) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat F A_13)) (tptp.hAPP_f22106695ol_nat _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) tptp.bot_bot_fun_nat_bool))))))))) (forall ((F tptp.fun_nat_int) (A_13 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f1599440987ol_int tptp.big_co1024481617at_int F))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_13) A)) (= (tptp.hAPP_f659380387ol_int _let_1 A) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int F A_13)) (tptp.hAPP_f659380387ol_int _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) tptp.bot_bot_fun_nat_bool))))))))) (forall ((F tptp.fun_Ho1026035802_a_int) (A_13 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_f1870360797ol_int tptp.big_co1560107922_a_int F))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a A_13) A)) (= (tptp.hAPP_f827914852ol_int _let_1 A) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_H811578610_a_int F A_13)) (tptp.hAPP_f827914852ol_int _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) tptp.bot_bo214064617a_bool))))))))) (forall ((F tptp.fun_int_int) (A_13 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f1926459811ol_int tptp.big_co230513141nt_int F))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_13) A)) (= (tptp.hAPP_f1594865479ol_int _let_1 A) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int F A_13)) (tptp.hAPP_f1594865479ol_int _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) tptp.bot_bot_fun_int_bool))))))))) (forall ((F tptp.fun_Ho864122878_a_nat) (A_13 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat F))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a A_13) A)) (= (tptp.hAPP_f190641160ol_nat _let_1 A) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_H174304918_a_nat F A_13)) (tptp.hAPP_f190641160ol_nat _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) tptp.bot_bo214064617a_bool))))))))) (forall ((F tptp.fun_int_nat) (A_13 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat F))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_13) A)) (= (tptp.hAPP_f957591787ol_nat _let_1 A) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_int_nat F A_13)) (tptp.hAPP_f957591787ol_nat _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) tptp.bot_bot_fun_int_bool))))))))) (forall ((G tptp.fun_nat_nat) (X_1 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1))) (let ((_let_2 (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_f22106695ol_nat _let_2 (tptp.hAPP_f800510211t_bool _let_1 A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat G X_1)) (tptp.hAPP_f22106695ol_nat _let_2 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool _let_1 tptp.bot_bot_fun_nat_bool))))))))) (forall ((G tptp.fun_nat_int) (X_1 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1))) (let ((_let_2 (tptp.hAPP_f1599440987ol_int tptp.big_co1024481617at_int G))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_f659380387ol_int _let_2 (tptp.hAPP_f800510211t_bool _let_1 A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int G X_1)) (tptp.hAPP_f659380387ol_int _let_2 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool _let_1 tptp.bot_bot_fun_nat_bool))))))))) (forall ((G tptp.fun_Ho1026035802_a_int) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1))) (let ((_let_2 (tptp.hAPP_f1870360797ol_int tptp.big_co1560107922_a_int G))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (= (tptp.hAPP_f827914852ol_int _let_2 (tptp.hAPP_f642208769a_bool _let_1 A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_H811578610_a_int G X_1)) (tptp.hAPP_f827914852ol_int _let_2 (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) (tptp.hAPP_f642208769a_bool _let_1 tptp.bot_bo214064617a_bool))))))))) (forall ((G tptp.fun_int_int) (X_1 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1))) (let ((_let_2 (tptp.hAPP_f1926459811ol_int tptp.big_co230513141nt_int G))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (= (tptp.hAPP_f1594865479ol_int _let_2 (tptp.hAPP_f1805168059t_bool _let_1 A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int G X_1)) (tptp.hAPP_f1594865479ol_int _let_2 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool _let_1 tptp.bot_bot_fun_int_bool))))))))) (forall ((G tptp.fun_Ho864122878_a_nat) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1))) (let ((_let_2 (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (= (tptp.hAPP_f190641160ol_nat _let_2 (tptp.hAPP_f642208769a_bool _let_1 A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_H174304918_a_nat G X_1)) (tptp.hAPP_f190641160ol_nat _let_2 (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) (tptp.hAPP_f642208769a_bool _let_1 tptp.bot_bo214064617a_bool))))))))) (forall ((G tptp.fun_int_nat) (X_1 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1))) (let ((_let_2 (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (= (tptp.hAPP_f957591787ol_nat _let_2 (tptp.hAPP_f1805168059t_bool _let_1 A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_int_nat G X_1)) (tptp.hAPP_f957591787ol_nat _let_2 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool _let_1 tptp.bot_bot_fun_int_bool))))))))) (forall ((F tptp.fun_nat_nat) (G tptp.fun_nat_nat) (A tptp.fun_nat_bool)) (= (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat (tptp.hAPP_f1914919701at_nat (tptp.hAPP_f1408247010at_nat tptp.cOMBS_nat_nat_nat (tptp.hAPP_f1639111240at_nat (tptp.hAPP_f1731313045at_nat tptp.cOMBB_963856155at_nat tptp.plus_plus_nat) F)) G)) A) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat F) A)) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat G) A)))) (forall ((F tptp.fun_int_nat) (G tptp.fun_int_nat) (A tptp.fun_int_bool)) (= (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat (tptp.hAPP_f2132704789nt_nat (tptp.hAPP_f1399363134nt_nat tptp.cOMBS_int_nat_nat (tptp.hAPP_f1463450952at_nat (tptp.hAPP_f1087393429at_nat tptp.cOMBB_1601129847at_int tptp.plus_plus_nat) F)) G)) A) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat F) A)) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat G) A)))) (forall ((F tptp.fun_Ho864122878_a_nat) (G tptp.fun_Ho864122878_a_nat) (A tptp.fun_Ho882550911a_bool)) (= (tptp.hAPP_f190641160ol_nat (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat (tptp.hAPP_f2075363285_a_nat (tptp.hAPP_f1659339553_a_nat tptp.cOMBS_885136444at_nat (tptp.hAPP_f731653896at_nat (tptp.hAPP_f648261589at_nat tptp.cOMBB_1416330906iple_a tptp.plus_plus_nat) F)) G)) A) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_f190641160ol_nat (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat F) A)) (tptp.hAPP_f190641160ol_nat (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat G) A)))) (forall ((G tptp.fun_nat_nat) (H tptp.fun_nat_nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (= (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat (tptp.hAPP_f1914919701at_nat (tptp.hAPP_f1408247010at_nat tptp.cOMBS_nat_nat_nat (tptp.hAPP_f1639111240at_nat (tptp.hAPP_f1731313045at_nat tptp.cOMBB_963856155at_nat tptp.plus_plus_nat) G)) H)) A) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat G) A)) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat H) A))))) (forall ((G tptp.fun_Ho864122878_a_nat) (H tptp.fun_Ho864122878_a_nat) (A tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (= (tptp.hAPP_f190641160ol_nat (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat (tptp.hAPP_f2075363285_a_nat (tptp.hAPP_f1659339553_a_nat tptp.cOMBS_885136444at_nat (tptp.hAPP_f731653896at_nat (tptp.hAPP_f648261589at_nat tptp.cOMBB_1416330906iple_a tptp.plus_plus_nat) G)) H)) A) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_f190641160ol_nat (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat G) A)) (tptp.hAPP_f190641160ol_nat (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat H) A))))) (forall ((G tptp.fun_Ho1026035802_a_int) (H tptp.fun_Ho1026035802_a_int) (A tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (= (tptp.hAPP_f827914852ol_int (tptp.hAPP_f1870360797ol_int tptp.big_co1560107922_a_int (tptp.hAPP_f1382137045_a_int (tptp.hAPP_f1031139617_a_int tptp.cOMBS_728441660nt_int (tptp.hAPP_f534508204nt_int (tptp.hAPP_f1566620885nt_int tptp.cOMBB_364359670iple_a tptp.plus_plus_int) G)) H)) A) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_f827914852ol_int (tptp.hAPP_f1870360797ol_int tptp.big_co1560107922_a_int G) A)) (tptp.hAPP_f827914852ol_int (tptp.hAPP_f1870360797ol_int tptp.big_co1560107922_a_int H) A))))) (forall ((G tptp.fun_int_nat) (H tptp.fun_int_nat) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (= (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat (tptp.hAPP_f2132704789nt_nat (tptp.hAPP_f1399363134nt_nat tptp.cOMBS_int_nat_nat (tptp.hAPP_f1463450952at_nat (tptp.hAPP_f1087393429at_nat tptp.cOMBB_1601129847at_int tptp.plus_plus_nat) G)) H)) A) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat G) A)) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat H) A))))) (forall ((F tptp.fun_nat_nat) (A_13 tptp.nat) (F_1 tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat F))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_13) F_1))) (= (tptp.hAPP_f22106695ol_nat _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) F_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat F A_13)) (tptp.hAPP_f22106695ol_nat _let_1 F_1))))))) (forall ((F tptp.fun_nat_int) (A_13 tptp.nat) (F_1 tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f1599440987ol_int tptp.big_co1024481617at_int F))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat A_13) F_1))) (= (tptp.hAPP_f659380387ol_int _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) F_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int F A_13)) (tptp.hAPP_f659380387ol_int _let_1 F_1))))))) (forall ((F tptp.fun_Ho1026035802_a_int) (A_13 tptp.hoare_2076525193iple_a) (F_1 tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_f1870360797ol_int tptp.big_co1560107922_a_int F))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a F_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a A_13) F_1))) (= (tptp.hAPP_f827914852ol_int _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) F_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_H811578610_a_int F A_13)) (tptp.hAPP_f827914852ol_int _let_1 F_1))))))) (forall ((F tptp.fun_Ho864122878_a_nat) (A_13 tptp.hoare_2076525193iple_a) (F_1 tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat F))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a F_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a A_13) F_1))) (= (tptp.hAPP_f190641160ol_nat _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) F_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_H174304918_a_nat F A_13)) (tptp.hAPP_f190641160ol_nat _let_1 F_1))))))) (forall ((F tptp.fun_int_nat) (A_13 tptp.int) (F_1 tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat F))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int F_1)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int A_13) F_1))) (= (tptp.hAPP_f957591787ol_nat _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) F_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_int_nat F A_13)) (tptp.hAPP_f957591787ol_nat _let_1 F_1))))))) (forall ((G tptp.fun_nat_nat) (X_1 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A))) (= (tptp.hAPP_f22106695ol_nat _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat G X_1)) (tptp.hAPP_f22106695ol_nat _let_1 A))))))) (forall ((G tptp.fun_nat_int) (X_1 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f1599440987ol_int tptp.big_co1024481617at_int G))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A))) (= (tptp.hAPP_f659380387ol_int _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int G X_1)) (tptp.hAPP_f659380387ol_int _let_1 A))))))) (forall ((G tptp.fun_Ho1026035802_a_int) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_f1870360797ol_int tptp.big_co1560107922_a_int G))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (=> (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A))) (= (tptp.hAPP_f827914852ol_int _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1) A)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_H811578610_a_int G X_1)) (tptp.hAPP_f827914852ol_int _let_1 A))))))) (forall ((G tptp.fun_Ho864122878_a_nat) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (=> (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A))) (= (tptp.hAPP_f190641160ol_nat _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1) A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_H174304918_a_nat G X_1)) (tptp.hAPP_f190641160ol_nat _let_1 A))))))) (forall ((G tptp.fun_int_nat) (X_1 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat G))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A))) (= (tptp.hAPP_f957591787ol_nat _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) A)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_int_nat G X_1)) (tptp.hAPP_f957591787ol_nat _let_1 A))))))) (forall ((A_13 tptp.int) (E tptp.int) (Ca tptp.int) (Ba tptp.int) (D_1 tptp.int)) (= (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_13) E)) Ca) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Ba) E)) D_1)) (= Ca (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Ba) A_13)) E)) D_1)))) (forall ((A_13 tptp.int) (E tptp.int) (Ca tptp.int) (Ba tptp.int) (D_1 tptp.int)) (= (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_13) E)) Ca) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Ba) E)) D_1)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A_13) Ba)) E)) Ca) D_1))) (forall ((A_42 tptp.int) (B_34 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A_42) B_34)) B_34) A_42)) (forall ((A_41 tptp.int) (B_33 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_41) B_33)) B_33) A_41)) (forall ((W tptp.nat) (Y_1 tptp.nat) (X_1 tptp.nat) (Z_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat X_1))) (let ((_let_2 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat W))) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_2 Y_1)) (tptp.hAPP_nat_nat _let_1 Z_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_2 Z_1)) (tptp.hAPP_nat_nat _let_1 Y_1))) (or (= W X_1) (= Y_1 Z_1)))))) (forall ((W tptp.int) (Y_1 tptp.int) (X_1 tptp.int) (Z_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int X_1))) (let ((_let_2 (tptp.hAPP_int_fun_int_int tptp.times_times_int W))) (= (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_2 Y_1)) (tptp.hAPP_int_int _let_1 Z_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_2 Z_1)) (tptp.hAPP_int_int _let_1 Y_1))) (or (= W X_1) (= Y_1 Z_1)))))) (forall ((A_40 tptp.nat) (E_1 tptp.nat) (B_32 tptp.nat) (C_28 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_40) E_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_32) E_1)) C_28)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_40) B_32)) E_1)) C_28))) (forall ((A_40 tptp.int) (E_1 tptp.int) (B_32 tptp.int) (C_28 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_40) E_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_32) E_1)) C_28)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_40) B_32)) E_1)) C_28))) (forall ((A_39 tptp.nat) (M_4 tptp.nat) (B_31 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_39) M_4)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_31) M_4)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_39) B_31)) M_4))) (forall ((A_39 tptp.int) (M_4 tptp.int) (B_31 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_39) M_4)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_31) M_4)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_39) B_31)) M_4))) (forall ((B_30 tptp.nat) (A_38 tptp.nat) (C_27 tptp.nat)) (=> (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_30) A_38) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C_27) A_38)) (= B_30 C_27))) (forall ((B_30 tptp.int) (A_38 tptp.int) (C_27 tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_30) A_38) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int C_27) A_38)) (= B_30 C_27))) (forall ((A_37 tptp.nat) (B_29 tptp.nat) (C_26 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_37))) (=> (= (tptp.hAPP_nat_nat _let_1 B_29) (tptp.hAPP_nat_nat _let_1 C_26)) (= B_29 C_26)))) (forall ((A_37 tptp.int) (B_29 tptp.int) (C_26 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_37))) (=> (= (tptp.hAPP_int_int _let_1 B_29) (tptp.hAPP_int_int _let_1 C_26)) (= B_29 C_26)))) (forall ((A_36 tptp.nat) (B_28 tptp.nat) (C_25 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_36))) (=> (= (tptp.hAPP_nat_nat _let_1 B_28) (tptp.hAPP_nat_nat _let_1 C_25)) (= B_28 C_25)))) (forall ((A_36 tptp.int) (B_28 tptp.int) (C_25 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_36))) (=> (= (tptp.hAPP_int_int _let_1 B_28) (tptp.hAPP_int_int _let_1 C_25)) (= B_28 C_25)))) (forall ((A_35 tptp.nat) (B_27 tptp.nat) (C_24 tptp.nat) (D_6 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_35))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 B_27)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C_24) D_6)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 C_24)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_27) D_6))))) (forall ((A_35 tptp.int) (B_27 tptp.int) (C_24 tptp.int) (D_6 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_35))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 B_27)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int C_24) D_6)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 C_24)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_27) D_6))))) (forall ((Ba tptp.nat) (A_13 tptp.nat) (Ca tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Ba) A_13) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Ca) A_13)) (= Ba Ca))) (forall ((Ba tptp.int) (A_13 tptp.int) (Ca tptp.int)) (= (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Ba) A_13) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Ca) A_13)) (= Ba Ca))) (forall ((A_13 tptp.nat) (Ba tptp.nat) (Ca tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_13))) (= (= (tptp.hAPP_nat_nat _let_1 Ba) (tptp.hAPP_nat_nat _let_1 Ca)) (= Ba Ca)))) (forall ((A_13 tptp.int) (Ba tptp.int) (Ca tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_13))) (= (= (tptp.hAPP_int_int _let_1 Ba) (tptp.hAPP_int_int _let_1 Ca)) (= Ba Ca)))) (forall ((A_34 tptp.nat) (B_26 tptp.nat) (C_23 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_34))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 B_26)) C_23) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 C_23)) B_26)))) (forall ((A_34 tptp.int) (B_26 tptp.int) (C_23 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_34))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 B_26)) C_23) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 C_23)) B_26)))) (forall ((A_33 tptp.nat) (B_25 tptp.nat) (C_22 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_33))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 B_25)) C_22) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_25) C_22))))) (forall ((A_33 tptp.int) (B_25 tptp.int) (C_22 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_33))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 B_25)) C_22) (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_25) C_22))))) (forall ((A_32 tptp.nat) (B_24 tptp.nat) (C_21 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_32))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 B_24)) C_21) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_24) C_21))))) (forall ((A_32 tptp.int) (B_24 tptp.int) (C_21 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_32))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 B_24)) C_21) (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_24) C_21))))) (forall ((A_31 tptp.nat) (C_20 tptp.nat) (D_5 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_31))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C_20) D_5)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 C_20)) D_5)))) (forall ((A_31 tptp.int) (C_20 tptp.int) (D_5 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_31))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int C_20) D_5)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 C_20)) D_5)))) (forall ((A_30 tptp.nat) (C_19 tptp.nat) (D_4 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_30))) (let ((_let_2 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C_19))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_2 D_4)) (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat _let_1 D_4)))))) (forall ((A_30 tptp.int) (C_19 tptp.int) (D_4 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_30))) (let ((_let_2 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int C_19))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int _let_2 D_4)) (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int _let_1 D_4)))))) (forall ((A_29 tptp.nat) (C_18 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_29) C_18) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C_18) A_29))) (forall ((A_29 tptp.int) (C_18 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_29) C_18) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int C_18) A_29))) (forall ((Lx_6 tptp.nat) (Ly_4 tptp.nat) (Rx_6 tptp.nat) (Ry_4 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Lx_6))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 Ly_4)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Rx_6) Ry_4)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 Rx_6)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Ly_4) Ry_4))))) (forall ((Lx_6 tptp.int) (Ly_4 tptp.int) (Rx_6 tptp.int) (Ry_4 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int Lx_6))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int _let_1 Ly_4)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Rx_6) Ry_4)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int _let_1 Rx_6)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Ly_4) Ry_4))))) (forall ((Lx_5 tptp.nat) (Ly_3 tptp.nat) (Rx_5 tptp.nat) (Ry_3 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Lx_5) Ly_3)))) (let ((_let_2 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Rx_5))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_2 Ry_3)) (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat _let_1 Ry_3)))))) (forall ((Lx_5 tptp.int) (Ly_3 tptp.int) (Rx_5 tptp.int) (Ry_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Lx_5) Ly_3)))) (let ((_let_2 (tptp.hAPP_int_fun_int_int tptp.times_times_int Rx_5))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int _let_2 Ry_3)) (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int _let_1 Ry_3)))))) (forall ((Lx_4 tptp.nat) (Ly_2 tptp.nat) (Rx_4 tptp.nat) (Ry_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Rx_4) Ry_2))) (let ((_let_2 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Lx_4))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat _let_2 Ly_2)) _let_1) (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Ly_2) _let_1)))))) (forall ((Lx_4 tptp.int) (Ly_2 tptp.int) (Rx_4 tptp.int) (Ry_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Rx_4) Ry_2))) (let ((_let_2 (tptp.hAPP_int_fun_int_int tptp.times_times_int Lx_4))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int _let_2 Ly_2)) _let_1) (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Ly_2) _let_1)))))) (forall ((Lx_3 tptp.nat) (Ly_1 tptp.nat) (Rx_3 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Lx_3))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 Ly_1)) Rx_3) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 Rx_3)) Ly_1)))) (forall ((Lx_3 tptp.int) (Ly_1 tptp.int) (Rx_3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int Lx_3))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int _let_1 Ly_1)) Rx_3) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int _let_1 Rx_3)) Ly_1)))) (forall ((Lx_2 tptp.nat) (Ly tptp.nat) (Rx_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Lx_2))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 Ly)) Rx_2) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Ly) Rx_2))))) (forall ((Lx_2 tptp.int) (Ly tptp.int) (Rx_2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int Lx_2))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int _let_1 Ly)) Rx_2) (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Ly) Rx_2))))) (forall ((A_28 tptp.nat) (B_23 tptp.nat) (C_17 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_28))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 B_23)) C_17) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_23) C_17))))) (forall ((A_28 tptp.int) (B_23 tptp.int) (C_17 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int A_28))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int _let_1 B_23)) C_17) (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_23) C_17))))) (forall ((Lx_1 tptp.nat) (Rx_1 tptp.nat) (Ry_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Lx_1))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Rx_1) Ry_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 Rx_1)) Ry_1)))) (forall ((Lx_1 tptp.int) (Rx_1 tptp.int) (Ry_1 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int Lx_1))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Rx_1) Ry_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int _let_1 Rx_1)) Ry_1)))) (forall ((Lx tptp.nat) (Rx tptp.nat) (Ry tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Lx))) (let ((_let_2 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Rx))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_2 Ry)) (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat _let_1 Ry)))))) (forall ((Lx tptp.int) (Rx tptp.int) (Ry tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int Lx))) (let ((_let_2 (tptp.hAPP_int_fun_int_int tptp.times_times_int Rx))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int _let_2 Ry)) (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int _let_1 Ry)))))) (forall ((A_27 tptp.nat) (B_22 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_27) B_22) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_22) A_27))) (forall ((A_27 tptp.int) (B_22 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_27) B_22) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_22) A_27))) (forall ((A_13 tptp.int) (Ba tptp.int) (Ca tptp.int) (D_1 tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A_13) Ba) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Ca) D_1)) (= (= A_13 Ba) (= Ca D_1)))) (forall ((X_27 tptp.nat) (Y_20 tptp.nat) (Z_10 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat X_27))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Y_20) Z_10)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 Y_20)) (tptp.hAPP_nat_nat _let_1 Z_10))))) (forall ((X_27 tptp.int) (Y_20 tptp.int) (Z_10 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int X_27))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Y_20) Z_10)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 Y_20)) (tptp.hAPP_int_int _let_1 Z_10))))) (forall ((Ca tptp.nat) (D_1 tptp.nat) (A_13 tptp.nat) (Ba tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Ba))) (let ((_let_2 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_13))) (= (and (not (= A_13 Ba)) (not (= Ca D_1))) (not (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_2 Ca)) (tptp.hAPP_nat_nat _let_1 D_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_2 D_1)) (tptp.hAPP_nat_nat _let_1 Ca)))))))) (forall ((Ca tptp.int) (D_1 tptp.int) (A_13 tptp.int) (Ba tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int Ba))) (let ((_let_2 (tptp.hAPP_int_fun_int_int tptp.times_times_int A_13))) (= (and (not (= A_13 Ba)) (not (= Ca D_1))) (not (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_2 Ca)) (tptp.hAPP_int_int _let_1 D_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_2 D_1)) (tptp.hAPP_int_int _let_1 Ca)))))))) (forall ((A_26 tptp.int) (B_21 tptp.int) (C_16 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_26) B_21)) C_16) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_26) C_16)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_21) C_16)))) (forall ((A_26 tptp.nat) (B_21 tptp.nat) (C_16 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_26) B_21)) C_16) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_26) C_16)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_21) C_16)))) (forall ((A_25 tptp.int) (B_20 tptp.int) (C_15 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_25) B_20)) C_15) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_25) C_15)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int B_20) C_15)))) (forall ((A_25 tptp.nat) (B_20 tptp.nat) (C_15 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_25) B_20)) C_15) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat A_25) C_15)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat B_20) C_15)))) (forall ((F tptp.fun_int_nat) (G tptp.fun_int_nat) (A tptp.fun_int_bool)) (=> (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) A)) (= (tptp.hAPP_int_nat F X_2) (tptp.hAPP_int_nat G X_2)))) (= (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat F) A) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat G) A)))) (forall ((F tptp.fun_Ho864122878_a_nat) (G tptp.fun_Ho864122878_a_nat) (A tptp.fun_Ho882550911a_bool)) (=> (forall ((X_2 tptp.hoare_2076525193iple_a)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_2) A)) (= (tptp.hAPP_H174304918_a_nat F X_2) (tptp.hAPP_H174304918_a_nat G X_2)))) (= (tptp.hAPP_f190641160ol_nat (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat F) A) (tptp.hAPP_f190641160ol_nat (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat G) A)))) (forall ((F tptp.fun_nat_nat) (G tptp.fun_nat_nat) (A tptp.fun_nat_bool)) (=> (forall ((X_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (= (tptp.hAPP_nat_nat F X_2) (tptp.hAPP_nat_nat G X_2)))) (= (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat F) A) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat G) A)))) (forall ((F tptp.fun_int_nat) (G tptp.fun_int_nat) (A tptp.fun_int_bool) (B tptp.fun_int_bool)) (=> (= A B) (=> (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) B)) (= (tptp.hAPP_int_nat F X_2) (tptp.hAPP_int_nat G X_2)))) (= (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat F) A) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat G) B))))) (forall ((F tptp.fun_Ho864122878_a_nat) (G tptp.fun_Ho864122878_a_nat) (A tptp.fun_Ho882550911a_bool) (B tptp.fun_Ho882550911a_bool)) (=> (= A B) (=> (forall ((X_2 tptp.hoare_2076525193iple_a)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_2) B)) (= (tptp.hAPP_H174304918_a_nat F X_2) (tptp.hAPP_H174304918_a_nat G X_2)))) (= (tptp.hAPP_f190641160ol_nat (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat F) A) (tptp.hAPP_f190641160ol_nat (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat G) B))))) (forall ((F tptp.fun_nat_nat) (G tptp.fun_nat_nat) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (=> (= A B) (=> (forall ((X_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) B)) (= (tptp.hAPP_nat_nat F X_2) (tptp.hAPP_nat_nat G X_2)))) (= (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat F) A) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat G) B))))) (forall ((H tptp.fun_int_nat) (G tptp.fun_int_nat) (A tptp.fun_int_bool) (B tptp.fun_int_bool)) (=> (= A B) (=> (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) B)) (= (tptp.hAPP_int_nat H X_2) (tptp.hAPP_int_nat G X_2)))) (= (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat H) A) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat G) B))))) (forall ((H tptp.fun_Ho864122878_a_nat) (G tptp.fun_Ho864122878_a_nat) (A tptp.fun_Ho882550911a_bool) (B tptp.fun_Ho882550911a_bool)) (=> (= A B) (=> (forall ((X_2 tptp.hoare_2076525193iple_a)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_2) B)) (= (tptp.hAPP_H174304918_a_nat H X_2) (tptp.hAPP_H174304918_a_nat G X_2)))) (= (tptp.hAPP_f190641160ol_nat (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat H) A) (tptp.hAPP_f190641160ol_nat (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat G) B))))) (forall ((H tptp.fun_nat_nat) (G tptp.fun_nat_nat) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (=> (= A B) (=> (forall ((X_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) B)) (= (tptp.hAPP_nat_nat H X_2) (tptp.hAPP_nat_nat G X_2)))) (= (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat H) A) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat G) B))))) (forall ((K_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat K_1) tptp.bot_bot_fun_nat_bool))) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool _let_1) (tptp.hAPP_n1699378549t_bool tptp.ord_lessThan_nat K_1)) _let_1))) (forall ((K_1 tptp.int)) (let ((_let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int K_1) tptp.bot_bot_fun_int_bool))) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool _let_1) (tptp.hAPP_i1948725293t_bool tptp.ord_lessThan_int K_1)) _let_1))) (forall ((F tptp.fun_Ho864122878_a_nat) (A tptp.fun_Ho882550911a_bool) (B tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat F))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a B)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool B) A)) (= (tptp.hAPP_f190641160ol_nat _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) B)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_f190641160ol_nat _let_1 A)) (tptp.hAPP_f190641160ol_nat _let_1 B))))))) (forall ((F tptp.fun_int_nat) (A tptp.fun_int_bool) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat F))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) A)) (= (tptp.hAPP_f957591787ol_nat _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_f957591787ol_nat _let_1 A)) (tptp.hAPP_f957591787ol_nat _let_1 B))))))) (forall ((F tptp.fun_nat_nat) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat F))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) A)) (= (tptp.hAPP_f22106695ol_nat _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_f22106695ol_nat _let_1 A)) (tptp.hAPP_f22106695ol_nat _let_1 B))))))) (forall ((X_1 tptp.fun_int_bool)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool X_1) X_1))) (forall ((X_1 tptp.fun_nat_bool)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_1) X_1))) (forall ((X_26 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_26) X_26))) (forall ((X_26 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_26) X_26))) (forall ((A tptp.fun_int_bool) (B tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) A)) (= A B)))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) A)) (= A B)))) (forall ((Ca tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (B tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a Ca))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 B)))))) (forall ((Ca tptp.int) (A tptp.fun_int_bool) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int Ca))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B)))))) (forall ((Ca tptp.nat) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat Ca))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B)))))) (forall ((A tptp.fun_nat_bool)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool tptp.bot_bot_fun_nat_bool) A))) (forall ((A tptp.fun_int_bool)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool tptp.bot_bot_fun_int_bool) A))) (forall ((A tptp.fun_Ho882550911a_bool)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool tptp.bot_bo214064617a_bool) A))) (forall ((A tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (tptp.hBOOL (tptp.hAPP_f1490793353l_bool tptp.finite1832883692a_bool (tptp.hAPP_f354682389l_bool tptp.collec416005674a_bool (tptp.hAPP_f256727871l_bool (tptp.hAPP_f246259945l_bool tptp.cOMBC_1515890438l_bool tptp.ord_le940607413a_bool) A)))))) (forall ((A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (tptp.hBOOL (tptp.hAPP_f215623910l_bool tptp.finite1395289673t_bool (tptp.hAPP_f1948010709l_bool tptp.collect_fun_int_bool (tptp.hAPP_f284875647l_bool (tptp.hAPP_f1399552105l_bool tptp.cOMBC_605892544l_bool tptp.ord_le951220754t_bool) A)))))) (forall ((A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (tptp.hBOOL (tptp.hAPP_f1637334154l_bool tptp.finite2012431853t_bool (tptp.hAPP_f1246832597l_bool tptp.collect_fun_nat_bool (tptp.hAPP_f103356543l_bool (tptp.hAPP_f643944041l_bool tptp.cOMBC_1693257480l_bool tptp.ord_le1568362934t_bool) A)))))) (forall ((R_1 tptp.fun_Ho882550911a_bool) (S_1 tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_f325481667a_bool tptp.cOMBC_1529670358l_bool tptp.member276146780iple_a))) (= (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool (tptp.hAPP_f642208769a_bool _let_1 R_1)) (tptp.hAPP_f642208769a_bool _let_1 S_1))) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool R_1) S_1))))) (forall ((R_1 tptp.fun_int_bool) (S_1 tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f202917053t_bool tptp.cOMBC_94739984l_bool tptp.member_int))) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.hAPP_f1805168059t_bool _let_1 R_1)) (tptp.hAPP_f1805168059t_bool _let_1 S_1))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool R_1) S_1))))) (forall ((R_1 tptp.fun_nat_bool) (S_1 tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat))) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f800510211t_bool _let_1 R_1)) (tptp.hAPP_f800510211t_bool _let_1 S_1))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool R_1) S_1))))) (forall ((X_25 tptp.int) (Y_19 tptp.int)) (=> (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_25) Y_19))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_19) X_25)))) (forall ((X_25 tptp.nat) (Y_19 tptp.nat)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_25) Y_19))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_19) X_25)))) (forall ((X_1 tptp.int) (F tptp.fun_int_bool) (G tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool F) G)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_int_bool F X_1)) (tptp.hAPP_int_bool G X_1))))) (forall ((X_1 tptp.nat) (F tptp.fun_nat_bool) (G tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool F) G)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_nat_bool F X_1)) (tptp.hAPP_nat_bool G X_1))))) (forall ((Z_1 tptp.fun_int_bool) (Y_1 tptp.fun_int_bool) (X_1 tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool Z_1))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool Y_1) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 Y_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 X_1)))))) (forall ((Z_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool) (X_1 tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Z_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_1) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 Y_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 X_1)))))) (forall ((Z_9 tptp.int) (Y_18 tptp.int) (X_24 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z_9))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_18) X_24)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_18)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X_24)))))) (forall ((Z_9 tptp.nat) (Y_18 tptp.nat) (X_24 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Z_9))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_18) X_24)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_18)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X_24)))))) (forall ((Y_1 tptp.fun_int_bool) (X_1 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool Y_1) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool X_1) Y_1)) (= X_1 Y_1)))) (forall ((Y_1 tptp.fun_nat_bool) (X_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_1) X_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_1) Y_1)) (= X_1 Y_1)))) (forall ((Y_17 tptp.int) (X_23 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_17) X_23)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_23) Y_17)) (= X_23 Y_17)))) (forall ((Y_17 tptp.nat) (X_23 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_17) X_23)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_23) Y_17)) (= X_23 Y_17)))) (forall ((Z_1 tptp.fun_int_bool) (X_1 tptp.fun_int_bool) (Y_1 tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 Y_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool Y_1) Z_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 Z_1)))))) (forall ((Z_1 tptp.fun_nat_bool) (X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 Y_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_1) Z_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 Z_1)))))) (forall ((Z_8 tptp.int) (X_22 tptp.int) (Y_16 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_22))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_16)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_16) Z_8)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Z_8)))))) (forall ((Z_8 tptp.nat) (X_22 tptp.nat) (Y_16 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_22))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_16)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_16) Z_8)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Z_8)))))) (forall ((X_1 tptp.fun_int_bool) (Y_1 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool X_1) Y_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool Y_1) X_1)) (= X_1 Y_1)))) (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_1) Y_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_1) X_1)) (= X_1 Y_1)))) (forall ((X_21 tptp.int) (Y_15 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_21) Y_15)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_15) X_21)) (= X_21 Y_15)))) (forall ((X_21 tptp.nat) (Y_15 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_21) Y_15)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_15) X_21)) (= X_21 Y_15)))) (forall ((Ca tptp.fun_int_bool) (Ba tptp.fun_int_bool) (A_13 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool Ba) A_13)) (=> (= Ba Ca) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool Ca) A_13))))) (forall ((Ca tptp.fun_nat_bool) (Ba tptp.fun_nat_bool) (A_13 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ba) A_13)) (=> (= Ba Ca) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ca) A_13))))) (forall ((C_14 tptp.int) (B_19 tptp.int) (A_24 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_19) A_24)) (=> (= B_19 C_14) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_14) A_24))))) (forall ((C_14 tptp.nat) (B_19 tptp.nat) (A_24 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_19) A_24)) (=> (= B_19 C_14) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C_14) A_24))))) (forall ((Ca tptp.fun_int_bool) (A_13 tptp.fun_int_bool) (Ba tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A_13))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 Ba)) (=> (= Ba Ca) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 Ca)))))) (forall ((Ca tptp.fun_nat_bool) (A_13 tptp.fun_nat_bool) (Ba tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_13))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 Ba)) (=> (= Ba Ca) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 Ca)))))) (forall ((C_13 tptp.int) (A_23 tptp.int) (B_18 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_23))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_18)) (=> (= B_18 C_13) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 C_13)))))) (forall ((C_13 tptp.nat) (A_23 tptp.nat) (B_18 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_23))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_18)) (=> (= B_18 C_13) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 C_13)))))) (forall ((Ca tptp.fun_int_bool) (A_13 tptp.fun_int_bool) (Ba tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool Ca))) (=> (= A_13 Ba) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 Ba)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A_13)))))) (forall ((Ca tptp.fun_nat_bool) (A_13 tptp.fun_nat_bool) (Ba tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ca))) (=> (= A_13 Ba) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 Ba)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A_13)))))) (forall ((C_12 tptp.int) (A_22 tptp.int) (B_17 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_12))) (=> (= A_22 B_17) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_17)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_22)))))) (forall ((C_12 tptp.nat) (A_22 tptp.nat) (B_17 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C_12))) (=> (= A_22 B_17) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_17)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_22)))))) (forall ((Ca tptp.fun_int_bool) (A_13 tptp.fun_int_bool) (Ba tptp.fun_int_bool)) (=> (= A_13 Ba) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool Ba) Ca)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A_13) Ca))))) (forall ((Ca tptp.fun_nat_bool) (A_13 tptp.fun_nat_bool) (Ba tptp.fun_nat_bool)) (=> (= A_13 Ba) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Ba) Ca)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_13) Ca))))) (forall ((C_11 tptp.int) (A_21 tptp.int) (B_16 tptp.int)) (=> (= A_21 B_16) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_16) C_11)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_21) C_11))))) (forall ((C_11 tptp.nat) (A_21 tptp.nat) (B_16 tptp.nat)) (=> (= A_21 B_16) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_16) C_11)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_21) C_11))))) (forall ((Y_1 tptp.fun_int_bool) (X_1 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool Y_1) X_1)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool X_1) Y_1)) (= X_1 Y_1)))) (forall ((Y_1 tptp.fun_nat_bool) (X_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_1) X_1)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_1) Y_1)) (= X_1 Y_1)))) (forall ((Y_1 tptp.int) (X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_1) X_1)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_1) Y_1)) (= X_1 Y_1)))) (forall ((Y_1 tptp.nat) (X_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_1) X_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_1)) (= X_1 Y_1)))) (forall ((X_1 tptp.int) (F tptp.fun_int_bool) (G tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool F) G)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_int_bool F X_1)) (tptp.hAPP_int_bool G X_1))))) (forall ((X_1 tptp.nat) (F tptp.fun_nat_bool) (G tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool F) G)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_nat_bool F X_1)) (tptp.hAPP_nat_bool G X_1))))) (forall ((X_1 tptp.fun_int_bool) (Y_1 tptp.fun_int_bool)) (=> (= X_1 Y_1) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool X_1) Y_1)))) (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (=> (= X_1 Y_1) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_1) Y_1)))) (forall ((X_20 tptp.int) (Y_14 tptp.int)) (=> (= X_20 Y_14) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_20) Y_14)))) (forall ((X_20 tptp.nat) (Y_14 tptp.nat)) (=> (= X_20 Y_14) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_20) Y_14)))) (forall ((X_1 tptp.fun_int_bool) (Y_1 tptp.fun_int_bool)) (= (= X_1 Y_1) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool Y_1) X_1))))) (forall ((X_1 tptp.fun_nat_bool) (Y_1 tptp.fun_nat_bool)) (= (= X_1 Y_1) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Y_1) X_1))))) (forall ((X_1 tptp.int) (Y_1 tptp.int)) (= (= X_1 Y_1) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_1) X_1))))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (= (= X_1 Y_1) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_1) X_1))))) (forall ((X_19 tptp.int) (Y_13 tptp.int)) (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_19) Y_13)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_13) X_19)))) (forall ((X_19 tptp.nat) (Y_13 tptp.nat)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_19) Y_13)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_13) X_19)))) (forall ((F tptp.fun_int_bool) (G tptp.fun_int_bool)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool F) G)) (forall ((X_2 tptp.int)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_int_bool F X_2)) (tptp.hAPP_int_bool G X_2)))))) (forall ((F tptp.fun_nat_bool) (G tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool F) G)) (forall ((X_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_nat_bool F X_2)) (tptp.hAPP_nat_bool G X_2)))))) (forall ((A tptp.fun_int_bool) (B tptp.fun_int_bool)) (=> (= A B) (not (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)) (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) A))))))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (=> (= A B) (not (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) A))))))) (forall ((C_5 tptp.fun_int_bool) (A tptp.fun_int_bool) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) C_5)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 C_5)))))) (forall ((C_5 tptp.fun_nat_bool) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) C_5)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 C_5)))))) (forall ((X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (B tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 B)))))) (forall ((X_1 tptp.int) (A tptp.fun_int_bool) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int X_1))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B)))))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat X_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B)))))) (forall ((B tptp.fun_Ho882550911a_bool) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool A) B)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 B)))))) (forall ((B tptp.fun_int_bool) (X_1 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int X_1))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B)))))) (forall ((B tptp.fun_nat_bool) (X_1 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat X_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B)))))) (forall ((X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (B tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 B)))))) (forall ((X_1 tptp.int) (A tptp.fun_int_bool) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int X_1))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B)))))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat X_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B)))))) (forall ((A tptp.fun_int_bool) (B tptp.fun_int_bool)) (=> (= A B) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) A)))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (=> (= A B) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) A)))) (forall ((A tptp.fun_int_bool) (B tptp.fun_int_bool)) (=> (= A B) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (=> (= A B) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)))) (forall ((A tptp.fun_int_bool) (B tptp.fun_int_bool)) (= (= A B) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) A))))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (= (= A B) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) A))))) (forall ((A tptp.fun_int_bool)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) A))) (forall ((A tptp.fun_nat_bool)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) A))) (forall ((X_1 tptp.int) (Pa tptp.fun_int_bool) (Q_1 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool Pa) Q_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa X_1)) (tptp.hBOOL (tptp.hAPP_int_bool Q_1 X_1))))) (forall ((X_1 tptp.nat) (Pa tptp.fun_nat_bool) (Q_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Pa) Q_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa X_1)) (tptp.hBOOL (tptp.hAPP_nat_bool Q_1 X_1))))) (forall ((Q_1 tptp.fun_int_bool) (Pa tptp.fun_int_bool) (X_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa X_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool Pa) Q_1)) (tptp.hBOOL (tptp.hAPP_int_bool Q_1 X_1))))) (forall ((Q_1 tptp.fun_nat_bool) (Pa tptp.fun_nat_bool) (X_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa X_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Pa) Q_1)) (tptp.hBOOL (tptp.hAPP_nat_bool Q_1 X_1))))) (forall ((X_1 tptp.int) (Y_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.hAPP_i1948725293t_bool tptp.ord_lessThan_int X_1)) (tptp.hAPP_i1948725293t_bool tptp.ord_lessThan_int Y_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_1) Y_1)))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_n1699378549t_bool tptp.ord_lessThan_nat X_1)) (tptp.hAPP_n1699378549t_bool tptp.ord_lessThan_nat Y_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_1)))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (= (= (tptp.hAPP_n1699378549t_bool tptp.ord_lessThan_nat X_1) (tptp.hAPP_n1699378549t_bool tptp.ord_lessThan_nat Y_1)) (= X_1 Y_1))) (forall ((C_10 tptp.int) (A_20 tptp.int) (B_15 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int C_10))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 A_20)) (tptp.hAPP_int_int _let_1 B_15))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_20) B_15))))) (forall ((C_10 tptp.nat) (A_20 tptp.nat) (B_15 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C_10))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 A_20)) (tptp.hAPP_nat_nat _let_1 B_15))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_20) B_15))))) (forall ((A_19 tptp.int) (C_9 tptp.int) (B_14 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_19) C_9)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_14) C_9))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_19) B_14)))) (forall ((A_19 tptp.nat) (C_9 tptp.nat) (B_14 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_19) C_9)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_14) C_9))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_19) B_14)))) (forall ((C_8 tptp.int) (D_3 tptp.int) (A_18 tptp.int) (B_13 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_18) B_13)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int C_8) D_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_18) C_8)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_13) D_3)))))) (forall ((C_8 tptp.nat) (D_3 tptp.nat) (A_18 tptp.nat) (B_13 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_18) B_13)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C_8) D_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_18) C_8)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_13) D_3)))))) (forall ((C_7 tptp.int) (A_17 tptp.int) (B_12 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int C_7))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_17) B_12)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 A_17)) (tptp.hAPP_int_int _let_1 B_12)))))) (forall ((C_7 tptp.nat) (A_17 tptp.nat) (B_12 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat C_7))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_17) B_12)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 A_17)) (tptp.hAPP_nat_nat _let_1 B_12)))))) (forall ((C_6 tptp.int) (A_16 tptp.int) (B_11 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_16) B_11)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_16) C_6)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int B_11) C_6))))) (forall ((C_6 tptp.nat) (A_16 tptp.nat) (B_11 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_16) B_11)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_16) C_6)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat B_11) C_6))))) (forall ((Ca tptp.int) (A_13 tptp.int) (Ba tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Ca))) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 A_13)) (tptp.hAPP_int_int _let_1 Ba))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_13) Ba))))) (forall ((Ca tptp.nat) (A_13 tptp.nat) (Ba tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Ca))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 A_13)) (tptp.hAPP_nat_nat _let_1 Ba))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_13) Ba))))) (forall ((A_13 tptp.int) (Ca tptp.int) (Ba tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int A_13) Ca)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Ba) Ca))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_13) Ba)))) (forall ((A_13 tptp.nat) (Ca tptp.nat) (Ba tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat A_13) Ca)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Ba) Ca))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_13) Ba)))) (forall ((A_13 tptp.bool)) (=> (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool A_13) tptp.bot_bot_bool)) (= (tptp.hBOOL A_13) (tptp.hBOOL tptp.bot_bot_bool)))) (forall ((A_13 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_13) tptp.bot_bot_fun_nat_bool)) (= A_13 tptp.bot_bot_fun_nat_bool))) (forall ((A_13 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A_13) tptp.bot_bot_fun_int_bool)) (= A_13 tptp.bot_bot_fun_int_bool))) (forall ((A_13 tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool A_13) tptp.bot_bo214064617a_bool)) (= A_13 tptp.bot_bo214064617a_bool))) (forall ((A_15 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_15) tptp.bot_bot_nat)) (= A_15 tptp.bot_bot_nat))) (forall ((A_13 tptp.bool)) (= (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool A_13) tptp.bot_bot_bool)) (= (tptp.hBOOL A_13) (tptp.hBOOL tptp.bot_bot_bool)))) (forall ((A_13 tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A_13) tptp.bot_bot_fun_nat_bool)) (= A_13 tptp.bot_bot_fun_nat_bool))) (forall ((A_13 tptp.fun_int_bool)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A_13) tptp.bot_bot_fun_int_bool)) (= A_13 tptp.bot_bot_fun_int_bool))) (forall ((A_13 tptp.fun_Ho882550911a_bool)) (= (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool A_13) tptp.bot_bo214064617a_bool)) (= A_13 tptp.bot_bo214064617a_bool))) (forall ((A_13 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_13) tptp.bot_bot_nat)) (= A_13 tptp.bot_bot_nat))) (forall ((A_13 tptp.bool)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool tptp.bot_bot_bool) A_13))) (forall ((A_13 tptp.fun_nat_bool)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool tptp.bot_bot_fun_nat_bool) A_13))) (forall ((A_13 tptp.fun_int_bool)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool tptp.bot_bot_fun_int_bool) A_13))) (forall ((A_13 tptp.fun_Ho882550911a_bool)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool tptp.bot_bo214064617a_bool) A_13))) (forall ((A_14 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.bot_bot_nat) A_14))) (forall ((A_13 tptp.int) (Ba tptp.int) (Ca tptp.int) (D_1 tptp.int)) (=> (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A_13) Ba) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Ca) D_1)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_13) Ba)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Ca) D_1))))) (forall ((A tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) tptp.bot_bot_fun_nat_bool)) (= A tptp.bot_bot_fun_nat_bool))) (forall ((A tptp.fun_int_bool)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) tptp.bot_bot_fun_int_bool)) (= A tptp.bot_bot_fun_int_bool))) (forall ((A tptp.fun_Ho882550911a_bool)) (= (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool A) tptp.bot_bo214064617a_bool)) (= A tptp.bot_bo214064617a_bool))) (forall ((A tptp.fun_Ho882550911a_bool) (B tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a B)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A))))) (forall ((A tptp.fun_int_bool) (B tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int B)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A))))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A))))) (forall ((A tptp.fun_Ho882550911a_bool) (B tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a B)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool A) B)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A))))) (forall ((A tptp.fun_int_bool) (B tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A))))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A))))) (forall ((A_13 tptp.nat) (C_5 tptp.fun_nat_bool) (D_2 tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool C_5) D_2)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f800510211t_bool _let_1 C_5)) (tptp.hAPP_f800510211t_bool _let_1 D_2)))))) (forall ((A_13 tptp.int) (C_5 tptp.fun_int_bool) (D_2 tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool C_5) D_2)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.hAPP_f1805168059t_bool _let_1 C_5)) (tptp.hAPP_f1805168059t_bool _let_1 D_2)))))) (forall ((A_13 tptp.hoare_2076525193iple_a) (C_5 tptp.fun_Ho882550911a_bool) (D_2 tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool C_5) D_2)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool (tptp.hAPP_f642208769a_bool _let_1 C_5)) (tptp.hAPP_f642208769a_bool _let_1 D_2)))))) (forall ((Ba tptp.nat) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Ba) B)))))) (forall ((Ba tptp.int) (A tptp.fun_int_bool) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int Ba) B)))))) (forall ((Ba tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (B tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool A))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 B)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a Ba) B)))))) (forall ((B tptp.fun_nat_bool) (X_1 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A))) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A))) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) B))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B)))))) (forall ((B tptp.fun_int_bool) (X_1 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A))) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A))) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) B))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B)))))) (forall ((B tptp.fun_Ho882550911a_bool) (X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool A))) (=> (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A))) (= (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1) B))) (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 B)))))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) A)) B)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) B)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B))))) (forall ((X_1 tptp.int) (A tptp.fun_int_bool) (B tptp.fun_int_bool)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) A)) B)) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) B)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B))))) (forall ((X_1 tptp.hoare_2076525193iple_a) (A tptp.fun_Ho882550911a_bool) (B tptp.fun_Ho882550911a_bool)) (= (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1) A)) B)) (and (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) B)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool A) B))))) (forall ((B tptp.fun_nat_bool) (A_13 tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_13) B)))) (forall ((B tptp.fun_int_bool) (A_13 tptp.int)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_13) B)))) (forall ((B tptp.fun_Ho882550911a_bool) (A_13 tptp.hoare_2076525193iple_a)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool B) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_13) B)))) (forall ((F tptp.fun_int_int) (A tptp.fun_int_bool) (B tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.image_int_int F A)) (tptp.image_int_int F B))))) (forall ((F tptp.fun_Ho1518252029iple_a) (A tptp.fun_Ho882550911a_bool) (B tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool A) B)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool (tptp.image_1416816325iple_a F A)) (tptp.image_1416816325iple_a F B))))) (forall ((F tptp.fun_nat_int) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.image_nat_int F A)) (tptp.image_nat_int F B))))) (forall ((F tptp.fun_nat_nat) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.image_nat_nat F A)) (tptp.image_nat_nat F B))))) (forall ((B tptp.fun_int_bool) (F tptp.fun_int_int) (A tptp.fun_int_bool)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) (tptp.image_int_int F A))) (exists ((AA tptp.fun_int_bool)) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool AA) A)) (= B (tptp.image_int_int F AA)))))) (forall ((B tptp.fun_Ho882550911a_bool) (F tptp.fun_Ho1518252029iple_a) (A tptp.fun_Ho882550911a_bool)) (= (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool B) (tptp.image_1416816325iple_a F A))) (exists ((AA tptp.fun_Ho882550911a_bool)) (and (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool AA) A)) (= B (tptp.image_1416816325iple_a F AA)))))) (forall ((B tptp.fun_int_bool) (F tptp.fun_nat_int) (A tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) (tptp.image_nat_int F A))) (exists ((AA tptp.fun_nat_bool)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool AA) A)) (= B (tptp.image_nat_int F AA)))))) (forall ((B tptp.fun_nat_bool) (F tptp.fun_nat_nat) (A tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) (tptp.image_nat_nat F A))) (exists ((AA tptp.fun_nat_bool)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool AA) A)) (= B (tptp.image_nat_nat F AA)))))) (forall ((C_5 tptp.fun_int_bool) (A tptp.fun_int_bool) (B tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) C_5)) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool B) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool C_5) A)) A)))) (forall ((C_5 tptp.fun_Ho882550911a_bool) (A tptp.fun_Ho882550911a_bool) (B tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool B) C_5)) (= (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool B) (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool C_5) A)) A)))) (forall ((C_5 tptp.fun_nat_bool) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) C_5)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool B) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool C_5) A)) A)))) (forall ((D_2 tptp.fun_int_bool) (B tptp.fun_int_bool) (A tptp.fun_int_bool) (C_5 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) C_5)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool D_2) B)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B)) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool C_5) D_2)))))) (forall ((D_2 tptp.fun_Ho882550911a_bool) (B tptp.fun_Ho882550911a_bool) (A tptp.fun_Ho882550911a_bool) (C_5 tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool A) C_5)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool D_2) B)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) B)) (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool C_5) D_2)))))) (forall ((D_2 tptp.fun_nat_bool) (B tptp.fun_nat_bool) (A tptp.fun_nat_bool) (C_5 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) C_5)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool D_2) B)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B)) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool C_5) D_2)))))) (forall ((A tptp.fun_int_bool) (B tptp.fun_int_bool)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B)) A))) (forall ((A tptp.fun_Ho882550911a_bool) (B tptp.fun_Ho882550911a_bool)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) B)) A))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B)) A))) (forall ((Ts tptp.fun_Ho882550911a_bool) (Ga tptp.fun_Ho882550911a_bool) (Ts_1 tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hoare_572465367rivs_a Ga))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 Ts_1)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool Ts) Ts_1)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 Ts)))))) (forall ((Ts tptp.fun_Ho882550911a_bool) (Ga tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool Ts) Ga)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hoare_572465367rivs_a Ga) Ts)))) (forall ((A tptp.fun_nat_bool) (X_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1) tptp.bot_bot_fun_nat_bool))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) _let_1)) (or (= A tptp.bot_bot_fun_nat_bool) (= A _let_1))))) (forall ((A tptp.fun_int_bool) (X_1 tptp.int)) (let ((_let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1) tptp.bot_bot_fun_int_bool))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) _let_1)) (or (= A tptp.bot_bot_fun_int_bool) (= A _let_1))))) (forall ((A tptp.fun_Ho882550911a_bool) (X_1 tptp.hoare_2076525193iple_a)) (let ((_let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1) tptp.bot_bo214064617a_bool))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool A) _let_1)) (or (= A tptp.bot_bo214064617a_bool) (= A _let_1))))) (forall ((B tptp.fun_int_bool) (F tptp.fun_int_int) (A tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) (tptp.image_int_int F A))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int B))))) (forall ((B tptp.fun_Ho882550911a_bool) (F tptp.fun_Ho1518252029iple_a) (A tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool B) (tptp.image_1416816325iple_a F A))) (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a B))))) (forall ((B tptp.fun_int_bool) (F tptp.fun_nat_int) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) (tptp.image_nat_int F A))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int B))))) (forall ((B tptp.fun_nat_bool) (F tptp.fun_nat_nat) (A tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) (tptp.image_nat_nat F A))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B))))) (forall ((F tptp.fun_int_int) (A tptp.fun_int_bool) (B tptp.fun_int_bool)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool (tptp.image_int_int F A)) (tptp.image_int_int F B))) (tptp.image_int_int F (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) B))))) (forall ((F tptp.fun_Ho1518252029iple_a) (A tptp.fun_Ho882550911a_bool) (B tptp.fun_Ho882550911a_bool)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool (tptp.image_1416816325iple_a F A)) (tptp.image_1416816325iple_a F B))) (tptp.image_1416816325iple_a F (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) B))))) (forall ((F tptp.fun_nat_int) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool (tptp.image_nat_int F A)) (tptp.image_nat_int F B))) (tptp.image_nat_int F (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B))))) (forall ((F tptp.fun_nat_nat) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool (tptp.image_nat_nat F A)) (tptp.image_nat_nat F B))) (tptp.image_nat_nat F (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) B))))) (forall ((A_13 tptp.int) (E tptp.int) (Ca tptp.int) (Ba tptp.int) (D_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_13) E)) Ca)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Ba) E)) D_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int A_13) Ba)) E)) Ca)) D_1)))) (forall ((A_13 tptp.int) (E tptp.int) (Ca tptp.int) (Ba tptp.int) (D_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int A_13) E)) Ca)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Ba) E)) D_1))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Ca) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Ba) A_13)) E)) D_1))))) (forall ((A tptp.fun_nat_bool) (X_1 tptp.nat) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool _let_1 tptp.bot_bot_fun_nat_bool))) B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) (tptp.hAPP_f800510211t_bool _let_1 B))))))) (forall ((A tptp.fun_int_bool) (X_1 tptp.int) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool _let_1 tptp.bot_bot_fun_int_bool))) B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) (tptp.hAPP_f1805168059t_bool _let_1 B))))))) (forall ((A tptp.fun_Ho882550911a_bool) (X_1 tptp.hoare_2076525193iple_a) (B tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) (tptp.hAPP_f642208769a_bool _let_1 tptp.bot_bo214064617a_bool))) B)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool A) (tptp.hAPP_f642208769a_bool _let_1 B))))))) (forall ((A tptp.fun_nat_bool) (X_1 tptp.nat) (B tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)))) (let ((_let_3 (tptp.hAPP_n1512601776t_bool tptp.insert_nat X_1))) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 (tptp.hAPP_f800510211t_bool _let_3 B))) (and (=> _let_2 (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) (tptp.hAPP_f800510211t_bool _let_3 tptp.bot_bot_fun_nat_bool))) B))) (=> (not _let_2) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B))))))))) (forall ((A tptp.fun_int_bool) (X_1 tptp.int) (B tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)))) (let ((_let_3 (tptp.hAPP_i1529485324t_bool tptp.insert_int X_1))) (= (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 (tptp.hAPP_f1805168059t_bool _let_3 B))) (and (=> _let_2 (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) (tptp.hAPP_f1805168059t_bool _let_3 tptp.bot_bot_fun_int_bool))) B))) (=> (not _let_2) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B))))))))) (forall ((A tptp.fun_Ho882550911a_bool) (X_1 tptp.hoare_2076525193iple_a) (B tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool A))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_1) A)))) (let ((_let_3 (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a X_1))) (= (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 (tptp.hAPP_f642208769a_bool _let_3 B))) (and (=> _let_2 (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) (tptp.hAPP_f642208769a_bool _let_3 tptp.bot_bo214064617a_bool))) B))) (=> (not _let_2) (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 B))))))))) (forall ((B tptp.fun_Ho882550911a_bool) (A tptp.fun_Ho882550911a_bool) (F tptp.fun_Ho483360497iple_a) (F_1 tptp.fun_fu253747899iple_a)) (let ((_let_1 (tptp.hAPP_f2009966983iple_a F_1 A))) (=> (tptp.hBOOL (tptp.finite1659845635iple_a F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a A)) (=> (not (= B tptp.bot_bo214064617a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool B) A)) (= (tptp.hAPP_H1789220885iple_a (tptp.hAPP_H1417936777iple_a F (tptp.hAPP_f2009966983iple_a F_1 B)) _let_1) _let_1))))))) (forall ((B tptp.fun_int_bool) (A tptp.fun_int_bool) (F tptp.fun_int_fun_int_int) (F_1 tptp.fun_fun_int_bool_int)) (let ((_let_1 (tptp.hAPP_f1594865479ol_int F_1 A))) (=> (tptp.hBOOL (tptp.finite1432773856em_int F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (not (= B tptp.bot_bot_fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) A)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int F (tptp.hAPP_f1594865479ol_int F_1 B)) _let_1) _let_1))))))) (forall ((B tptp.fun_nat_bool) (A tptp.fun_nat_bool) (F tptp.fun_nat_fun_nat_nat) (F_1 tptp.fun_fun_nat_bool_nat)) (let ((_let_1 (tptp.hAPP_f22106695ol_nat F_1 A))) (=> (tptp.hBOOL (tptp.finite795500164em_nat F F_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (not (= B tptp.bot_bot_fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) A)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat F (tptp.hAPP_f22106695ol_nat F_1 B)) _let_1) _let_1))))))) (forall ((Pa tptp.fun_fu425979586l_bool) (A tptp.fun_nat_bool) (F_1 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F_1)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool F_1) A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa tptp.bot_bot_fun_nat_bool)) (=> (forall ((A_12 tptp.nat) (F_2 tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat A_12))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat F_2)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 F_2))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat A_12) F_2))))))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool Pa F_1))))))) (forall ((Pa tptp.fun_fu819804446l_bool) (A tptp.fun_int_bool) (F_1 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int F_1)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool F_1) A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa tptp.bot_bot_fun_int_bool)) (=> (forall ((A_12 tptp.int) (F_2 tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int A_12))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int F_2)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 F_2))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int A_12) F_2))))))))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool Pa F_1))))))) (forall ((Pa tptp.fun_fu2026518849l_bool) (A tptp.fun_Ho882550911a_bool) (F_1 tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a F_1)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool F_1) A)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool Pa tptp.bot_bo214064617a_bool)) (=> (forall ((A_12 tptp.hoare_2076525193iple_a) (F_2 tptp.fun_Ho882550911a_bool)) (let ((_let_1 (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a A_12))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a F_2)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 A)) (=> (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 F_2))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool Pa F_2)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool Pa (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a A_12) F_2))))))))) (tptp.hBOOL (tptp.hAPP_f500854239l_bool Pa F_1))))))) (forall ((B tptp.fun_Ho882550911a_bool) (A tptp.fun_Ho882550911a_bool)) (=> (forall ((X_2 tptp.hoare_2076525193iple_a)) (let ((_let_1 (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_2))) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool _let_1 B))))) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool A) B)))) (forall ((B tptp.fun_int_bool) (A tptp.fun_int_bool)) (=> (forall ((X_2 tptp.int)) (let ((_let_1 (tptp.hAPP_i2112223885l_bool tptp.member_int X_2))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool _let_1 B))))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)))) (forall ((B tptp.fun_nat_bool) (A tptp.fun_nat_bool)) (=> (forall ((X_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_n215258509l_bool tptp.member_nat X_2))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool _let_1 B))))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)))) (forall ((F tptp.fun_int_int) (A tptp.fun_int_bool) (B tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) (tptp.image_int_int F A))) (exists ((C_4 tptp.fun_int_bool)) (and (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool C_4) A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int C_4)) (= B (tptp.image_int_int F C_4))))))) (forall ((F tptp.fun_Ho1518252029iple_a) (A tptp.fun_Ho882550911a_bool) (B tptp.fun_Ho882550911a_bool)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a B)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool B) (tptp.image_1416816325iple_a F A))) (exists ((C_4 tptp.fun_Ho882550911a_bool)) (and (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool C_4) A)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool tptp.finite217552220iple_a C_4)) (= B (tptp.image_1416816325iple_a F C_4))))))) (forall ((F tptp.fun_nat_int) (A tptp.fun_nat_bool) (B tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool B) (tptp.image_nat_int F A))) (exists ((C_4 tptp.fun_nat_bool)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool C_4) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat C_4)) (= B (tptp.image_nat_int F C_4))))))) (forall ((F tptp.fun_nat_nat) (A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool B) (tptp.image_nat_nat F A))) (exists ((C_4 tptp.fun_nat_bool)) (and (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool C_4) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat C_4)) (= B (tptp.image_nat_nat F C_4))))))) (forall ((F tptp.fun_int_nat) (G tptp.fun_int_nat) (K_3 tptp.fun_int_bool)) (=> (forall ((I_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int I_2) K_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_int_nat F I_2)) (tptp.hAPP_int_nat G I_2))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat F) K_3)) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_f1109019371ol_nat tptp.big_co1740723097nt_nat G) K_3))))) (forall ((F tptp.fun_Ho864122878_a_nat) (G tptp.fun_Ho864122878_a_nat) (K_3 tptp.fun_Ho882550911a_bool)) (=> (forall ((I_2 tptp.hoare_2076525193iple_a)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a I_2) K_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_H174304918_a_nat F I_2)) (tptp.hAPP_H174304918_a_nat G I_2))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f190641160ol_nat (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat F) K_3)) (tptp.hAPP_f190641160ol_nat (tptp.hAPP_f1697440293ol_nat tptp.big_co922834230_a_nat G) K_3))))) (forall ((F tptp.fun_nat_nat) (G tptp.fun_nat_nat) (K_3 tptp.fun_nat_bool)) (=> (forall ((I_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat I_2) K_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat F I_2)) (tptp.hAPP_nat_nat G I_2))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat F) K_3)) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat G) K_3))))) (forall ((F tptp.fun_int_int) (B tptp.fun_int_bool) (A tptp.fun_int_bool)) (=> (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_2) A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_int_int F X_2)) B)))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.image_int_int F A)) B)))) (forall ((F tptp.fun_Ho1518252029iple_a) (B tptp.fun_Ho882550911a_bool) (A tptp.fun_Ho882550911a_bool)) (=> (forall ((X_2 tptp.hoare_2076525193iple_a)) (=> (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a X_2) A)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool tptp.member276146780iple_a (tptp.hAPP_H1789220885iple_a F X_2)) B)))) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool (tptp.image_1416816325iple_a F A)) B)))) (forall ((F tptp.fun_nat_int) (B tptp.fun_int_bool) (A tptp.fun_nat_bool)) (=> (forall ((X_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_nat_int F X_2)) B)))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.image_nat_int F A)) B)))) (forall ((F tptp.fun_nat_nat) (B tptp.fun_nat_bool) (A tptp.fun_nat_bool)) (=> (forall ((X_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) A)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat (tptp.hAPP_nat_nat F X_2)) B)))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.image_nat_nat F A)) B)))) (forall ((F tptp.fun_int_bool) (G tptp.fun_int_bool)) (=> (forall ((X_2 tptp.int)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_int_bool F X_2)) (tptp.hAPP_int_bool G X_2)))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool F) G)))) (forall ((F tptp.fun_nat_bool) (G tptp.fun_nat_bool)) (=> (forall ((X_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.ord_less_eq_bool (tptp.hAPP_nat_bool F X_2)) (tptp.hAPP_nat_bool G X_2)))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool F) G)))) (forall ((A tptp.fun_int_bool) (Ba tptp.int)) (let ((_let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int Ba) tptp.bot_bot_fun_int_bool))) (let ((_let_2 (tptp.hAPP_f1594865479ol_int (tptp.partial_flat_lub_int Ba) A))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) _let_1)))) (and (=> _let_3 (= _let_2 Ba)) (=> (not _let_3) (= _let_2 (tptp.hAPP_f1594865479ol_int tptp.the_int (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f202917053t_bool tptp.cOMBC_94739984l_bool tptp.member_int) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool tptp.minus_1449998731t_bool A) _let_1)))))))))) (forall ((A tptp.fun_Ho882550911a_bool) (Ba tptp.hoare_2076525193iple_a)) (let ((_let_1 (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool tptp.insert1582918915iple_a Ba) tptp.bot_bo214064617a_bool))) (let ((_let_2 (tptp.hAPP_f2009966983iple_a (tptp.partia428461311iple_a Ba) A))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool A) _let_1)))) (and (=> _let_3 (= _let_2 Ba)) (=> (not _let_3) (= _let_2 (tptp.hAPP_f2009966983iple_a tptp.the_Ho1456473914iple_a (tptp.hAPP_f642208769a_bool (tptp.hAPP_f325481667a_bool tptp.cOMBC_1529670358l_bool tptp.member276146780iple_a) (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool tptp.minus_1649626414a_bool A) _let_1)))))))))) (forall ((A tptp.fun_nat_bool) (Ba tptp.nat)) (let ((_let_1 (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool tptp.insert_nat Ba) tptp.bot_bot_fun_nat_bool))) (let ((_let_2 (tptp.hAPP_f22106695ol_nat (tptp.partial_flat_lub_nat Ba) A))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) _let_1)))) (and (=> _let_3 (= _let_2 Ba)) (=> (not _let_3) (= _let_2 (tptp.hAPP_f22106695ol_nat tptp.the_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool tptp.member_nat) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool tptp.minus_2067140911t_bool A) _let_1)))))))))) (forall ((N_1 tptp.nat) (Q_1 tptp.fun_nat_nat) (Pa tptp.fun_nat_nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_lessThan_nat N_1))) (=> (forall ((X_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat Q_1 X_2)) (tptp.hAPP_nat_nat Pa X_2)))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat Pa) _let_1)) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat Q_1) _let_1)) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_f782000547ol_nat tptp.big_co387207925at_nat (tptp.hAPP_f1914919701at_nat (tptp.hAPP_f1408247010at_nat tptp.cOMBS_nat_nat_nat (tptp.hAPP_f1639111240at_nat (tptp.hAPP_f1731313045at_nat tptp.cOMBB_963856155at_nat tptp.minus_minus_nat) Pa)) Q_1)) _let_1))))) (forall ((B tptp.fun_int_bool) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.finite_fold1_int tptp.ord_min_int))) (=> (not (= A tptp.bot_bot_fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int B)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_f1594865479ol_int _let_1 B)) (tptp.hAPP_f1594865479ol_int _let_1 A)))))))) (forall ((B tptp.fun_nat_bool) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.finite_fold1_nat tptp.ord_min_nat))) (=> (not (= A tptp.bot_bot_fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat B)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f22106695ol_nat _let_1 B)) (tptp.hAPP_f22106695ol_nat _let_1 A)))))))) (forall ((Q_1 tptp.fun_int_bool) (Pa tptp.fun_int_bool)) (=> (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa X_2)) (tptp.hBOOL (tptp.hAPP_int_bool Q_1 X_2)))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool Pa) Q_1)))) (forall ((Q_1 tptp.fun_nat_bool) (Pa tptp.fun_nat_bool)) (=> (forall ((X_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa X_2)) (tptp.hBOOL (tptp.hAPP_nat_bool Q_1 X_2)))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool Pa) Q_1)))) (forall ((Q_1 tptp.fun_int_bool) (Pa tptp.fun_int_bool)) (=> (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa X_2)) (tptp.hBOOL (tptp.hAPP_int_bool Q_1 X_2)))) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.hAPP_f1805168059t_bool tptp.collect_int Pa)) (tptp.hAPP_f1805168059t_bool tptp.collect_int Q_1))))) (forall ((Q_1 tptp.fun_Ho882550911a_bool) (Pa tptp.fun_Ho882550911a_bool)) (=> (forall ((X_2 tptp.hoare_2076525193iple_a)) (=> (tptp.hBOOL (tptp.hAPP_H454055633a_bool Pa X_2)) (tptp.hBOOL (tptp.hAPP_H454055633a_bool Q_1 X_2)))) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.ord_le940607413a_bool (tptp.hAPP_f642208769a_bool tptp.collec977865374iple_a Pa)) (tptp.hAPP_f642208769a_bool tptp.collec977865374iple_a Q_1))))) (forall ((Q_1 tptp.fun_nat_bool) (Pa tptp.fun_nat_bool)) (=> (forall ((X_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool Pa X_2)) (tptp.hBOOL (tptp.hAPP_nat_bool Q_1 X_2)))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool (tptp.hAPP_f800510211t_bool tptp.collect_nat Pa)) (tptp.hAPP_f800510211t_bool tptp.collect_nat Q_1))))) (forall ((M_3 tptp.fun_int_bool) (N_3 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool M_3) N_3)) (=> (not (= M_3 tptp.bot_bot_fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int N_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_f1594865479ol_int tptp.big_linorder_Min_int N_3)) (tptp.hAPP_f1594865479ol_int tptp.big_linorder_Min_int M_3))))))) (forall ((M_3 tptp.fun_nat_bool) (N_3 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool M_3) N_3)) (=> (not (= M_3 tptp.bot_bot_fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat N_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f22106695ol_nat tptp.big_linorder_Min_nat N_3)) (tptp.hAPP_f22106695ol_nat tptp.big_linorder_Min_nat M_3))))))) (forall ((M_3 tptp.fun_int_bool) (N_3 tptp.fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool M_3) N_3)) (=> (not (= M_3 tptp.bot_bot_fun_int_bool)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int N_3)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_f1594865479ol_int tptp.big_linorder_Max_int M_3)) (tptp.hAPP_f1594865479ol_int tptp.big_linorder_Max_int N_3))))))) (forall ((M_3 tptp.fun_nat_bool) (N_3 tptp.fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool M_3) N_3)) (=> (not (= M_3 tptp.bot_bot_fun_nat_bool)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat N_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_f22106695ol_nat tptp.big_linorder_Max_nat M_3)) (tptp.hAPP_f22106695ol_nat tptp.big_linorder_Max_nat N_3))))))) (forall ((K_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_n1699378549t_bool tptp.ord_lessThan_nat K_1)))) (forall ((K_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.ord_less_eq_nat) K_1))))) (forall ((N_3 tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat N_3)) (exists ((M_1 tptp.nat)) (forall ((X_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) N_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_2) M_1))))))) (forall ((X_1 tptp.int) (A tptp.fun_int_bool)) (let ((_let_1 (tptp.hAPP_f1594865479ol_int tptp.big_linorder_Min_int A))) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int A)) (=> (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int X_1) A)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.ord_min_int X_1) _let_1) _let_1))))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool)) (let ((_let_1 (tptp.hAPP_f22106695ol_nat tptp.big_linorder_Min_nat A))) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat X_1) _let_1) _let_1))))) (forall ((X_18 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat X_18) X_18) X_18)) (forall ((X_17 tptp.nat) (Y_12 tptp.nat) (Z_7 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat X_17))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat (tptp.hAPP_nat_nat _let_1 Y_12)) Z_7) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat Y_12) Z_7))))) (forall ((A_11 tptp.nat) (B_10 tptp.nat) (C_3 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat A_11))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat (tptp.hAPP_nat_nat _let_1 B_10)) C_3) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat B_10) C_3))))) (forall ((X_16 tptp.nat) (Y_11 tptp.nat) (Z_6 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat X_16))) (let ((_let_2 (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat Y_11))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_2 Z_6)) (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat _let_1 Z_6)))))) (forall ((B_9 tptp.nat) (A_10 tptp.nat) (C_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat B_9))) (let ((_let_2 (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat A_10))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_2 C_2)) (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat _let_1 C_2)))))) (forall ((X_15 tptp.nat) (Y_10 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat X_15))) (let ((_let_2 (tptp.hAPP_nat_nat _let_1 Y_10))) (= (tptp.hAPP_nat_nat _let_1 _let_2) _let_2)))) (forall ((A_9 tptp.nat) (B_8 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat A_9))) (let ((_let_2 (tptp.hAPP_nat_nat _let_1 B_8))) (= (tptp.hAPP_nat_nat _let_1 _let_2) _let_2)))) (forall ((X_14 tptp.nat) (Y_9 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat X_14) Y_9) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat Y_9) X_14))) (forall ((A_8 tptp.nat) (B_7 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat A_8) B_7) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat B_7) A_8))) (forall ((A_7 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat A_7) A_7) A_7)) (forall ((X_1 tptp.nat) (Y_1 tptp.nat) (Z_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat X_1) Y_1)) Z_1)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Z_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_1) Z_1))))) (forall ((X_1 tptp.int) (Y_1 tptp.int) (Z_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.ord_min_int X_1) Y_1)) Z_1)) (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_1) Z_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_1) Z_1))))) (forall ((X_13 tptp.nat) (A_6 tptp.nat) (B_6 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_13))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat A_6) B_6))) (not (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_6)) (not (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_6)))))))) (forall ((X_13 tptp.int) (A_6 tptp.int) (B_6 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_13))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.ord_min_int A_6) B_6))) (not (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_6)) (not (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_6)))))))) (forall ((B_5 tptp.nat) (D tptp.nat) (A_5 tptp.nat) (C_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_5) C_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_5) D)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat A_5) B_5)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat C_1) D)))))) (forall ((B_5 tptp.int) (D tptp.int) (A_5 tptp.int) (C_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_5) C_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_5) D)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.ord_min_int A_5) B_5)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.ord_min_int C_1) D)))))) (forall ((Z_5 tptp.nat) (X_12 tptp.nat) (Y_8 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_12))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_8)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Z_5)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat Y_8) Z_5))))))) (forall ((Z_5 tptp.int) (X_12 tptp.int) (Y_8 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_12))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_8)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Z_5)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.ord_min_int Y_8) Z_5))))))) (forall ((B_4 tptp.nat) (X_11 tptp.nat) (A_4 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_11))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 A_4)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 B_4)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat A_4) B_4))))))) (forall ((B_4 tptp.int) (X_11 tptp.int) (A_4 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_11))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 A_4)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 B_4)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.ord_min_int A_4) B_4))))))) (forall ((Y_7 tptp.nat) (X_10 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat Y_7) X_10)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat X_10) Y_7) Y_7))) (forall ((Y_7 tptp.int) (X_10 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Y_7) X_10)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.ord_min_int X_10) Y_7) Y_7))) (forall ((X_9 tptp.nat) (Y_6 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_9) Y_6)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat X_9) Y_6) X_9))) (forall ((X_9 tptp.int) (Y_6 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_9) Y_6)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.ord_min_int X_9) Y_6) X_9))) (forall ((A_3 tptp.nat) (B_3 tptp.nat) (X_8 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat B_3) X_8)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat A_3) B_3)) X_8)))) (forall ((A_3 tptp.int) (B_3 tptp.int) (X_8 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int B_3) X_8)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.ord_min_int A_3) B_3)) X_8)))) (forall ((B_2 tptp.nat) (A_2 tptp.nat) (X_7 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat A_2) X_7)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat A_2) B_2)) X_7)))) (forall ((B_2 tptp.int) (A_2 tptp.int) (X_7 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int A_2) X_7)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.ord_min_int A_2) B_2)) X_7)))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat) (Z_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat Y_1) Z_1))) (and (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y_1)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Z_1)))))) (forall ((X_1 tptp.int) (Y_1 tptp.int) (Z_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_1))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.ord_min_int Y_1) Z_1))) (and (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y_1)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Z_1)))))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_1)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat X_1) Y_1) X_1))) (forall ((X_1 tptp.int) (Y_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int X_1) Y_1)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.ord_min_int X_1) Y_1) X_1))) (forall ((X_6 tptp.nat) (Y_5 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat X_6) Y_5)) Y_5))) (forall ((X_6 tptp.int) (Y_5 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.ord_min_int X_6) Y_5)) Y_5))) (forall ((X_5 tptp.nat) (Y_4 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat X_5) Y_4)) X_5))) (forall ((X_5 tptp.int) (Y_4 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.ord_min_int X_5) Y_4)) X_5))) (forall ((X_4 tptp.int) (Y_3 tptp.int) (Z_4 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.ord_min_int X_4) Y_3)) Z_4) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.ord_min_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X_4) Z_4)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Y_3) Z_4)))) (forall ((X_4 tptp.nat) (Y_3 tptp.nat) (Z_4 tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat X_4) Y_3)) Z_4) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat X_4) Z_4)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Y_3) Z_4)))) (forall ((X_3 tptp.int) (Y_2 tptp.int) (Z_3 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.ord_min_int X_3) Y_2)) Z_3) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.ord_min_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int X_3) Z_3)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Y_2) Z_3)))) (forall ((U tptp.nat) (F tptp.fun_nat_nat)) (=> (forall ((N_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N_2) (tptp.hAPP_nat_nat F N_2)))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool (tptp.hAPP_f618557131t_bool (tptp.hAPP_f1505651103t_bool tptp.cOMBB_800536526ol_nat tptp.ord_less_eq_nat) F)) U)))))) (forall ((N_1 tptp.nat) (K_1 tptp.nat) (M_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M_2) K_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_1) K_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2) N_1))))))) (forall ((K tptp.nat) (L_1 tptp.nat) (I tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I) J)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) L_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I) K)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J) L_1)))))) (forall ((K tptp.nat) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I) J)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 I)) (tptp.hAPP_nat_nat _let_1 J)))))) (forall ((K tptp.nat) (I tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I) J)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I) K)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J) K))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_1 M)))))) (forall ((M tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) M)))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) N))) (forall ((M tptp.nat) (N tptp.nat)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)))) (forall ((K tptp.nat) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J) K)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 K)))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M)) (= M N)))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) K)) N)) (not (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) N))))))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) K)) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) K)) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) N)))) (forall ((K tptp.nat) (L_1 tptp.nat) (I tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I) J)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) L_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I) K)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J) L_1)))))) (forall ((K tptp.nat) (I tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I) J)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I) K)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J) K))))) (forall ((M tptp.nat) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) J)))))) (forall ((M tptp.nat) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J) M)))))) (forall ((K_1 tptp.nat) (M_2 tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat K_1))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 M_2)) (tptp.hAPP_nat_nat _let_1 N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2) N_1))))) (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2) N_1)) (exists ((K_2 tptp.nat)) (= N_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_2) K_2))))) (forall ((N tptp.nat) (M tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) M)))) (forall ((N tptp.nat) (M tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) N)))) (forall ((M tptp.nat) (I tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) I)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N) I)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_min_nat M) N)) I))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 N))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) N)) N) M)) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) M)) N) M)) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat I))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 J)) K) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J) K))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat I))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 J)) K) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 K)) J)))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N)) K) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) K)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat N) K)))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat K))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N)))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) K)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) K)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N)) M))) (forall ((I tptp.nat) (K tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) J)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat I) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J) K)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I) K)) J)))) (forall ((J_1 tptp.nat) (K_1 tptp.nat) (I_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J_1) K_1)) I_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_1) K_1))))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) M)) K))))) (forall ((L_1 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat L_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat _let_1 N)) (tptp.hAPP_nat_nat _let_1 M)))))) (forall ((L_1 tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) L_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N) L_1))))) (forall ((I tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I) N)) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_1 I)) I)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N)) M))) (forall ((I tptp.nat) (K tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) J)) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J) K)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 J)) K))))) (forall ((I_1 tptp.nat) (K_1 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1) J_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J_1) K_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_1) K_1)) J_1))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N)) N) M))) (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J_1)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J_1) I_1) K_1) (= J_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat K_1) I_1))))) (forall ((I tptp.nat) (K tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) J)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 J)) K) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J) K)))))) (forall ((I tptp.nat) (K tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) J)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J) K)) I) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J) I)) K)))) (forall ((I tptp.nat) (K tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K) J)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J) I)) K) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J) K)) I)))) (forall ((N_1 tptp.nat) (K_1 tptp.nat) (M_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N_1)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M_2) K_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_1) K_1)) (= M_2 N_1)))))) (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 M)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 N)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat _let_1 K)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N) K)) (tptp.hAPP_nat_nat _let_1 N))))))) (forall ((U tptp.nat) (M_2 tptp.nat) (N_1 tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J_1)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I_1) U)) M_2) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J_1) U)) N_1)) (= M_2 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J_1) I_1)) U)) N_1))))) (forall ((U_1 tptp.nat) (M tptp.nat) (N tptp.nat) (I tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I) J)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I) U_1)) M)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J) U_1)) N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J) I)) U_1)) N))))) (forall ((U tptp.nat) (M_2 tptp.nat) (N_1 tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I_1) U)) M_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J_1) U)) N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J_1) I_1)) U)) N_1)))))) (forall ((U tptp.nat) (M_2 tptp.nat) (N_1 tptp.nat) (J_1 tptp.nat) (I_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J_1) I_1)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I_1) U)) M_2) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J_1) U)) N_1)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat I_1) J_1)) U)) M_2) N_1)))) (forall ((U_1 tptp.nat) (M tptp.nat) (N tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J) I)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I) U_1)) M)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J) U_1)) N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat I) J)) U_1)) M)) N)))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat _let_1 N)) K) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat N) K))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat N) M))) (forall ((M_2 tptp.nat) (K_1 tptp.nat) (N_1 tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_2) K_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N_1) K_1)) (= M_2 N_1))) (forall ((K_1 tptp.nat) (M_2 tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat K_1))) (= (= (tptp.hAPP_nat_nat _let_1 M_2) (tptp.hAPP_nat_nat _let_1 N_1)) (= M_2 N_1)))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 N)) K) (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) K))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat X))) (let ((_let_2 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Y))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat _let_2 Z)) (tptp.hAPP_nat_nat _let_2 (tptp.hAPP_nat_nat _let_1 Z)))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) M))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat K))) (= (tptp.hAPP_nat_nat _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) N)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 N))))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) N)) K) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) K)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat N) K)))) (forall ((I tptp.nat) (U_1 tptp.nat) (J tptp.nat) (K tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I) U_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J) U_1)) K)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I) J)) U_1)) K))) (forall ((U tptp.nat) (M_2 tptp.nat) (N_1 tptp.nat) (J_1 tptp.nat) (I_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J_1) I_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I_1) U)) M_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J_1) U)) N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat I_1) J_1)) U)) M_2)) N_1))))) (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Y) Z)))))) (forall ((Y tptp.nat) (X tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Z)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Y) Z)))))) (forall ((N tptp.nat) (M tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N) M)) M) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.ord_max_nat N) M))) (forall ((U tptp.nat)) (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.hAPP_n1699378549t_bool tptp.ord_lessThan_nat U)) U)) (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (= (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_2) N_1) tptp.one_one_nat) (and (= M_2 tptp.one_one_nat) (= N_1 tptp.one_one_nat)))) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat N) tptp.one_one_nat) N)) (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (= (= tptp.one_one_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M_2) N_1)) (and (= M_2 tptp.one_one_nat) (= N_1 tptp.one_one_nat)))) (forall ((N tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat tptp.one_one_nat) N) N)) (forall ((M tptp.nat) (N tptp.nat) (Z tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)) Z)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) N))) Z))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) N)))) (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_2)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2) N_1)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat M) N)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)))) (= _let_11 tptp.one_one_int) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat N) M)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N))))) (forall ((N tptp.nat) (M tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int N))) (tptp.hAPP_nat_int tptp.semiri1621563631at_int M)))) (forall ((L tptp.nat) (U tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_n1699378549t_bool (tptp.ord_at238088361st_nat L) U)))) (forall ((K_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.ord_less_nat) K_1))))) (forall ((W tptp.int) (Z_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W) Z_1)) (exists ((N_2 tptp.nat)) (= Z_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int W) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_2)))))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat M) N)) (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M)) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M)) N) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat M) N)))) (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (= (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_2) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_1)) (= M_2 N_1))) (forall ((Z tptp.int) (W_1 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int tptp.uminus_uminus_int Z)) W_1) (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Z) W_1)))) (forall ((Z tptp.int) (W_1 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z) (tptp.hAPP_int_int tptp.uminus_uminus_int W_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Z) W_1))) (forall ((Z tptp.int) (W_1 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Z) W_1) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z) (tptp.hAPP_int_int tptp.uminus_uminus_int W_1)))) (forall ((Z tptp.int) (W_1 tptp.int)) (= (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z) W_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int tptp.uminus_uminus_int Z)) (tptp.hAPP_int_int tptp.uminus_uminus_int W_1)))) (forall ((W_1 tptp.int)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W_1) W_1))) (forall ((Z tptp.int) (W_1 tptp.int)) (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z) W_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W_1) Z)))) (forall ((K tptp.int) (I tptp.int) (J tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int I))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 J)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int J) K)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 K)))))) (forall ((Z tptp.int) (W_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z) W_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W_1) Z)) (= Z W_1)))) (forall ((Z1 tptp.int) (Z2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int Z1))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int _let_1 Z2)) Z3) (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Z2) Z3))))) (forall ((X tptp.int) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int X))) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_nat_int _let_1 Y)) Z) (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat Y) Z))))) (forall ((Z tptp.int) (W_1 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Z) W_1) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int W_1) Z))) (forall ((Z1 tptp.int) (Z2 tptp.int) (W_1 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Z1) Z2)) W_1) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Z1) W_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Z2) W_1)))) (forall ((W_1 tptp.int) (Z1 tptp.int) (Z2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int W_1))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Z1) Z2)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_int_int _let_1 Z1)) (tptp.hAPP_int_int _let_1 Z2))))) (forall ((Z1 tptp.int) (Z2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z1))) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 Z2)) Z3) (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z2) Z3))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X))) (let ((_let_2 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Y))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int _let_2 Z)) (tptp.hAPP_int_int _let_2 (tptp.hAPP_int_int _let_1 Z)))))) (forall ((Z tptp.int) (W_1 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z) W_1) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int W_1) Z))) (forall ((X tptp.int) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.hAPP_int_fun_nat_int tptp.power_power_int X))) (= (tptp.hAPP_nat_int _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Y) Z)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_nat_int _let_1 Y)) (tptp.hAPP_nat_int _let_1 Z))))) (forall ((W_1 tptp.int) (Z1 tptp.int) (Z2 tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int W_1))) (= (tptp.hAPP_int_int _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z1) Z2)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int _let_1 Z1)) (tptp.hAPP_int_int _let_1 Z2))))) (forall ((Z1 tptp.int) (Z2 tptp.int) (W_1 tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z1) Z2)) W_1) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Z1) W_1)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Z2) W_1)))) (forall ((K tptp.int) (I tptp.int) (J tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.plus_plus_int K))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int I) J)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int _let_1 I)) (tptp.hAPP_int_int _let_1 J)))))) (forall ((Z tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int Z) tptp.one_one_int) Z)) (forall ((Z tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int tptp.one_one_int) Z) Z)) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I) J)) K)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) K)))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat) (L_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat K) L_1)) (=> (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) L_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat K) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N))))) (forall ((K tptp.nat) (L_1 tptp.nat) (I tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) J)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat K) L_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I) K)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J) L_1)))))) (forall ((K tptp.nat) (I tptp.nat) (J tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I) J)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I) K)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J) K))))) (forall ((M tptp.nat) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M) J)))))) (forall ((M tptp.nat) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 J)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J) M)))))) (forall ((K_1 tptp.nat) (M_2 tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat K_1))) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 M_2)) (tptp.hAPP_nat_nat _let_1 N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_2) N_1))))) (forall ((J tptp.nat) (I tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J) I)) I)))) (forall ((I tptp.nat) (J tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I) J)) I)))) (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_2) N_1)) (and (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2) N_1)) (not (= M_2 N_1))))) (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M_2) N_1)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_2) N_1)) (= M_2 N_1)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)) (=> (not (= M N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)) (= M N)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat M) N)))) (forall ((N tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat J) K)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J) N)) K)))) (forall ((L_1 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat L_1))) (let ((_let_2 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 N)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_2 L_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 N)) (tptp.hAPP_nat_nat _let_1 M)))))))) (forall ((Pa tptp.fun_nat_fun_nat_bool) (M_2 tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool Pa N_1) M_2)))) (=> (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_2) N_1)) _let_1) (=> (=> (= M_2 N_1) _let_1) (=> (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_1) M_2)) _let_1) _let_1))))) (forall ((S tptp.nat) (T tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat S) T)) (not (= S T)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) M)) (not (= M N)))) (forall ((N tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) N)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X) Y))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat Y) X))))) (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (= (not (= M_2 N_1)) (or (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_2) N_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N_1) M_2))))) (forall ((N tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) N)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X) Y)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X) Y)))) (forall ((Y tptp.nat) (X tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Z)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Y) Z)))))) (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat Y) Z)))))) (forall ((K_1 tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (= (tptp.image_nat_nat (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat tptp.plus_plus_nat) K_1) (tptp.hAPP_n1699378549t_bool (tptp.ord_at238088361st_nat I_1) J_1)) (tptp.hAPP_n1699378549t_bool (tptp.ord_at238088361st_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_1) K_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat J_1) K_1)))) (forall ((N_3 tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat N_3)) (exists ((M_1 tptp.nat)) (forall ((X_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) N_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_2) M_1))))))) (forall ((Pa tptp.fun_nat_bool) (I_1 tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_f800510211t_bool (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat tptp.fconj) Pa)) (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.ord_less_nat) I_1)))))) (forall ((N_1 tptp.nat)) (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat (tptp.hAPP_f800510211t_bool tptp.collect_nat (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool tptp.ord_less_nat) N_1))) N_1)) (forall ((M tptp.nat) (N tptp.nat)) (=> (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N))) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M) N)) M))) (forall ((I_1 tptp.nat) (J_1 tptp.nat) (K_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_1) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J_1) K_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat I_1) K_1)) J_1)))) (forall ((N_1 tptp.nat) (K_1 tptp.nat) (M_2 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat K_1))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 M_2)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 N_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat M_2) K_1)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat N_1) K_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_2) N_1))))))) (forall ((C tptp.nat) (A_1 tptp.nat) (B_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat A_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat C) A_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat A_1) C)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat B_1) C)))))) (forall ((U tptp.nat) (M_2 tptp.nat) (N_1 tptp.nat) (J_1 tptp.nat) (I_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat J_1) I_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I_1) U)) M_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J_1) U)) N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat I_1) J_1)) U)) M_2)) N_1))))) (forall ((U tptp.nat) (M_2 tptp.nat) (N_1 tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J_1)) (= (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat I_1) U)) M_2)) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat J_1) U)) N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_2) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.minus_minus_nat J_1) I_1)) U)) N_1)))))) (forall ((N tptp.nat) (M tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int N)) (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M)))))) (forall ((Z_1 tptp.int) (W tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Z_1) W)) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z_1) W)) (not (= Z_1 W))))) (forall ((K tptp.int) (I tptp.int) (J tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int I) J)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int I) K)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int J) K))))) (forall ((Z tptp.int)) (= (tptp.hAPP_int_int tptp.uminus_uminus_int (tptp.hAPP_int_int tptp.uminus_uminus_int Z)) Z)) (forall ((Z_2 tptp.int) (Z tptp.int) (W_2 tptp.int) (W_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_2) W_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int Z_2) Z)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int W_2) Z_2)) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int W_1) Z)))))) (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_2)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_2) N_1)))) (forall ((W tptp.int) (Z_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W))) (= (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z_1) tptp.one_one_int))) (or (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Z_1)) (= W Z_1))))) (forall ((M_2 tptp.int) (N_1 tptp.int)) (let ((_let_1 (tptp.ord_at875362053st_int M_2))) (let ((_let_2 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) N_1))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int M_2) _let_2)) (= (tptp.hAPP_i1948725293t_bool _let_1 _let_2) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int _let_2) (tptp.hAPP_i1948725293t_bool _let_1 N_1))))))) (forall ((W_1 tptp.int) (Z tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W_1) Z)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int W_1) tptp.one_one_int)) Z)))) (forall ((W tptp.int) (Z_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int W) tptp.one_one_int)) Z_1)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W) Z_1)))) (forall ((W tptp.int) (Z_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int Z_1) tptp.one_one_int))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W) Z_1)))) (forall ((W tptp.int) (Z_1 tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int W) (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int Z_1) tptp.one_one_int))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int W) Z_1)))) (forall ((Pa tptp.fun_int_bool) (I_1 tptp.int) (K_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int I_1) K_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa K_1)) (=> (forall ((I_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int I_2) K_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa I_2)) (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int I_2) tptp.one_one_int)))))) (tptp.hBOOL (tptp.hAPP_int_bool Pa I_1)))))) (forall ((L tptp.int) (U tptp.int)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int L) U)))) (forall ((X tptp.int) (Y tptp.int)) (or (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int X) Y)) (= X Y) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int Y) X)))) (forall ((J_1 tptp.int) (I_1 tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int I_1) J_1))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int J_1) I_1)))) (and (=> _let_2 (= _let_1 tptp.bot_bot_fun_int_bool)) (=> (not _let_2) (= _let_1 (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool tptp.insert_int I_1) (tptp.hAPP_i1948725293t_bool (tptp.ord_at875362053st_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int I_1) tptp.one_one_int)) J_1)))))))) (forall ((Pa tptp.fun_int_bool) (I_1 tptp.int) (K_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int I_1) K_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int K_1) tptp.one_one_int))) (=> (forall ((I_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int I_2) K_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa I_2)) (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int I_2) tptp.one_one_int)))))) (tptp.hBOOL (tptp.hAPP_int_bool Pa I_1)))))) (forall ((A tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool tptp.finite_finite_int (tptp.image_nat_int tptp.semiri1621563631at_int A))))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le1568362934t_bool A) B)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le951220754t_bool (tptp.image_nat_int tptp.semiri1621563631at_int A)) (tptp.image_nat_int tptp.semiri1621563631at_int B))))) (forall ((X_1 tptp.nat) (A tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_1) A)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool tptp.member_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_1)) (tptp.image_nat_int tptp.semiri1621563631at_int A))))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (= (= A B) (= (tptp.image_nat_int tptp.semiri1621563631at_int A) (tptp.image_nat_int tptp.semiri1621563631at_int B)))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat) (Pa tptp.bool)) (let ((_let_1 (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat (tptp.if_nat Pa) X_1) Y_1)))) (let ((_let_2 (tptp.hBOOL Pa))) (and (=> _let_2 (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_1) _let_1)) (=> (not _let_2) (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int Y_1) _let_1)))))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (= (= (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_1) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Y_1)) (= X_1 Y_1))) (forall ((A tptp.fun_nat_bool) (B tptp.fun_nat_bool)) (= (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.ord_le382113706t_bool A) B)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.ord_le1912455174t_bool (tptp.image_nat_int tptp.semiri1621563631at_int A)) (tptp.image_nat_int tptp.semiri1621563631at_int B))))) (forall ((A tptp.fun_nat_bool)) (= (tptp.hAPP_f22106695ol_nat tptp.finite_card_nat A) (tptp.hAPP_f957591787ol_nat tptp.finite_card_int (tptp.image_nat_int tptp.semiri1621563631at_int A)))) (= tptp.bot_bot_fun_int_bool (tptp.image_nat_int tptp.semiri1621563631at_int tptp.bot_bot_fun_nat_bool)) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_1)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Y_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_1) Y_1)))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_1)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Y_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat X_1) Y_1)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int X)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Y)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat X) Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int X)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Y)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.times_times_nat X) Y)))) (= tptp.one_one_int _let_11) (forall ((X tptp.nat) (N tptp.nat)) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int X)) N) (tptp.hAPP_nat_int tptp.semiri1621563631at_int (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X) N)))) (forall ((Pa tptp.fun_int_bool) (K_1 tptp.int) (I_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_1) I_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int K_1) tptp.one_one_int))) (=> (forall ((I_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_1) I_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa I_2)) (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int I_2) tptp.one_one_int)))))) (tptp.hBOOL (tptp.hAPP_int_bool Pa I_1)))))) (forall ((Pa tptp.fun_int_bool) (K_1 tptp.int) (I_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K_1) I_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa K_1)) (=> (forall ((I_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K_1) I_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa I_2)) (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int I_2) tptp.one_one_int)))))) (tptp.hBOOL (tptp.hAPP_int_bool Pa I_1)))))) (forall ((M_2 tptp.nat) (K_1 tptp.nat) (F tptp.fun_nat_nat)) (=> (forall ((M_1 tptp.nat) (N_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M_1) N_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat F M_1)) (tptp.hAPP_nat_nat F N_2))))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat (tptp.hAPP_nat_nat F M_2)) K_1)) (tptp.hAPP_nat_nat F (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.plus_plus_nat M_2) K_1)))))) (forall ((N_1 tptp.nat) (N_3 tptp.fun_nat_bool)) (=> (forall ((X_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool tptp.member_nat X_2) N_3)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat X_2) N_1)))) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat N_3)))) (forall ((Z tptp.int)) (not (forall ((M_1 tptp.nat) (N_2 tptp.nat)) (not (= Z (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int M_1)) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_2))))))) (forall ((I_1 tptp.nat) (J_1 tptp.nat) (F tptp.fun_nat_nat)) (=> (forall ((I_2 tptp.nat) (J_2 tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat I_2) J_2)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat F I_2)) (tptp.hAPP_nat_nat F J_2))))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat I_1) J_1)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat (tptp.hAPP_nat_nat F I_1)) (tptp.hAPP_nat_nat F J_1)))))) (forall ((I_1 tptp.int) (Pa tptp.fun_int_bool) (K_1 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa K_1)) (=> (forall ((I_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int K_1) I_2)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa I_2)) (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int I_2) tptp.one_one_int)))))) (=> (forall ((I_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int I_2) K_1)) (=> (tptp.hBOOL (tptp.hAPP_int_bool Pa I_2)) (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int I_2) tptp.one_one_int)))))) (tptp.hBOOL (tptp.hAPP_int_bool Pa I_1)))))) (forall ((N tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) N))) (forall ((L tptp.nat) (U tptp.nat)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool tptp.finite_finite_nat (tptp.hAPP_n1699378549t_bool (tptp.ord_gr375877188st_nat L) U)))) (forall ((N tptp.nat) (X tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.power_power_int X) N)))))) (forall ((Pa tptp.fun_int_bool)) (= (forall ((X_2 tptp.int)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_2)) (tptp.hBOOL (tptp.hAPP_int_bool Pa X_2)))) (forall ((X_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_2)))))) (forall ((Pa tptp.fun_int_bool)) (= (exists ((X_2 tptp.int)) (and (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) X_2)) (tptp.hBOOL (tptp.hAPP_int_bool Pa X_2)))) (exists ((X_2 tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool Pa (tptp.hAPP_nat_int tptp.semiri1621563631at_int X_2)))))) (forall ((Z tptp.nat)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.hAPP_nat_int tptp.semiri1621563631at_int Z)))) (tptp.hBOOL (tptp.hAPP_int_bool _let_10 tptp.zero_zero_int)) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.plus_plus_int X) Y))))))) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (tptp.hAPP_i1948725293t_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP_int_bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP_int_bool _let_1 (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.times_times_int X) Y))))))) (tptp.hBOOL (tptp.hAPP_int_bool _let_10 tptp.one_one_int)) (forall ((K tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_nat_int tptp.semiri1621563631at_int K)) tptp.zero_zero_int)))) (forall ((N_1 tptp.nat)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.hAPP_nat_int tptp.semiri1621563631at_int N_1))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)))) (forall ((K_1 tptp.int) (L tptp.int)) (= (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int K_1) L)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.minus_minus_int K_1) L)) tptp.zero_zero_int)))) (forall ((K tptp.int) (I tptp.int) (J tptp.int)) (let ((_let_1 (tptp.hAPP_int_fun_int_int tptp.times_times_int K))) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int I) J)) (=> (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) K)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int (tptp.hAPP_int_int _let_1 I)) (tptp.hAPP_int_int _let_1 J))))))) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int)) (forall ((X_1 tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat))) (= (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat X_1) N_1))) (or (tptp.hBOOL (tptp.hAPP_nat_bool _let_1 X_1)) (= N_1 tptp.zero_zero_nat))))) (forall ((M tptp.nat) (N tptp.nat) (I tptp.nat)) (let ((_let_1 (tptp.hAPP_nat_fun_nat_nat tptp.power_power_nat I))) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) I)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat (tptp.hAPP_nat_nat _let_1 M)) (tptp.hAPP_nat_nat _let_1 N))) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)))))) (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat M) N)) (not (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) tptp.zero_zero_nat)))) (forall ((N_1 tptp.nat)) (= (not (= N_1 tptp.zero_zero_nat)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat tptp.zero_zero_nat) N_1)))) (forall ((N tptp.nat)) (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.ord_less_nat N) tptp.zero_zero_nat)))) (forall ((P tptp.bool)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool tptp.fNot P))) (not (tptp.hBOOL P)))) (forall ((P tptp.bool)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP_bool_bool tptp.fNot P)))) (forall ((Q tptp.bool) (P tptp.bool)) (or (not (tptp.hBOOL P)) (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q))) (tptp.hBOOL P))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fconj P) Q))) (tptp.hBOOL Q))) (forall ((Q tptp.bool) (P tptp.bool)) (or (not (tptp.hBOOL P)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fdisj P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fdisj P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fdisj P) Q))) (tptp.hBOOL P) (tptp.hBOOL Q))) (not (tptp.hBOOL tptp.fFalse)) (forall ((P tptp.bool)) (or (= P tptp.fTrue) (= P tptp.fFalse))) (forall ((Q tptp.bool) (P tptp.bool)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fimplies P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fimplies P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.hBOOL (tptp.hAPP_bool_bool (tptp.hAPP_b589554111l_bool tptp.fimplies P) Q))) (not (tptp.hBOOL P)) (tptp.hBOOL Q))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat (tptp.if_nat tptp.fTrue) X) Y) X)) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat (tptp.if_nat tptp.fFalse) X) Y) Y)) (forall ((P tptp.bool)) (or (= P tptp.fTrue) (= P tptp.fFalse))) (forall ((P tptp.int)) (= (tptp.hAPP_int_int tptp.cOMBI_int P) P)) (forall ((P tptp.nat)) (= (tptp.hAPP_nat_nat tptp.cOMBI_nat P) P)) (forall ((X tptp.int) (Y tptp.int)) (or (not (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.fequal_int X) Y))) (= X Y))) (forall ((X tptp.int) (Y tptp.int)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool tptp.fequal_int X) Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (or (not (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.fequal_nat X) Y))) (= X Y))) (forall ((X tptp.nat) (Y tptp.nat)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool tptp.fequal_nat X) Y)))) (forall ((X tptp.state) (Y tptp.state)) (or (not (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool tptp.fequal_state X) Y))) (= X Y))) (forall ((X tptp.state) (Y tptp.state)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool tptp.fequal_state X) Y)))) (forall ((P tptp.int) (Q tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_int_fun_int_int tptp.cOMBK_int_int P) Q) P)) (forall ((P tptp.int) (Q tptp.nat)) (= (tptp.hAPP_nat_int (tptp.hAPP_int_fun_nat_int tptp.cOMBK_int_nat P) Q) P)) (forall ((P tptp.nat) (Q tptp.int)) (= (tptp.hAPP_int_nat (tptp.hAPP_nat_fun_int_nat tptp.cOMBK_nat_int P) Q) P)) (forall ((P tptp.nat) (Q tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat tptp.cOMBK_nat_nat P) Q) P)) _let_9 (forall ((P tptp.bool) (Q tptp.nat)) (= (tptp.hAPP_nat_bool (tptp.hAPP_b1013836512t_bool tptp.cOMBK_bool_nat P) Q) P)) _let_8 (forall ((X tptp.fun_int_bool) (Y tptp.fun_int_bool)) (or (not (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.fequal_fun_int_bool X) Y))) (= X Y))) (forall ((X tptp.fun_int_bool) (Y tptp.fun_int_bool)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool tptp.fequal_fun_int_bool X) Y)))) (forall ((X tptp.fun_nat_bool) (Y tptp.fun_nat_bool)) (or (not (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.fequal_fun_nat_bool X) Y))) (= X Y))) (forall ((X tptp.fun_nat_bool) (Y tptp.fun_nat_bool)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool tptp.fequal_fun_nat_bool X) Y)))) (forall ((P tptp.fun_int_int) (Q tptp.fun_nat_int) (R tptp.nat)) (= (tptp.hAPP_nat_int (tptp.hAPP_f1139079189at_int (tptp.hAPP_f1431025877at_int tptp.cOMBB_int_int_nat P) Q) R) (tptp.hAPP_int_int P (tptp.hAPP_nat_int Q R)))) (forall ((P tptp.fun_nat_int) (Q tptp.fun_int_nat) (R tptp.int)) (= (tptp.hAPP_int_int (tptp.hAPP_f147134065nt_int (tptp.hAPP_f1673907925nt_int tptp.cOMBB_nat_int_int P) Q) R) (tptp.hAPP_nat_int P (tptp.hAPP_int_nat Q R)))) (forall ((P tptp.fun_nat_nat) (Q tptp.fun_int_nat) (R tptp.int)) (= (tptp.hAPP_int_nat (tptp.hAPP_f2132704789nt_nat (tptp.hAPP_f901215189nt_nat tptp.cOMBB_nat_nat_int P) Q) R) (tptp.hAPP_nat_nat P (tptp.hAPP_int_nat Q R)))) (forall ((P tptp.fun_nat_nat) (Q tptp.fun_nat_nat) (R tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_f1914919701at_nat (tptp.hAPP_f1585078997at_nat tptp.cOMBB_nat_nat_nat P) Q) R) (tptp.hAPP_nat_nat P (tptp.hAPP_nat_nat Q R)))) (forall ((P tptp.fun_int_fun_int_nat) (Q tptp.int) (R tptp.int)) (= (tptp.hAPP_int_nat (tptp.hAPP_int_fun_int_nat (tptp.hAPP_f909851349nt_nat tptp.cOMBC_int_int_nat P) Q) R) (tptp.hAPP_int_nat (tptp.hAPP_int_fun_int_nat P R) Q))) (forall ((P tptp.fun_int_fun_nat_nat) (Q tptp.nat) (R tptp.int)) (= (tptp.hAPP_int_nat (tptp.hAPP_nat_fun_int_nat (tptp.hAPP_f879494613nt_nat tptp.cOMBC_int_nat_nat P) Q) R) (tptp.hAPP_nat_nat (tptp.hAPP_int_fun_nat_nat P R) Q))) (forall ((P tptp.fun_nat_fun_int_nat) (Q tptp.int) (R tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_int_fun_nat_nat (tptp.hAPP_f446977493at_nat tptp.cOMBC_nat_int_nat P) Q) R) (tptp.hAPP_int_nat (tptp.hAPP_nat_fun_int_nat P R) Q))) (forall ((P tptp.fun_nat_fun_nat_nat) (Q tptp.nat) (R tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f416620757at_nat tptp.cOMBC_nat_nat_nat P) Q) R) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat P R) Q))) (forall ((P tptp.fun_int_fun_nat_nat) (Q tptp.fun_int_nat) (R tptp.int)) (= (tptp.hAPP_int_nat (tptp.hAPP_f2132704789nt_nat (tptp.hAPP_f1399363134nt_nat tptp.cOMBS_int_nat_nat P) Q) R) (tptp.hAPP_nat_nat (tptp.hAPP_int_fun_nat_nat P R) (tptp.hAPP_int_nat Q R)))) (forall ((P tptp.fun_nat_fun_nat_nat) (Q tptp.fun_nat_nat) (R tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_f1914919701at_nat (tptp.hAPP_f1408247010at_nat tptp.cOMBS_nat_nat_nat P) Q) R) (tptp.hAPP_nat_nat (tptp.hAPP_nat_fun_nat_nat P R) (tptp.hAPP_nat_nat Q R)))) (forall ((P tptp.fun_int_fun_int_bool) (Q tptp.int) (R tptp.int)) (= (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool tptp.cOMBC_int_int_bool P) Q) R) (tptp.hAPP_int_bool (tptp.hAPP_i1948725293t_bool P R) Q))) (forall ((P tptp.fun_int_fun_nat_bool) (Q tptp.nat) (R tptp.int)) (= (tptp.hAPP_int_bool (tptp.hAPP_n1082236369t_bool (tptp.hAPP_f175561985t_bool tptp.cOMBC_int_nat_bool P) Q) R) (tptp.hAPP_nat_bool (tptp.hAPP_i418383825t_bool P R) Q))) (forall ((P tptp.fun_nat_fun_int_bool) (Q tptp.int) (R tptp.nat)) (= (tptp.hAPP_nat_bool (tptp.hAPP_i418383825t_bool (tptp.hAPP_f482008321t_bool tptp.cOMBC_nat_int_bool P) Q) R) (tptp.hAPP_int_bool (tptp.hAPP_n1082236369t_bool P R) Q))) (forall ((P tptp.fun_nat_fun_nat_bool) (Q tptp.nat) (R tptp.nat)) (= (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f229349961t_bool tptp.cOMBC_nat_nat_bool P) Q) R) (tptp.hAPP_nat_bool (tptp.hAPP_n1699378549t_bool P R) Q))) (forall ((P tptp.fun_bool_bool) (Q tptp.fun_int_bool) (R tptp.int)) (= (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f627970963t_bool tptp.cOMBB_bool_bool_int P) Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_int_bool Q R)))) (forall ((P tptp.fun_bool_bool) (Q tptp.fun_nat_bool) (R tptp.nat)) (= (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_f894608603t_bool tptp.cOMBB_bool_bool_nat P) Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_nat_bool Q R)))) (forall ((P tptp.fun_in531499254l_bool) (Q tptp.fun_int_bool) (R tptp.int)) (= (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f727283836t_bool tptp.cOMBS_int_bool_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_i68813070l_bool P R) (tptp.hAPP_int_bool Q R)))) (forall ((P tptp.fun_na1469252690l_bool) (Q tptp.fun_nat_bool) (R tptp.nat)) (= (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_f561022312t_bool tptp.cOMBS_nat_bool_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_n1006566506l_bool P R) (tptp.hAPP_nat_bool Q R)))) _let_7 (forall ((P tptp.fun_bool_bool) (Q tptp.fun_state_bool) (R tptp.state)) (= (tptp.hAPP_state_bool (tptp.hAPP_f1759915619e_bool (tptp.hAPP_f2073279419e_bool tptp.cOMBB_160679318_state P) Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_state_bool Q R)))) (forall ((P tptp.fun_st2063251938l_bool) (Q tptp.bool) (R tptp.state)) (= (tptp.hAPP_state_bool (tptp.hAPP_b2019457360e_bool (tptp.hAPP_f167292325e_bool tptp.cOMBC_231445413l_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_s58564346l_bool P R) Q))) (forall ((P tptp.fun_st2063251938l_bool) (Q tptp.fun_state_bool) (R tptp.state)) (= (tptp.hAPP_state_bool (tptp.hAPP_f1759915619e_bool (tptp.hAPP_f644196280e_bool tptp.cOMBS_1378840469l_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_s58564346l_bool P R) (tptp.hAPP_state_bool Q R)))) (forall ((P tptp.fun_st2072884720_state) (Q tptp.fun_state_nat) (R tptp.state)) (= (tptp.hAPP_state_state (tptp.hAPP_f871651461_state (tptp.hAPP_f851239890_state tptp.cOMBS_777315357_state P) Q) R) (tptp.hAPP_nat_state (tptp.hAPP_s1892499976_state P R) (tptp.hAPP_state_nat Q R)))) (forall ((P tptp.fun_state_bool) (Q tptp.fun_state_state) (R tptp.state)) (= (tptp.hAPP_state_bool (tptp.hAPP_f746301080e_bool (tptp.hAPP_f162060345e_bool tptp.cOMBB_844853809_state P) Q) R) (tptp.hAPP_state_bool P (tptp.hAPP_state_state Q R)))) (forall ((P tptp.fun_st1506752259e_bool) (Q tptp.state) (R tptp.state)) (= (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool (tptp.hAPP_f817621513e_bool tptp.cOMBC_2027030106e_bool P) Q) R) (tptp.hAPP_state_bool (tptp.hAPP_s1806633685e_bool P R) Q))) (forall ((P tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H1789220885iple_a tptp.cOMBI_1928055558iple_a P) P)) (forall ((X tptp.hoare_2076525193iple_a) (Y tptp.hoare_2076525193iple_a)) (or (not (tptp.hBOOL (tptp.hAPP_H454055633a_bool (tptp.hAPP_H2077279219a_bool tptp.fequal1589671816iple_a X) Y))) (= X Y))) (forall ((X tptp.hoare_2076525193iple_a) (Y tptp.hoare_2076525193iple_a)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_H454055633a_bool (tptp.hAPP_H2077279219a_bool tptp.fequal1589671816iple_a X) Y)))) (forall ((P tptp.fun_a_998512028e_bool) (Q tptp.bool) (R tptp.x_a)) (= (tptp.hAPP_a2036067514e_bool (tptp.hAPP_b540892988e_bool (tptp.hAPP_f1824947087e_bool tptp.cOMBC_41962815e_bool P) Q) R) (tptp.hAPP_b2019457360e_bool (tptp.hAPP_a723219176e_bool P R) Q))) (forall ((P tptp.int) (Q tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H811578610_a_int (tptp.hAPP_i1058170057_a_int tptp.cOMBK_1633947825iple_a P) Q) P)) (forall ((P tptp.nat) (Q tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H174304918_a_nat (tptp.hAPP_n1236213193_a_nat tptp.cOMBK_1654814733iple_a P) Q) P)) (forall ((P tptp.bool) (Q tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H454055633a_bool (tptp.hAPP_b1299643615a_bool tptp.cOMBK_861658160iple_a P) Q) P)) (forall ((P tptp.fun_nat_fun_nat_nat) (Q tptp.fun_int_nat) (R tptp.int)) (= (tptp.hAPP_int_fun_nat_nat (tptp.hAPP_f1463450952at_nat (tptp.hAPP_f1087393429at_nat tptp.cOMBB_1601129847at_int P) Q) R) (tptp.hAPP_nat_fun_nat_nat P (tptp.hAPP_int_nat Q R)))) (forall ((P tptp.fun_nat_fun_nat_nat) (Q tptp.fun_nat_nat) (R tptp.nat)) (= (tptp.hAPP_nat_fun_nat_nat (tptp.hAPP_f1639111240at_nat (tptp.hAPP_f1731313045at_nat tptp.cOMBB_963856155at_nat P) Q) R) (tptp.hAPP_nat_fun_nat_nat P (tptp.hAPP_nat_nat Q R)))) (forall ((P tptp.fun_int_fun_int_bool) (Q tptp.fun_int_int) (R tptp.int)) (= (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f1791153283t_bool (tptp.hAPP_f1399575567t_bool tptp.cOMBB_118231410ol_int P) Q) R) (tptp.hAPP_i1948725293t_bool P (tptp.hAPP_int_int Q R)))) (forall ((P tptp.fun_int_fun_int_bool) (Q tptp.fun_nat_int) (R tptp.nat)) (= (tptp.hAPP_n1082236369t_bool (tptp.hAPP_f1533130627t_bool (tptp.hAPP_f879109391t_bool tptp.cOMBB_1628441366ol_nat P) Q) R) (tptp.hAPP_i1948725293t_bool P (tptp.hAPP_nat_int Q R)))) (forall ((P tptp.fun_nat_fun_nat_bool) (Q tptp.fun_int_nat) (R tptp.int)) (= (tptp.hAPP_i418383825t_bool (tptp.hAPP_f876579787t_bool (tptp.hAPP_f2026117279t_bool tptp.cOMBB_1437810218ol_int P) Q) R) (tptp.hAPP_n1699378549t_bool P (tptp.hAPP_int_nat Q R)))) (forall ((P tptp.fun_nat_fun_nat_bool) (Q tptp.fun_nat_nat) (R tptp.nat)) (= (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f618557131t_bool (tptp.hAPP_f1505651103t_bool tptp.cOMBB_800536526ol_nat P) Q) R) (tptp.hAPP_n1699378549t_bool P (tptp.hAPP_nat_nat Q R)))) (forall ((P tptp.fun_fun_int_bool_nat) (Q tptp.fun_int_fun_int_bool) (R tptp.int)) (= (tptp.hAPP_int_nat (tptp.hAPP_f1134349059nt_nat (tptp.hAPP_f2100446809nt_nat tptp.cOMBB_2018621492at_int P) Q) R) (tptp.hAPP_f957591787ol_nat P (tptp.hAPP_i1948725293t_bool Q R)))) (forall ((P tptp.fun_fun_int_bool_nat) (Q tptp.fun_nat_fun_int_bool) (R tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_f389300155at_nat (tptp.hAPP_f109563153at_nat tptp.cOMBB_1381347800at_nat P) Q) R) (tptp.hAPP_f957591787ol_nat P (tptp.hAPP_n1082236369t_bool Q R)))) (forall ((P tptp.fun_fun_nat_bool_nat) (Q tptp.fun_int_fun_nat_bool) (R tptp.int)) (= (tptp.hAPP_int_nat (tptp.hAPP_f1161717855nt_nat (tptp.hAPP_f1964560145nt_nat tptp.cOMBB_1125113304at_int P) Q) R) (tptp.hAPP_f22106695ol_nat P (tptp.hAPP_i418383825t_bool Q R)))) (forall ((P tptp.fun_in1172847482ol_nat) (Q tptp.fun_nat_bool) (R tptp.int)) (= (tptp.hAPP_int_nat (tptp.hAPP_f787214110nt_nat (tptp.hAPP_f261731407nt_nat tptp.cOMBC_462113011ol_nat P) Q) R) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_i1530422220ol_nat P R) Q))) (forall ((P tptp.fun_na1402637250ol_nat) (Q tptp.fun_int_bool) (R tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_f1473602334at_nat (tptp.hAPP_f630508183at_nat tptp.cOMBC_1505178355ol_nat P) Q) R) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_n259507732ol_nat P R) Q))) (forall ((P tptp.fun_in1461553182ol_nat) (Q tptp.fun_int_fun_int_bool) (R tptp.int)) (= (tptp.hAPP_int_nat (tptp.hAPP_f1134349059nt_nat (tptp.hAPP_f446447448nt_nat tptp.cOMBS_1999073191ol_nat P) Q) R) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_i318423664ol_nat P R) (tptp.hAPP_i1948725293t_bool Q R)))) (forall ((P tptp.fun_in1172847482ol_nat) (Q tptp.fun_int_fun_nat_bool) (R tptp.int)) (= (tptp.hAPP_int_nat (tptp.hAPP_f1161717855nt_nat (tptp.hAPP_f369809936nt_nat tptp.cOMBS_1063588099ol_nat P) Q) R) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_i1530422220ol_nat P R) (tptp.hAPP_i418383825t_bool Q R)))) (forall ((P tptp.fun_na1402637250ol_nat) (Q tptp.fun_nat_fun_int_bool) (R tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_f389300155at_nat (tptp.hAPP_f1750007732at_nat tptp.cOMBS_2106653443ol_nat P) Q) R) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_n259507732ol_nat P R) (tptp.hAPP_n1082236369t_bool Q R)))) (forall ((P tptp.fun_fu819804446l_bool) (Q tptp.fun_int_fun_int_bool) (R tptp.int)) (= (tptp.hAPP_int_bool (tptp.hAPP_f2119767738t_bool (tptp.hAPP_f423804115t_bool tptp.cOMBB_1418110531ol_int P) Q) R) (tptp.hAPP_f448129468l_bool P (tptp.hAPP_i1948725293t_bool Q R)))) (forall ((P tptp.fun_fu425979586l_bool) (Q tptp.fun_nat_fun_nat_bool) (R tptp.nat)) (= (tptp.hAPP_nat_bool (tptp.hAPP_f158894502t_bool (tptp.hAPP_f1777703707t_bool tptp.cOMBB_955900739ol_nat P) Q) R) (tptp.hAPP_f54304608l_bool P (tptp.hAPP_n1699378549t_bool Q R)))) (forall ((P tptp.fun_in938817141l_bool) (Q tptp.fun_int_bool) (R tptp.int)) (= (tptp.hAPP_int_bool (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f202917053t_bool tptp.cOMBC_94739984l_bool P) Q) R) (tptp.hAPP_f448129468l_bool (tptp.hAPP_i2112223885l_bool P R) Q))) (forall ((P tptp.fun_na1436237685l_bool) (Q tptp.fun_nat_bool) (R tptp.nat)) (= (tptp.hAPP_nat_bool (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1722879237t_bool tptp.cOMBC_226598744l_bool P) Q) R) (tptp.hAPP_f54304608l_bool (tptp.hAPP_n215258509l_bool P R) Q))) (forall ((P tptp.fun_bo1549164019l_bool) (Q tptp.fun_int_bool) (R tptp.int)) (= (tptp.hAPP_i68813070l_bool (tptp.hAPP_f2144054103l_bool (tptp.hAPP_f1734373249l_bool tptp.cOMBB_1652995168ol_int P) Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_int_bool Q R)))) (forall ((P tptp.fun_bo1549164019l_bool) (Q tptp.fun_nat_bool) (R tptp.nat)) (= (tptp.hAPP_n1006566506l_bool (tptp.hAPP_f1146629647l_bool (tptp.hAPP_f1080886329l_bool tptp.cOMBB_1015721476ol_nat P) Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_nat_bool Q R)))) (forall ((P tptp.fun_bo1549164019l_bool) (Q tptp.fun_state_bool) (R tptp.state)) (= (tptp.hAPP_s58564346l_bool (tptp.hAPP_f1259673775l_bool (tptp.hAPP_f1561913689l_bool tptp.cOMBB_188601460_state P) Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_state_bool Q R)))) (forall ((P tptp.fun_st1816159843_state) (Q tptp.vname) (R tptp.state)) (= (tptp.hAPP_s1892499976_state (tptp.hAPP_v365393659_state (tptp.hAPP_f1542232213_state tptp.cOMBC_1193272608_state P) Q) R) (tptp.hAPP_v594194232_state (tptp.hAPP_s712361723_state P R) Q))) (forall ((X tptp.fun_Ho882550911a_bool) (Y tptp.fun_Ho882550911a_bool)) (or (not (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.fequal291249344a_bool X) Y))) (= X Y))) (forall ((X tptp.fun_Ho882550911a_bool) (Y tptp.fun_Ho882550911a_bool)) (or (not (= X Y)) (tptp.hBOOL (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool tptp.fequal291249344a_bool X) Y)))) (forall ((P tptp.fun_nat_nat) (Q tptp.fun_Ho864122878_a_nat) (R tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H174304918_a_nat (tptp.hAPP_f2075363285_a_nat (tptp.hAPP_f375421205_a_nat tptp.cOMBB_1877004557iple_a P) Q) R) (tptp.hAPP_nat_nat P (tptp.hAPP_H174304918_a_nat Q R)))) (forall ((P tptp.fun_Ho1488374613nt_nat) (Q tptp.int) (R tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H174304918_a_nat (tptp.hAPP_i896257133_a_nat (tptp.hAPP_f1096027413_a_nat tptp.cOMBC_1149022448nt_nat P) Q) R) (tptp.hAPP_int_nat (tptp.hAPP_H1774516717nt_nat P R) Q))) (forall ((P tptp.fun_Ho1036508337at_nat) (Q tptp.nat) (R tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H174304918_a_nat (tptp.hAPP_n1236213193_a_nat (tptp.hAPP_f668391445_a_nat tptp.cOMBC_1942990924at_nat P) Q) R) (tptp.hAPP_nat_nat (tptp.hAPP_H421001545at_nat P R) Q))) (forall ((P tptp.fun_in501186901_a_nat) (Q tptp.hoare_2076525193iple_a) (R tptp.int)) (= (tptp.hAPP_int_nat (tptp.hAPP_H1774516717nt_nat (tptp.hAPP_f287449365nt_nat tptp.cOMBC_1499522794_a_nat P) Q) R) (tptp.hAPP_H174304918_a_nat (tptp.hAPP_i896257133_a_nat P R) Q))) (forall ((P tptp.fun_na841142961_a_nat) (Q tptp.hoare_2076525193iple_a) (R tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_H421001545at_nat (tptp.hAPP_f982543381at_nat tptp.cOMBC_23578254_a_nat P) Q) R) (tptp.hAPP_H174304918_a_nat (tptp.hAPP_n1236213193_a_nat P R) Q))) (forall ((P tptp.fun_Ho1977546161nt_int) (Q tptp.fun_Ho1026035802_a_int) (R tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H811578610_a_int (tptp.hAPP_f1382137045_a_int (tptp.hAPP_f1031139617_a_int tptp.cOMBS_728441660nt_int P) Q) R) (tptp.hAPP_int_int (tptp.hAPP_H1936429641nt_int P R) (tptp.hAPP_H811578610_a_int Q R)))) (forall ((P tptp.fun_Ho1036508337at_nat) (Q tptp.fun_Ho864122878_a_nat) (R tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H174304918_a_nat (tptp.hAPP_f2075363285_a_nat (tptp.hAPP_f1659339553_a_nat tptp.cOMBS_885136444at_nat P) Q) R) (tptp.hAPP_nat_nat (tptp.hAPP_H421001545at_nat P R) (tptp.hAPP_H174304918_a_nat Q R)))) (forall ((P tptp.fun_Ho1608761598t_bool) (Q tptp.int) (R tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H454055633a_bool (tptp.hAPP_i28602320a_bool (tptp.hAPP_f1732083583a_bool tptp.cOMBC_1771170551t_bool P) Q) R) (tptp.hAPP_int_bool (tptp.hAPP_H287744592t_bool P R) Q))) (forall ((P tptp.fun_Ho1349715618t_bool) (Q tptp.nat) (R tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H454055633a_bool (tptp.hAPP_n1335981428a_bool (tptp.hAPP_f1040149703a_bool tptp.cOMBC_240829083t_bool P) Q) R) (tptp.hAPP_nat_bool (tptp.hAPP_H904886772t_bool P R) Q))) (forall ((P tptp.fun_in451447550a_bool) (Q tptp.hoare_2076525193iple_a) (R tptp.int)) (= (tptp.hAPP_int_bool (tptp.hAPP_H287744592t_bool (tptp.hAPP_f510295935t_bool tptp.cOMBC_1135948669a_bool P) Q) R) (tptp.hAPP_H454055633a_bool (tptp.hAPP_i28602320a_bool P R) Q))) (forall ((P tptp.fun_na1758826658a_bool) (Q tptp.hoare_2076525193iple_a) (R tptp.nat)) (= (tptp.hAPP_nat_bool (tptp.hAPP_H904886772t_bool (tptp.hAPP_f1460432071t_bool tptp.cOMBC_2097822937a_bool P) Q) R) (tptp.hAPP_H454055633a_bool (tptp.hAPP_n1335981428a_bool P R) Q))) (forall ((P tptp.fun_bool_bool) (Q tptp.fun_Ho882550911a_bool) (R tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H454055633a_bool (tptp.hAPP_f642208769a_bool (tptp.hAPP_f629438041a_bool tptp.cOMBB_361863589iple_a P) Q) R) (tptp.hAPP_bool_bool P (tptp.hAPP_H454055633a_bool Q R)))) (forall ((P tptp.fun_Ho2037816211l_bool) (Q tptp.fun_Ho882550911a_bool) (R tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H454055633a_bool (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1004093413a_bool tptp.cOMBS_1108095524l_bool P) Q) R) (tptp.hAPP_bool_bool (tptp.hAPP_H421140395l_bool P R) (tptp.hAPP_H454055633a_bool Q R)))) (forall ((P tptp.fun_a_2117018159e_bool) (Q tptp.fun_state_bool) (R tptp.x_a)) (= (tptp.hAPP_a2036067514e_bool (tptp.hAPP_f762886889e_bool (tptp.hAPP_f1261923407e_bool tptp.cOMBC_892787026e_bool P) Q) R) (tptp.hAPP_f1759915619e_bool (tptp.hAPP_a1200519163e_bool P R) Q))) (forall ((P tptp.fun_a_340690546e_bool) (Q tptp.fun_state_state) (R tptp.x_a)) (= (tptp.hAPP_a2036067514e_bool (tptp.hAPP_f100967412e_bool (tptp.hAPP_f1460451647e_bool tptp.cOMBC_524597097e_bool P) Q) R) (tptp.hAPP_f746301080e_bool (tptp.hAPP_a1224971408e_bool P R) Q))) (forall ((P tptp.fun_in1791225684at_nat) (Q tptp.fun_nat_nat) (R tptp.int)) (= (tptp.hAPP_int_fun_nat_nat (tptp.hAPP_f1169617132at_nat (tptp.hAPP_f701299925at_nat tptp.cOMBC_1294079849at_nat P) Q) R) (tptp.hAPP_f1914919701at_nat (tptp.hAPP_i1876697324at_nat P R) Q))) (forall ((P tptp.fun_na266550704nt_nat) (Q tptp.fun_int_nat) (R tptp.nat)) (= (tptp.hAPP_nat_fun_int_nat (tptp.hAPP_f237327688nt_nat (tptp.hAPP_f1633513941nt_nat tptp.cOMBC_1218031117nt_nat P) Q) R) (tptp.hAPP_f2132704789nt_nat (tptp.hAPP_n74706760nt_nat P R) Q))) (forall ((P tptp.fun_fu554825757t_bool) (Q tptp.fun_int_fun_int_bool) (R tptp.int)) (= (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f428220345t_bool (tptp.hAPP_f654702867t_bool tptp.cOMBB_591320580ol_int P) Q) R) (tptp.hAPP_f1805168059t_bool P (tptp.hAPP_i1948725293t_bool Q R)))) (forall ((P tptp.fun_fu554825757t_bool) (Q tptp.fun_nat_fun_int_bool) (R tptp.nat)) (= (tptp.hAPP_n1082236369t_bool (tptp.hAPP_f2022049025t_bool (tptp.hAPP_f1986088027t_bool tptp.cOMBB_2101530536ol_nat P) Q) R) (tptp.hAPP_f1805168059t_bool P (tptp.hAPP_n1082236369t_bool Q R)))) (forall ((P tptp.fun_fu821463397t_bool) (Q tptp.fun_int_fun_nat_bool) (R tptp.int)) (= (tptp.hAPP_i418383825t_bool (tptp.hAPP_f783004929t_bool (tptp.hAPP_f1410409747t_bool tptp.cOMBB_1746576572ol_int P) Q) R) (tptp.hAPP_f800510211t_bool P (tptp.hAPP_i418383825t_bool Q R)))) (forall ((P tptp.fun_in719570932t_bool) (Q tptp.fun_int_bool) (R tptp.int)) (= (tptp.hAPP_i1948725293t_bool (tptp.hAPP_f1048215610t_bool (tptp.hAPP_f472159229t_bool tptp.cOMBC_1683390479t_bool P) Q) R) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_i1529485324t_bool P R) Q))) (forall ((P tptp.fun_na35521688t_bool) (Q tptp.fun_nat_bool) (R tptp.nat)) (= (tptp.hAPP_n1699378549t_bool (tptp.hAPP_f1570313510t_bool (tptp.hAPP_f688831301t_bool tptp.cOMBC_178881787t_bool P) Q) R) (tptp.hAPP_f800510211t_bool (tptp.hAPP_n1512601776t_bool P R) Q))) (forall ((P tptp.fun_fu1151772339l_bool) (Q tptp.fun_int_bool) (R tptp.fun_int_bool)) (= (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool (tptp.hAPP_f1399552105l_bool tptp.cOMBC_605892544l_bool P) Q) R) (tptp.hAPP_f448129468l_bool (tptp.hAPP_f284875647l_bool P R) Q))) (forall ((P tptp.fun_fu1217155507l_bool) (Q tptp.fun_nat_bool) (R tptp.fun_nat_bool)) (= (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool (tptp.hAPP_f643944041l_bool tptp.cOMBC_1693257480l_bool P) Q) R) (tptp.hAPP_f54304608l_bool (tptp.hAPP_f103356543l_bool P R) Q))) (forall ((P tptp.hoare_2076525193iple_a) (Q tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H1789220885iple_a (tptp.hAPP_H1417936777iple_a tptp.cOMBK_788297294iple_a P) Q) P)) (forall ((P tptp.fun_int_fun_int_int) (Q tptp.fun_Ho1026035802_a_int) (R tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H1936429641nt_int (tptp.hAPP_f534508204nt_int (tptp.hAPP_f1566620885nt_int tptp.cOMBB_364359670iple_a P) Q) R) (tptp.hAPP_int_fun_int_int P (tptp.hAPP_H811578610_a_int Q R)))) (forall ((P tptp.fun_nat_fun_nat_nat) (Q tptp.fun_Ho864122878_a_nat) (R tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H421001545at_nat (tptp.hAPP_f731653896at_nat (tptp.hAPP_f648261589at_nat tptp.cOMBB_1416330906iple_a P) Q) R) (tptp.hAPP_nat_fun_nat_nat P (tptp.hAPP_H174304918_a_nat Q R)))) (forall ((P tptp.fun_int_fun_int_bool) (Q tptp.fun_Ho1026035802_a_int) (R tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H287744592t_bool (tptp.hAPP_f841024195t_bool (tptp.hAPP_f1444703951t_bool tptp.cOMBB_2132063381iple_a P) Q) R) (tptp.hAPP_i1948725293t_bool P (tptp.hAPP_H811578610_a_int Q R)))) (forall ((P tptp.fun_nat_fun_nat_bool) (Q tptp.fun_Ho864122878_a_nat) (R tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H904886772t_bool (tptp.hAPP_f570970635t_bool (tptp.hAPP_f2096737119t_bool tptp.cOMBB_2017898829iple_a P) Q) R) (tptp.hAPP_n1699378549t_bool P (tptp.hAPP_H174304918_a_nat Q R)))) (forall ((P tptp.fun_fu328701628ol_nat) (Q tptp.fun_na1758826658a_bool) (R tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_f420120536at_nat (tptp.hAPP_f228445643at_nat tptp.cOMBB_605112827at_nat P) Q) R) (tptp.hAPP_f190641160ol_nat P (tptp.hAPP_n1335981428a_bool Q R)))) (forall ((P tptp.fun_fun_int_bool_nat) (Q tptp.fun_Ho1608761598t_bool) (R tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H174304918_a_nat (tptp.hAPP_f10452157_a_nat (tptp.hAPP_f296893331_a_nat tptp.cOMBB_1983399767iple_a P) Q) R) (tptp.hAPP_f957591787ol_nat P (tptp.hAPP_H287744592t_bool Q R)))) (forall ((P tptp.fun_fun_nat_bool_nat) (Q tptp.fun_Ho1349715618t_bool) (R tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H174304918_a_nat (tptp.hAPP_f1753252377_a_nat (tptp.hAPP_f456064075_a_nat tptp.cOMBB_1733887227iple_a P) Q) R) (tptp.hAPP_f22106695ol_nat P (tptp.hAPP_H904886772t_bool Q R)))) (forall ((P tptp.fun_Ho1345928733ol_nat) (Q tptp.fun_nat_bool) (R tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H174304918_a_nat (tptp.hAPP_f1047071419_a_nat (tptp.hAPP_f1217804815_a_nat tptp.cOMBC_1664565648ol_nat P) Q) R) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_H2118836847ol_nat P R) Q))) (forall ((P tptp.fun_na228779103ol_nat) (Q tptp.fun_Ho882550911a_bool) (R tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_f479558075at_nat (tptp.hAPP_f1173305809at_nat tptp.cOMBC_129115664ol_nat P) Q) R) (tptp.hAPP_f190641160ol_nat (tptp.hAPP_n370719537ol_nat P R) Q))) (forall ((P tptp.fun_Ho1634634433ol_nat) (Q tptp.fun_Ho1608761598t_bool) (R tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H174304918_a_nat (tptp.hAPP_f10452157_a_nat (tptp.hAPP_f209886133_a_nat tptp.cOMBS_1838073924ol_nat P) Q) R) (tptp.hAPP_f957591787ol_nat (tptp.hAPP_H906838291ol_nat P R) (tptp.hAPP_H287744592t_bool Q R)))) (forall ((P tptp.fun_Ho1345928733ol_nat) (Q tptp.fun_Ho1349715618t_bool) (R tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H174304918_a_nat (tptp.hAPP_f1753252377_a_nat (tptp.hAPP_f991915629_a_nat tptp.cOMBS_902588832ol_nat P) Q) R) (tptp.hAPP_f22106695ol_nat (tptp.hAPP_H2118836847ol_nat P R) (tptp.hAPP_H904886772t_bool Q R)))) (forall ((P tptp.fun_in149899451ol_nat) (Q tptp.fun_in451447550a_bool) (R tptp.int)) (= (tptp.hAPP_int_nat (tptp.hAPP_f1503898400nt_nat (tptp.hAPP_f807099282nt_nat tptp.cOMBS_443177668ol_nat P) Q) R) (tptp.hAPP_f190641160ol_nat (tptp.hAPP_i291839885ol_nat P R) (tptp.hAPP_i28602320a_bool Q R)))) (forall ((P tptp.fun_na228779103ol_nat) (Q tptp.fun_na1758826658a_bool) (R tptp.nat)) (= (tptp.hAPP_nat_nat (tptp.hAPP_f420120536at_nat (tptp.hAPP_f1323480046at_nat tptp.cOMBS_1514622496ol_nat P) Q) R) (tptp.hAPP_f190641160ol_nat (tptp.hAPP_n370719537ol_nat P R) (tptp.hAPP_n1335981428a_bool Q R)))) (forall ((P tptp.fun_bo1549164019l_bool) (Q tptp.fun_Ho882550911a_bool) (R tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H421140395l_bool (tptp.hAPP_f268025233l_bool (tptp.hAPP_f1261090107l_bool tptp.cOMBB_345279363iple_a P) Q) R) (tptp.hAPP_b589554111l_bool P (tptp.hAPP_H454055633a_bool Q R)))) (forall ((P tptp.fun_fu1658206819l_bool) (Q tptp.fun_a_fun_state_bool) (R tptp.x_a)) (= (tptp.hAPP_a849909144l_bool (tptp.hAPP_f1509969235l_bool (tptp.hAPP_f1178339559l_bool tptp.cOMBB_1355796797bool_a P) Q) R) (tptp.hAPP_f1259673775l_bool P (tptp.hAPP_a2036067514e_bool Q R)))) (forall ((P tptp.fun_fu670292377ol_nat) (Q tptp.fun_int_fun_int_nat) (R tptp.int)) (= (tptp.hAPP_i318423664ol_nat (tptp.hAPP_f1548925761ol_nat (tptp.hAPP_f1331458699ol_nat tptp.cOMBB_2091167284at_int P) Q) R) (tptp.hAPP_f1109019371ol_nat P (tptp.hAPP_int_fun_int_nat Q R)))) (forall ((P tptp.fun_fu670292377ol_nat) (Q tptp.fun_nat_fun_int_nat) (R tptp.nat)) (= (tptp.hAPP_n259507732ol_nat (tptp.hAPP_f299305025ol_nat (tptp.hAPP_f1632710027ol_nat tptp.cOMBB_1453893592at_nat P) Q) R) (tptp.hAPP_f1109019371ol_nat P (tptp.hAPP_nat_fun_int_nat Q R)))) (forall ((P tptp.fun_fu990052945ol_nat) (Q tptp.fun_int_fun_nat_nat) (R tptp.int)) (= (tptp.hAPP_i1530422220ol_nat (tptp.hAPP_f1501159417ol_nat (tptp.hAPP_f1029311995ol_nat tptp.cOMBB_1562322300at_int P) Q) R) (tptp.hAPP_f782000547ol_nat P (tptp.hAPP_int_fun_nat_nat Q R)))) (forall ((P tptp.fun_Ho943022881a_bool) (Q tptp.hoare_2076525193iple_a) (R tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H454055633a_bool (tptp.hAPP_H2077279219a_bool (tptp.hAPP_f877684549a_bool tptp.cOMBC_1047656090a_bool P) Q) R) (tptp.hAPP_H454055633a_bool (tptp.hAPP_H2077279219a_bool P R) Q))) (forall ((P tptp.fun_fu1075512626t_bool) (Q tptp.fun_int_bool) (R tptp.fun_int_bool)) (= (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool (tptp.hAPP_f194616807t_bool tptp.cOMBC_922884543t_bool P) Q) R) (tptp.hAPP_f1805168059t_bool (tptp.hAPP_f1223193598t_bool P R) Q))) (forall ((P tptp.fun_fu915923926t_bool) (Q tptp.fun_nat_bool) (R tptp.fun_nat_bool)) (= (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool (tptp.hAPP_f1311642927t_bool tptp.cOMBC_646315179t_bool P) Q) R) (tptp.hAPP_f800510211t_bool (tptp.hAPP_f1730770594t_bool P R) Q))) (forall ((P tptp.fun_Ho755902321at_nat) (Q tptp.fun_nat_nat) (R tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H421001545at_nat (tptp.hAPP_f1016910345at_nat (tptp.hAPP_f1112019605at_nat tptp.cOMBC_340603916at_nat P) Q) R) (tptp.hAPP_f1914919701at_nat (tptp.hAPP_H1504435465at_nat P R) Q))) (forall ((P tptp.fun_fu554825757t_bool) (Q tptp.fun_Ho1608761598t_bool) (R tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H287744592t_bool (tptp.hAPP_f741913983t_bool (tptp.hAPP_f1871962969t_bool tptp.cOMBB_349652263iple_a P) Q) R) (tptp.hAPP_f1805168059t_bool P (tptp.hAPP_H287744592t_bool Q R)))) (forall ((P tptp.fun_fu821463397t_bool) (Q tptp.fun_Ho1349715618t_bool) (R tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H904886772t_bool (tptp.hAPP_f631038663t_bool (tptp.hAPP_f69420889t_bool tptp.cOMBB_1063904223iple_a P) Q) R) (tptp.hAPP_f800510211t_bool P (tptp.hAPP_H904886772t_bool Q R)))) (forall ((P tptp.fun_fu1219323149e_bool) (Q tptp.fun_a_1632297036l_bool) (R tptp.x_a)) (= (tptp.hAPP_a723219176e_bool (tptp.hAPP_f340725611e_bool (tptp.hAPP_f1006724181e_bool tptp.cOMBB_1348041619bool_a P) Q) R) (tptp.hAPP_f167292325e_bool P (tptp.hAPP_a849909144l_bool Q R)))) (forall ((P tptp.fun_fu773339453nt_nat) (Q tptp.fun_nat_fun_nat_nat) (R tptp.nat)) (= (tptp.hAPP_n74706760nt_nat (tptp.hAPP_f2080483477nt_nat (tptp.hAPP_f1701814485nt_nat tptp.cOMBB_737513486at_nat P) Q) R) (tptp.hAPP_f901215189nt_nat P (tptp.hAPP_nat_fun_nat_nat Q R)))) (forall ((P tptp.fun_fu1179887677at_nat) (Q tptp.fun_int_fun_nat_nat) (R tptp.int)) (= (tptp.hAPP_i1876697324at_nat (tptp.hAPP_f1033905301at_nat (tptp.hAPP_f1315855317at_nat tptp.cOMBB_891709290at_int P) Q) R) (tptp.hAPP_f1585078997at_nat P (tptp.hAPP_int_fun_nat_nat Q R)))) (forall ((P tptp.fun_fu2127278875e_bool) (Q tptp.fun_a_fun_state_bool) (R tptp.x_a)) (= (tptp.hAPP_a1224971408e_bool (tptp.hAPP_f1406200875e_bool (tptp.hAPP_f635443597e_bool tptp.cOMBB_2139825703bool_a P) Q) R) (tptp.hAPP_f162060345e_bool P (tptp.hAPP_a2036067514e_bool Q R)))) (forall ((P tptp.fun_Ho943022881a_bool) (Q tptp.fun_in1219646560iple_a) (R tptp.int)) (= (tptp.hAPP_i28602320a_bool (tptp.hAPP_f1362463689a_bool (tptp.hAPP_f438022427a_bool tptp.cOMBB_952878892ol_int P) Q) R) (tptp.hAPP_H2077279219a_bool P (tptp.hAPP_i867006584iple_a Q R)))) (forall ((P tptp.fun_Ho943022881a_bool) (Q tptp.fun_na1240513468iple_a) (R tptp.nat)) (= (tptp.hAPP_n1335981428a_bool (tptp.hAPP_f1324734153a_bool (tptp.hAPP_f946563611a_bool tptp.cOMBB_315605200ol_nat P) Q) R) (tptp.hAPP_H2077279219a_bool P (tptp.hAPP_n887873492iple_a Q R)))) (forall ((P tptp.fun_fu1075512626t_bool) (Q tptp.fun_int_fun_int_bool) (R tptp.int)) (= (tptp.hAPP_i1529485324t_bool (tptp.hAPP_f1468280982t_bool (tptp.hAPP_f1596157055t_bool tptp.cOMBB_765314529ol_int P) Q) R) (tptp.hAPP_f1223193598t_bool P (tptp.hAPP_i1948725293t_bool Q R)))) (forall ((P tptp.fun_fu915923926t_bool) (Q tptp.fun_nat_fun_nat_bool) (R tptp.nat)) (= (tptp.hAPP_n1512601776t_bool (tptp.hAPP_f10625010t_bool (tptp.hAPP_f1115950719t_bool tptp.cOMBB_1654519265ol_nat P) Q) R) (tptp.hAPP_f1730770594t_bool P (tptp.hAPP_n1699378549t_bool Q R)))) (forall ((P tptp.fun_fu2026518849l_bool) (Q tptp.fun_Ho943022881a_bool) (R tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H454055633a_bool (tptp.hAPP_f338738851a_bool (tptp.hAPP_f1827400025a_bool tptp.cOMBB_1676209667iple_a P) Q) R) (tptp.hAPP_f500854239l_bool P (tptp.hAPP_H2077279219a_bool Q R)))) (forall ((P tptp.fun_Ho1910759733l_bool) (Q tptp.fun_Ho882550911a_bool) (R tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H454055633a_bool (tptp.hAPP_f642208769a_bool (tptp.hAPP_f325481667a_bool tptp.cOMBC_1529670358l_bool P) Q) R) (tptp.hAPP_f500854239l_bool (tptp.hAPP_H1566092493l_bool P R) Q))) (forall ((P tptp.fun_fu670292377ol_nat) (Q tptp.fun_Ho1488374613nt_nat) (R tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H906838291ol_nat (tptp.hAPP_f1998933761ol_nat (tptp.hAPP_f1772247755ol_nat tptp.cOMBB_1701789015iple_a P) Q) R) (tptp.hAPP_f1109019371ol_nat P (tptp.hAPP_H1774516717nt_nat Q R)))) (forall ((P tptp.fun_fu990052945ol_nat) (Q tptp.fun_Ho1036508337at_nat) (R tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H2118836847ol_nat (tptp.hAPP_f1296292793ol_nat (tptp.hAPP_f153943611ol_nat tptp.cOMBB_636937375iple_a P) Q) R) (tptp.hAPP_f782000547ol_nat P (tptp.hAPP_H421001545at_nat Q R)))) (forall ((P tptp.fun_fu1047394976e_bool) (Q tptp.fun_a_1632297036l_bool) (R tptp.x_a)) (= (tptp.hAPP_a1200519163e_bool (tptp.hAPP_f963367678e_bool (tptp.hAPP_f375255701e_bool tptp.cOMBB_145932198bool_a P) Q) R) (tptp.hAPP_f644196280e_bool P (tptp.hAPP_a849909144l_bool Q R)))) (forall ((P tptp.fun_na1588060912_a_nat) (Q tptp.fun_Ho864122878_a_nat) (R tptp.nat)) (= (tptp.hAPP_n1236213193_a_nat (tptp.hAPP_f536288520_a_nat (tptp.hAPP_f928984021_a_nat tptp.cOMBC_130242509_a_nat P) Q) R) (tptp.hAPP_f2075363285_a_nat (tptp.hAPP_n226523272_a_nat P R) Q))) (forall ((P tptp.fun_fu1663341283a_bool) (Q tptp.fun_in451447550a_bool) (R tptp.int)) (= (tptp.hAPP_i28602320a_bool (tptp.hAPP_f1500465535a_bool (tptp.hAPP_f967504915a_bool tptp.cOMBB_1848875326ol_int P) Q) R) (tptp.hAPP_f642208769a_bool P (tptp.hAPP_i28602320a_bool Q R)))) (forall ((P tptp.fun_fu1663341283a_bool) (Q tptp.fun_na1758826658a_bool) (R tptp.nat)) (= (tptp.hAPP_n1335981428a_bool (tptp.hAPP_f1869543111a_bool (tptp.hAPP_f1882853211a_bool tptp.cOMBB_1211601634ol_nat P) Q) R) (tptp.hAPP_f642208769a_bool P (tptp.hAPP_n1335981428a_bool Q R)))) (forall ((P tptp.fun_fu1789210355l_bool) (Q tptp.fun_Ho882550911a_bool) (R tptp.fun_Ho882550911a_bool)) (= (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool (tptp.hAPP_f246259945l_bool tptp.cOMBC_1515890438l_bool P) Q) R) (tptp.hAPP_f500854239l_bool (tptp.hAPP_f256727871l_bool P R) Q))) (forall ((P tptp.fun_fu1179887677at_nat) (Q tptp.fun_Ho1036508337at_nat) (R tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H1504435465at_nat (tptp.hAPP_f564893909at_nat (tptp.hAPP_f250842005at_nat tptp.cOMBB_151870093iple_a P) Q) R) (tptp.hAPP_f1585078997at_nat P (tptp.hAPP_H421001545at_nat Q R)))) (forall ((P tptp.fun_Ho943022881a_bool) (Q tptp.fun_Ho1518252029iple_a) (R tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H2077279219a_bool (tptp.hAPP_f1075886601a_bool (tptp.hAPP_f256103387a_bool tptp.cOMBB_135702095iple_a P) Q) R) (tptp.hAPP_H2077279219a_bool P (tptp.hAPP_H1789220885iple_a Q R)))) (forall ((P tptp.fun_fu827349075ol_nat) (Q tptp.fun_in501186901_a_nat) (R tptp.int)) (= (tptp.hAPP_i291839885ol_nat (tptp.hAPP_f1914880763ol_nat (tptp.hAPP_f534494591ol_nat tptp.cOMBB_434376058at_int P) Q) R) (tptp.hAPP_f1697440293ol_nat P (tptp.hAPP_i896257133_a_nat Q R)))) (forall ((P tptp.fun_fu827349075ol_nat) (Q tptp.fun_na841142961_a_nat) (R tptp.nat)) (= (tptp.hAPP_n370719537ol_nat (tptp.hAPP_f1356625915ol_nat (tptp.hAPP_f2033836159ol_nat tptp.cOMBB_1944586014at_nat P) Q) R) (tptp.hAPP_f1697440293ol_nat P (tptp.hAPP_n1236213193_a_nat Q R)))) (forall ((P tptp.fun_Ho112928087a_bool) (Q tptp.fun_Ho882550911a_bool) (R tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H2077279219a_bool (tptp.hAPP_f219434403a_bool (tptp.hAPP_f1824299331a_bool tptp.cOMBC_175592824a_bool P) Q) R) (tptp.hAPP_f642208769a_bool (tptp.hAPP_H1940471919a_bool P R) Q))) (forall ((P tptp.fun_fu1437424253_a_nat) (Q tptp.fun_nat_fun_nat_nat) (R tptp.nat)) (= (tptp.hAPP_n226523272_a_nat (tptp.hAPP_f935848405_a_nat (tptp.hAPP_f450378965_a_nat tptp.cOMBB_1353751246at_nat P) Q) R) (tptp.hAPP_f375421205_a_nat P (tptp.hAPP_nat_fun_nat_nat Q R)))) (forall ((P tptp.fun_fu2051904533a_bool) (Q tptp.fun_Ho882550911a_bool) (R tptp.fun_Ho882550911a_bool)) (= (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool (tptp.hAPP_f86610733a_bool tptp.cOMBC_2005334440a_bool P) Q) R) (tptp.hAPP_f642208769a_bool (tptp.hAPP_f1418638817a_bool P R) Q))) (forall ((P tptp.fun_fu2051904533a_bool) (Q tptp.fun_Ho943022881a_bool) (R tptp.hoare_2076525193iple_a)) (= (tptp.hAPP_H1940471919a_bool (tptp.hAPP_f102426163a_bool (tptp.hAPP_f300022271a_bool tptp.cOMBB_2036667361iple_a P) Q) R) (tptp.hAPP_f1418638817a_bool P (tptp.hAPP_H2077279219a_bool Q R)))) _let_6 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 6.71/6.89  )
% 6.71/6.89  % SZS output end Proof for SWW470_3
% 6.71/6.89  % cvc5---1.0.5 exiting
% 6.71/6.89  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------